GW1_Stochastic_Modelling.ipynb

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      "source": [
        "#Import Libraries\n",
        "import gdown\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "from scipy.integrate import quad\n",
        "from scipy.optimize import brute, fmin\n",
        "import matplotlib.pyplot as plt"
      ],
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      "execution_count": null,
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      "source": [
        "#Define Functions\n",
        "#Step 1 - Team Member A\n",
        "def load_excel_from_google_drive(google_drive_link, local_file_path):\n",
        "    \"\"\"\n",
        "    Download an Excel file from Google Drive and load it into a Pandas DataFrame.\n",
        "\n",
        "    Args:\n",
        "        google_drive_link (str): The shareable link of the Google Drive file.\n",
        "        local_file_path (str): The local file path where you want to save the downloaded Excel file.\n",
        "\n",
        "    Returns:\n",
        "        pd.DataFrame: A Pandas DataFrame containing the data from the Excel file.\n",
        "    \"\"\"\n",
        "    # Extract the file ID from the Google Drive link\n",
        "    file_id = google_drive_link.split(\"/\")[-2]\n",
        "\n",
        "    # Construct the download link\n",
        "    download_link = f\"https://drive.google.com/uc?id={file_id}\"\n",
        "\n",
        "    # Download the Excel file from Google Drive\n",
        "    gdown.download(download_link, local_file_path, quiet=False)\n",
        "\n",
        "    # Load the Excel file into a Pandas DataFrame\n",
        "    df = pd.read_excel(local_file_path)\n",
        "\n",
        "    return df\n",
        "\n",
        "# Function to calculate model prices for put options using put-call parity\n",
        "def calculate_put_model_prices(model_prices, S, K, r, T):\n",
        "    put_model_prices = []\n",
        "    for call_price in call_model_prices:\n",
        "        put_price = call_price - S + K * np.exp(-r * T)\n",
        "        put_model_prices.append(put_price)\n",
        "    return put_model_prices\n",
        "\n",
        "def H93_char_func(u, T, r, kappa_v, theta_v, sigma_v, rho, v0):\n",
        "    \"\"\"Characteristic function for Asian call option in Heston (1993) model.\"\"\"\n",
        "    c1 = kappa_v * theta_v\n",
        "    c2 = -np.sqrt(\n",
        "        (rho * sigma_v * u * 1j - kappa_v) ** 2 - sigma_v ** 2 * (-u * 1j - u ** 2)\n",
        "    )\n",
        "    c3 = (kappa_v - rho * sigma_v * u * 1j + c2) / (\n",
        "        kappa_v - rho * sigma_v * u * 1j - c2\n",
        "    )\n",
        "    H1 = r * u * 1j * T + (c1 / sigma_v ** 2) * (\n",
        "        (kappa_v - rho * sigma_v * u * 1j + c2) * T\n",
        "        - 2 * np.log((1 - c3 * np.exp(c2 * T)) / (1 - c3))\n",
        "    )\n",
        "    H2 = (\n",
        "        (kappa_v - rho * sigma_v * u * 1j + c2)\n",
        "        / sigma_v ** 2\n",
        "        * ((1 - np.exp(c2 * T)) / (1 - c3 * np.exp(c2 * T)))\n",
        "    )\n",
        "    char_func_value = np.exp(H1 + H2 * v0)\n",
        "    return char_func_value\n",
        "\n",
        "def H93_int_func(u, S0, K, T, r, kappa_v, theta_v, sigma_v, rho, v0):\n",
        "    \"\"\"Integration function for Asian call option in Heston (1993) model.\"\"\"\n",
        "    char_func_value = H93_char_func(u - 1j * 0.5, T, r, kappa_v, theta_v, sigma_v, rho, v0)\n",
        "    int_func_value = (\n",
        "        1\n",
        "        / (u ** 2 + 0.25)\n",
        "        * (np.exp(1j * u * np.log(S0 / K)) * char_func_value).real\n",
        "    )\n",
        "    return int_func_value\n",
        "\n",
        "def H93_asian_call_value(S0, K, T, r, kappa_v, theta_v, sigma_v, rho, v0, N, M, seed_value):\n",
        "    \"\"\"Valuation of Asian call option in H93 model via Lewis (2001), with Monte Carlo for Asian option payoff\n",
        "\n",
        "    Parameters:\n",
        "    ==========\n",
        "    S0: float\n",
        "        Initial stock/index level\n",
        "    K: float\n",
        "        Strike price\n",
        "    T: float\n",
        "        Time-to-maturity (for t=0)\n",
        "    r: float\n",
        "        Constant risk-free short rate\n",
        "    kappa_v: float\n",
        "        Mean-reversion factor for variance\n",
        "    theta_v: float\n",
        "        Long-run mean of variance\n",
        "    sigma_v: float\n",
        "        Volatility of variance\n",
        "    rho: float\n",
        "        Correlation between variance and stock/index level\n",
        "    v0: float\n",
        "        Initial level of variance\n",
        "    N: int\n",
        "        Number of monitoring points for the Asian option\n",
        "    M: int\n",
        "        Number of Monte Carlo simulations\n",
        "    seed_value: int\n",
        "        Seed for random number generator\n",
        "    Returns:\n",
        "    =======\n",
        "    asian_call_value: float\n",
        "        Present value of Asian call option\n",
        "    \"\"\"\n",
        "    int_value = quad(\n",
        "        lambda u: H93_int_func(u, S0, K, T, r, kappa_v, theta_v, sigma_v, rho, v0),\n",
        "        0,\n",
        "        np.inf,\n",
        "        limit=250,\n",
        "    )[0]\n",
        "    # Initialize variables\n",
        "    np.random.seed(seed_value)\n",
        "    dt = T / N  # Define time step\n",
        "    u = np.exp(sigma_v * np.sqrt(dt))  # Define u\n",
        "    d = np.exp(-sigma_v * np.sqrt(dt))  # Define d\n",
        "    p = (np.exp(r * dt) - d) / (u - d)  # risk neutral probs\n",
        "    Asian = np.zeros([M])  # Asian prices\n",
        "    S = np.zeros([M, N + 1])  # underlying price\n",
        "    S[:, 0] = S0\n",
        "\n",
        "    for j in range(0, M):\n",
        "        random = np.random.binomial(1, p, N + 1)\n",
        "        Total = S0\n",
        "        for i in range(1, N + 1):\n",
        "            if random[i] == 1:\n",
        "                S[j, i] = S[j, i - 1] * u\n",
        "                Total = Total + S[j, i]\n",
        "            else:\n",
        "                S[j, i] = S[j, i - 1] * d\n",
        "                Total = Total + S[j, i]\n",
        "\n",
        "        Asian[j] = np.exp(-r * T)  * max((Total / (N + 1) - K), 0)\n",
        "        average = np.mean(Asian)\n",
        "\n",
        "    return average\n",
        "\n",
        "\n",
        "def H93_error_function(p0):\n",
        "    \"\"\"\n",
        "    Error function for parameter calibration via Lewis (2001) Fourier approach for Heston (1993).\n",
        "    Parameters:\n",
        "        kappa_v: float, mean-reversion factor\n",
        "        theta_v: float, long-run mean of variance\n",
        "        sigma_v: float, volatility of variance\n",
        "        rho: float, correlation between variance and stock/index level\n",
        "        v0: float, initial, instantaneous variance\n",
        "    Returns:\n",
        "        MSE: float, mean squared error\n",
        "    \"\"\"\n",
        "    global i, min_MSE\n",
        "    kappa_v, theta_v, sigma_v, rho, v0 = p0\n",
        "    if kappa_v < 0.0 or theta_v < 0.005 or sigma_v < 0.0 or rho < -1.0 or rho > 1.0:\n",
        "        return 500.0\n",
        "    if 2 * kappa_v * theta_v < sigma_v**2:\n",
        "        return 500.0\n",
        "    se = []\n",
        "    for row, option in options.iterrows():\n",
        "        model_value = H93_asian_call_value(\n",
        "            S0,\n",
        "            option[\"Strike\"],\n",
        "            option[\"T\"],\n",
        "            option[\"r\"],\n",
        "            kappa_v,\n",
        "            theta_v,\n",
        "            sigma_v,\n",
        "            rho,\n",
        "            v0,\n",
        "            N,\n",
        "            M,\n",
        "            seed_value\n",
        "        )\n",
        "        se.append((model_value - option[\"Call\"]) ** 2)\n",
        "    MSE = np.mean(se)  # Calculate the mean squared error correctly\n",
        "    min_MSE = min(min_MSE, MSE)\n",
        "    if i % 25 == 0:\n",
        "        print(\"%4d |\" % i, np.array(p0), \"| %7.3f | %7.3f\" % (MSE, min_MSE))\n",
        "    i += 1\n",
        "    return MSE\n",
        "\n",
        "def H93_calibration_full():\n",
        "    \"\"\"Calibrates Heston (1993) stochastic volatility model to market quotes.\"\"\"\n",
        "    # First run with brute force (scan sensible regions for faster convergence)\n",
        "    p0 = brute(\n",
        "        H93_error_function,\n",
        "        (\n",
        "            (2.5, 10.6, 5.0),  # kappa_v\n",
        "            (0.01, 0.041, 0.01),  # theta_v\n",
        "            (0.05, 0.251, 0.1),  # sigma_v\n",
        "            (-0.75, 0.01, 0.25),  # rho\n",
        "            (0.01, 0.031, 0.01),\n",
        "        ),\n",
        "        finish=None,\n",
        "    )\n",
        "\n",
        "    # Second run with local, convex minimization (dig deeper where promising results)\n",
        "    opt = fmin(\n",
        "        H93_error_function, p0, xtol=0.000001, ftol=0.000001, maxiter=1000, maxfun=1500\n",
        "    )\n",
        "    return opt\n",
        "\n",
        "#********************************************Put Option Minimization*******************************************************************************************\n",
        "def H93_asian_put_value(S0, K, T, r, kappa_v, theta_v, sigma_v, rho, v0, N, M, seed_value):\n",
        "    \"\"\"Valuation of Asian put option in H93 model via Lewis (2001), with Monte Carlo for Asian option payoff\n",
        "\n",
        "    Parameters:\n",
        "    ==========\n",
        "    S0: float\n",
        "        Initial stock/index level\n",
        "    K: float\n",
        "        Strike price\n",
        "    T: float\n",
        "        Time-to-maturity (for t=0)\n",
        "    r: float\n",
        "        Constant risk-free short rate\n",
        "    kappa_v: float\n",
        "        Mean-reversion factor for variance\n",
        "    theta_v: float\n",
        "        Long-run mean of variance\n",
        "    sigma_v: float\n",
        "        Volatility of variance\n",
        "    rho: float\n",
        "        Correlation between variance and stock/index level\n",
        "    v0: float\n",
        "        Initial level of variance\n",
        "    N: int\n",
        "        Number of monitoring points for the Asian option\n",
        "    M: int\n",
        "        Number of Monte Carlo simulations\n",
        "    seed_value: int\n",
        "        Seed for random number generator\n",
        "    Returns:\n",
        "    =======\n",
        "    asian_put_value: float\n",
        "        Present value of Asian put option\n",
        "    \"\"\"\n",
        "    int_value = quad(\n",
        "        lambda u: H93_int_func(u, S0, K, T, r, kappa_v, theta_v, sigma_v, rho, v0),\n",
        "        0,\n",
        "        np.inf,\n",
        "        limit=250,\n",
        "    )[0]\n",
        "    # Initialize variables\n",
        "    np.random.seed(seed_value)\n",
        "    dt = T / N  # Define time step\n",
        "    u = np.exp(sigma_v * np.sqrt(dt))  # Define u\n",
        "    d = np.exp(-sigma_v * np.sqrt(dt))  # Define d\n",
        "    p = (np.exp(r * dt) - d) / (u - d)  # risk-neutral probabilities\n",
        "    Asian = np.zeros([M])  # Asian prices\n",
        "    S = np.zeros([M, N + 1])  # underlying price\n",
        "    S[:, 0] = S0\n",
        "\n",
        "    for j in range(0, M):\n",
        "        random = np.random.binomial(1, p, N + 1)\n",
        "        Total = S0\n",
        "        for i in range(1, N + 1):\n",
        "            if random[i] == 1:\n",
        "                S[j, i] = S[j, i - 1] * u\n",
        "                Total = Total + S[j, i]\n",
        "            else:\n",
        "                S[j, i] = S[j, i - 1] * d\n",
        "                Total = Total + S[j, i]\n",
        "\n",
        "        Asian[j] = np.exp(-r * T) * max((K - Total / (N + 1)), 0)  # Asian put option payoff\n",
        "        average = np.mean(Asian)\n",
        "\n",
        "    return average\n",
        "\n",
        "\n",
        "def H93_put_error_function(p0):\n",
        "    \"\"\"\n",
        "    Error function for parameter calibration via Lewis (2001) Fourier approach for Heston (1993).\n",
        "    Parameters:\n",
        "        kappa_v: float, mean-reversion factor\n",
        "        theta_v: float, long-run mean of variance\n",
        "        sigma_v: float, volatility of variance\n",
        "        rho: float, correlation between variance and stock/index level\n",
        "        v0: float, initial, instantaneous variance\n",
        "    Returns:\n",
        "        MSE: float, mean squared error\n",
        "    \"\"\"\n",
        "    global i, min_MSE\n",
        "    kappa_v, theta_v, sigma_v, rho, v0 = p0\n",
        "    if kappa_v < 0.0 or theta_v < 0.005 or sigma_v < 0.0 or rho < -1.0 or rho > 1.0:\n",
        "        return 500.0\n",
        "    if 2 * kappa_v * theta_v < sigma_v**2:\n",
        "        return 500.0\n",
        "    se = []\n",
        "    for row, option in options.iterrows():\n",
        "        model_value = H93_asian_put_value(\n",
        "            S0,\n",
        "            option[\"Strike\"],\n",
        "            option[\"T\"],\n",
        "            option[\"r\"],\n",
        "            kappa_v,\n",
        "            theta_v,\n",
        "            sigma_v,\n",
        "            rho,\n",
        "            v0,\n",
        "            N,\n",
        "            M,\n",
        "            seed_value\n",
        "        )\n",
        "        se.append((model_value - option[\"Put\"]) ** 2)\n",
        "    MSE = np.mean(se)  # Calculate the mean squared error correctly\n",
        "    min_MSE = min(min_MSE, MSE)\n",
        "    if i % 25 == 0:\n",
        "        print(\"%4d |\" % i, np.array(p0), \"| %7.3f | %7.3f\" % (MSE, min_MSE))\n",
        "    i += 1\n",
        "    return MSE\n",
        "\n",
        "def H93_put_calibration_full():\n",
        "    \"\"\"Calibrates Heston (1993) stochastic volatility model to market quotes.\"\"\"\n",
        "    # First run with brute force (scan sensible regions for faster convergence)\n",
        "    p0 = brute(\n",
        "        H93_put_error_function,\n",
        "        (\n",
        "            (2.5, 10.6, 5.0),  # kappa_v\n",
        "            (0.01, 0.041, 0.01),  # theta_v\n",
        "            (0.05, 0.251, 0.1),  # sigma_v\n",
        "            (-0.75, 0.01, 0.25),  # rho\n",
        "            (0.01, 0.031, 0.01),\n",
        "        ),\n",
        "        finish=None,\n",
        "    )\n",
        "\n",
        "    # Second run with local, convex minimization (dig deeper where promising results)\n",
        "    opt = fmin(\n",
        "        H93_put_error_function, p0, xtol=0.000001, ftol=0.000001, maxiter=1000, maxfun=1500\n",
        "    )\n",
        "    return opt\n",
        "\n",
        "#*************************Visualization********************************************************************************\n",
        "#*************************Heston Call & Put**********************************************************\n",
        "def calculate_model_values_heston_lewis(p0, is_call=True):\n",
        "    \"\"\"Calculates all model values given parameter vector p0.\"\"\"\n",
        "    kappa_v, theta_v, sigma_v, rho, v0 = p0\n",
        "    values = []\n",
        "    for row, option in options.iterrows():\n",
        "        T = (option[\"Days to maturity\"]) / 250\n",
        "        r = 0.015\n",
        "        if is_call:\n",
        "            model_value = H93_asian_call_value(\n",
        "                S0,\n",
        "                option[\"Strike\"],\n",
        "                T,\n",
        "                r,\n",
        "                kappa_v,\n",
        "                theta_v,\n",
        "                sigma_v,\n",
        "                rho,\n",
        "                v0, N, M, seed_value\n",
        "            )\n",
        "        else:\n",
        "            model_value = H93_asian_put_value(\n",
        "                S0,\n",
        "                option[\"Strike\"],\n",
        "                T,\n",
        "                r,\n",
        "                kappa_v,\n",
        "                theta_v,\n",
        "                sigma_v,\n",
        "                rho,\n",
        "                v0, N, M, seed_value\n",
        "            )\n",
        "        values.append(model_value)\n",
        "    return np.array(values)\n",
        "\n",
        "def plot_calibration_results(p0, option_type=\"call\"):\n",
        "    if option_type not in [\"call\", \"put\"]:\n",
        "        raise ValueError(\"Invalid option_type. Use 'call' or 'put'.\")\n",
        "\n",
        "    if option_type == \"call\":\n",
        "        model_column = \"Model_Heston_Lewis_Call\"\n",
        "        title_prefix = \"Call Options\"\n",
        "        is_call = True\n",
        "    else:\n",
        "        model_column = \"Model_Heston_Lewis_Put\"\n",
        "        title_prefix = \"Put Options\"\n",
        "        is_call = False\n",
        "\n",
        "    options[model_column] = calculate_model_values_heston_lewis(p0, is_call=is_call)\n",
        "    unique_maturities = options[\"Days to maturity\"].unique()\n",
        "\n",
        "    for i in unique_maturities:\n",
        "        selected_rows = options[options['Days to maturity'] == i]\n",
        "        plt.figure(figsize=(8, 6))\n",
        "        plt.subplot(211)\n",
        "        plt.grid()\n",
        "        plt.title(\"%s - Maturity %s\" % (title_prefix, str(selected_rows[\"Days to maturity\"].iloc[0])[:10] + \" Days\"))\n",
        "        plt.ylabel(\"option values\")\n",
        "        plt.plot(selected_rows.Strike, selected_rows[option_type.capitalize()], \"b\", label=\"market\")\n",
        "        plt.plot(selected_rows.Strike, selected_rows[model_column], \"ro\", label=\"model\")\n",
        "        plt.legend(loc=0)\n",
        "\n",
        "        plt.subplot(212)\n",
        "        plt.grid()\n",
        "        wi = 5.0\n",
        "        diffs = selected_rows[model_column].values - selected_rows[option_type.capitalize()].values\n",
        "        plt.bar(selected_rows.Strike.values - wi / 2, diffs, width=wi)\n",
        "        plt.ylabel(\"difference\")\n",
        "        plt.tight_layout()\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "#Step 2 _ Team Member A\n",
        "#*********************Asian Call Option Calibration************************************\n",
        "def H93_char_func(u, T, r, kappa_v, theta_v, sigma_v, rho, v0):\n",
        "    \"\"\"Valuation of European call option in H93 model via Lewis (2001)\n",
        "    Fourier-based approach: characteristic function.\n",
        "    Parameter definitions see function BCC_call_value.\"\"\"\n",
        "    c1 = kappa_v * theta_v\n",
        "    c2 = -np.sqrt(\n",
        "        (rho * sigma_v * u * 1j - kappa_v) ** 2 - sigma_v**2 * (-u * 1j - u**2)\n",
        "    )\n",
        "    c3 = (kappa_v - rho * sigma_v * u * 1j + c2) / (\n",
        "        kappa_v - rho * sigma_v * u * 1j - c2\n",
        "    )\n",
        "    H1 = r * u * 1j * T + (c1 / sigma_v**2) * (\n",
        "        (kappa_v - rho * sigma_v * u * 1j + c2) * T\n",
        "        - 2 * np.log((1 - c3 * np.exp(c2 * T)) / (1 - c3))\n",
        "    )\n",
        "    H2 = (\n",
        "        (kappa_v - rho * sigma_v * u * 1j + c2)\n",
        "        / sigma_v**2\n",
        "        * ((1 - np.exp(c2 * T)) / (1 - c3 * np.exp(c2 * T)))\n",
        "    )\n",
        "    char_func_value = np.exp(H1 + H2 * v0)\n",
        "    return char_func_value\n",
        "\n",
        "def M76J_char_func(u, T, lamb, mu, delta):\n",
        "    \"\"\"\n",
        "    Adjusted Characteristic function for Merton '76 model: Only jump component\n",
        "    \"\"\"\n",
        "\n",
        "    omega = -lamb * (np.exp(mu + 0.5 * delta**2) - 1)\n",
        "    char_func_value = np.exp(\n",
        "        (1j * u * omega + lamb * (np.exp(1j * u * mu - u**2 * delta**2 * 0.5) - 1))\n",
        "        * T\n",
        "    )\n",
        "    return char_func_value\n",
        "\n",
        "def B96_char_func(u, T, r, kappa_v, theta_v, sigma_v, rho, v0, lamb, mu, delta):\n",
        "    \"\"\"\n",
        "    Bates (1996) characteristic function\n",
        "    \"\"\"\n",
        "    H93 = H93_char_func(u, T, r, kappa_v, theta_v, sigma_v, rho, v0)\n",
        "    M76J = M76J_char_func(u, T, lamb, mu, delta)\n",
        "    return H93 * M76J\n",
        "\n",
        "def B96_call_FFT(S0, K, T, r, kappa_v, theta_v, sigma_v, rho, v0, lamb, mu, delta, N, M, seed_value):\n",
        "    \"\"\"\n",
        "    Call option price in Bates (1996) under FFT\n",
        "    \"\"\"\n",
        "\n",
        "    k = np.log(K / S0)\n",
        "    g = 1  # Factor to increase accuracy\n",
        "    N = g * 4096\n",
        "    eps = (g * 150) ** -1\n",
        "    eta = 2 * np.pi / (N * eps)\n",
        "    b = 0.5 * N * eps - k\n",
        "    u = np.arange(1, N + 1, 1)\n",
        "    vo = eta * (u - 1)\n",
        "\n",
        "    # Modifications to ensure integrability\n",
        "    if S0 >= 0.95 * K:  # ITM Case\n",
        "        alpha = 1.5\n",
        "        v = vo - (alpha + 1) * 1j\n",
        "        modcharFunc = np.exp(-r * T) * (\n",
        "            B96_char_func(v, T, r, kappa_v, theta_v, sigma_v, rho, v0, lamb, mu, delta)\n",
        "            / (alpha**2 + alpha - vo**2 + 1j * (2 * alpha + 1) * vo)\n",
        "        )\n",
        "\n",
        "    else:\n",
        "        alpha = 1.1\n",
        "        v = (vo - 1j * alpha) - 1j\n",
        "        modcharFunc1 = np.exp(-r * T) * (\n",
        "            1 / (1 + 1j * (vo - 1j * alpha))\n",
        "            - np.exp(r * T) / (1j * (vo - 1j * alpha))\n",
        "            - B96_char_func(\n",
        "                v, T, r, kappa_v, theta_v, sigma_v, rho, v0, lamb, mu, delta\n",
        "            )\n",
        "            / ((vo - 1j * alpha) ** 2 - 1j * (vo - 1j * alpha))\n",
        "        )\n",
        "\n",
        "        v = (vo + 1j * alpha) - 1j\n",
        "\n",
        "        modcharFunc2 = np.exp(-r * T) * (\n",
        "            1 / (1 + 1j * (vo + 1j * alpha))\n",
        "            - np.exp(r * T) / (1j * (vo + 1j * alpha))\n",
        "            - B96_char_func(\n",
        "                v, T, r, kappa_v, theta_v, sigma_v, rho, v0, lamb, mu, delta\n",
        "            )\n",
        "            / ((vo + 1j * alpha) ** 2 - 1j * (vo + 1j * alpha))\n",
        "        )\n",
        "\n",
        "    # Numerical FFT Routine\n",
        "    delt = np.zeros(N)\n",
        "    delt[0] = 1\n",
        "    j = np.arange(1, N + 1, 1)\n",
        "    SimpsonW = (3 + (-1) ** j - delt) / 3\n",
        "    if S0 >= 0.95 * K:\n",
        "        FFTFunc = np.exp(1j * b * vo) * modcharFunc * eta * SimpsonW\n",
        "        payoff = (np.fft.fft(FFTFunc)).real\n",
        "        CallValueM = np.exp(-alpha * k) / np.pi * payoff\n",
        "    else:\n",
        "        FFTFunc = (\n",
        "            np.exp(1j * b * vo) * (modcharFunc1 - modcharFunc2) * 0.5 * eta * SimpsonW\n",
        "        )\n",
        "        payoff = (np.fft.fft(FFTFunc)).real\n",
        "        CallValueM = payoff / (np.sinh(alpha * k) * np.pi)\n",
        "\n",
        "    pos = int((k + b) / eps)\n",
        "    CallValue = CallValueM[pos] * S0\n",
        "\n",
        "    return CallValue\n",
        "\n",
        "def B96_error_function(p0):\n",
        "    \"\"\"\n",
        "    Error function for Bates (1996) model\n",
        "\n",
        "    Parameters:\n",
        "    -------------\n",
        "    lamb: float\n",
        "        jump intensity\n",
        "    mu: float\n",
        "        expected jump size\n",
        "    delta: float\n",
        "        standard deviation of jump\n",
        "    Returns\n",
        "    -------------\n",
        "    MSE: float\n",
        "        mean squared error\n",
        "    \"\"\"\n",
        "\n",
        "    global i, min_MSE, local_opt, opt1\n",
        "    lamb, mu, delta = p0\n",
        "    if lamb < 0.0 or mu < -0.6 or mu > 0.0 or delta < 0.0:\n",
        "        return 5000.0\n",
        "    se = []\n",
        "    for row, option in options.iterrows():\n",
        "        model_value = B96_call_FFT(\n",
        "            S0,\n",
        "            option[\"Strike\"],\n",
        "            option[\"T\"],\n",
        "            option[\"r\"],\n",
        "            kappa_v,\n",
        "            theta_v,\n",
        "            sigma_v,\n",
        "            rho,\n",
        "            v0,\n",
        "            lamb,\n",
        "            mu,\n",
        "            delta,\n",
        "            N, M, seed_value\n",
        "        )\n",
        "        se.append((model_value - option[\"Call\"]) ** 2)\n",
        "    MSE = sum(se) / len(se)\n",
        "    min_MSE = min(min_MSE, MSE)\n",
        "    if i % 25 == 0:\n",
        "        print(\"%4d |\" % i, np.array(p0), \"| %7.3f | %7.3f\" % (MSE, min_MSE))\n",
        "    i += 1\n",
        "    if local_opt:\n",
        "        penalty = np.sqrt(np.sum((p0 - opt1) ** 2)) * 1\n",
        "        return MSE + penalty\n",
        "    return MSE\n",
        "\n",
        "def B96_calibration_short():\n",
        "    \"\"\"\n",
        "    Calibrates jump component of Bates (1996) model to market prices\n",
        "    \"\"\"\n",
        "    # First, we run with brute force\n",
        "    # (scan sensible regions)\n",
        "    opt1 = 0.0\n",
        "    opt1 = brute(\n",
        "        B96_error_function,\n",
        "        (\n",
        "            (0.0, 0.51, 0.1),  # lambda\n",
        "            (-0.5, -0.11, 0.1),  # mu\n",
        "            (0.0, 0.51, 0.25),\n",
        "        ),  # delta\n",
        "        finish=None,\n",
        "    )\n",
        "\n",
        "    # Second, we run with local, convex minimization\n",
        "    # (dig deeper where promising)\n",
        "    opt2 = fmin(\n",
        "        B96_error_function,\n",
        "        opt1,\n",
        "        xtol=0.0000001,\n",
        "        ftol=0.0000001,\n",
        "        maxiter=1000,\n",
        "        maxfun=1500,\n",
        "    )\n",
        "    return opt2\n",
        "\n",
        "#*************Heston - CarrMadan Put Calculation**********************************************************************\n",
        "def B96_put_FFT(S0, K, T, r, kappa_v, theta_v, sigma_v, rho, v0, lamb, mu, delta, N, M, seed_value):\n",
        "    \"\"\"\n",
        "    Put option price in Bates (1996) under FFT\n",
        "    \"\"\"\n",
        "\n",
        "    k = np.log(K / S0)\n",
        "    g = 1  # Factor to increase accuracy\n",
        "    N = g * 4096\n",
        "    eps = (g * 150) ** -1\n",
        "    eta = 2 * np.pi / (N * eps)\n",
        "    b = 0.5 * N * eps - k\n",
        "    u = np.arange(1, N + 1, 1)\n",
        "    vo = eta * (u - 1)\n",
        "\n",
        "    # Modifications to ensure integrability\n",
        "    if S0 >= 0.95 * K:  # ITM Case\n",
        "        alpha = 1.5\n",
        "        v = vo - (alpha + 1) * 1j\n",
        "        modcharFunc = np.exp(-r * T) * (\n",
        "            B96_char_func(v, T, r, kappa_v, theta_v, sigma_v, rho, v0, lamb, mu, delta)\n",
        "            / (alpha**2 + alpha - vo**2 + 1j * (2 * alpha + 1) * vo)\n",
        "        )\n",
        "\n",
        "    else:\n",
        "        alpha = 1.1\n",
        "        v = (vo - 1j * alpha) - 1j\n",
        "        modcharFunc1 = np.exp(-r * T) * (\n",
        "            1 / (1 + 1j * (vo - 1j * alpha))\n",
        "            - np.exp(r * T) / (1j * (vo - 1j * alpha))\n",
        "            - B96_char_func(\n",
        "                v, T, r, kappa_v, theta_v, sigma_v, rho, v0, lamb, mu, delta\n",
        "            )\n",
        "            / ((vo - 1j * alpha) ** 2 - 1j * (vo - 1j * alpha))\n",
        "        )\n",
        "\n",
        "        v = (vo + 1j * alpha) - 1j\n",
        "\n",
        "        modcharFunc2 = np.exp(-r * T) * (\n",
        "            1 / (1 + 1j * (vo + 1j * alpha))\n",
        "            - np.exp(r * T) / (1j * (vo + 1j * alpha))\n",
        "            - B96_char_func(\n",
        "                v, T, r, kappa_v, theta_v, sigma_v, rho, v0, lamb, mu, delta\n",
        "            )\n",
        "            / ((vo + 1j * alpha) ** 2 - 1j * (vo + 1j * alpha))\n",
        "        )\n",
        "\n",
        "    # Numerical FFT Routine\n",
        "    delt = np.zeros(N)\n",
        "    delt[0] = 1\n",
        "    j = np.arange(1, N + 1, 1)\n",
        "    SimpsonW = (3 + (-1) ** j - delt) / 3\n",
        "    if S0 >= 0.95 * K:\n",
        "        FFTFunc = np.exp(1j * b * vo) * modcharFunc * eta * SimpsonW\n",
        "        payoff = (np.fft.fft(FFTFunc)).real\n",
        "        PutValueM = np.exp(-alpha * k) / np.pi * payoff\n",
        "    else:\n",
        "        FFTFunc = (\n",
        "            np.exp(1j * b * vo) * (modcharFunc1 - modcharFunc2) * 0.5 * eta * SimpsonW\n",
        "        )\n",
        "        payoff = (np.fft.fft(FFTFunc)).real\n",
        "        PutValueM = payoff / (np.sinh(alpha * k) * np.pi)\n",
        "\n",
        "    pos = int((k + b) / eps)\n",
        "    PutValue = PutValueM[pos] * K * np.exp(-r * T)\n",
        "\n",
        "    return PutValue\n",
        "\n",
        "def B96_put_error_function(p0):\n",
        "    \"\"\"\n",
        "    Error function for Bates (1996) model\n",
        "\n",
        "    Parameters:\n",
        "    -------------\n",
        "    lamb: float\n",
        "        jump intensity\n",
        "    mu: float\n",
        "        expected jump size\n",
        "    delta: float\n",
        "        standard deviation of jump\n",
        "    Returns\n",
        "    -------------\n",
        "    MSE: float\n",
        "        mean squared error\n",
        "    \"\"\"\n",
        "\n",
        "    global i, min_MSE, local_opt, opt1\n",
        "    lamb, mu, delta = p0\n",
        "    if lamb < 0.0 or mu < -0.6 or mu > 0.0 or delta < 0.0:\n",
        "        return 5000.0\n",
        "    se = []\n",
        "    for row, option in options.iterrows():\n",
        "        model_value = B96_call_FFT(\n",
        "            S0,\n",
        "            option[\"Strike\"],\n",
        "            option[\"T\"],\n",
        "            option[\"r\"],\n",
        "            kappa_v,\n",
        "            theta_v,\n",
        "            sigma_v,\n",
        "            rho,\n",
        "            v0,\n",
        "            lamb,\n",
        "            mu,\n",
        "            delta,\n",
        "            N, M, seed_value\n",
        "        )\n",
        "        se.append((model_value - option[\"Put\"]) ** 2)\n",
        "    MSE = sum(se) / len(se)\n",
        "    min_MSE = min(min_MSE, MSE)\n",
        "    if i % 25 == 0:\n",
        "        print(\"%4d |\" % i, np.array(p0), \"| %7.3f | %7.3f\" % (MSE, min_MSE))\n",
        "    i += 1\n",
        "    if local_opt:\n",
        "        penalty = np.sqrt(np.sum((p0 - opt1) ** 2)) * 1\n",
        "        return MSE + penalty\n",
        "    return MSE\n",
        "\n",
        "def B96_put_calibration_short():\n",
        "    \"\"\"\n",
        "    Calibrates jump component of Bates (1996) model to market prices\n",
        "    \"\"\"\n",
        "    # First, we run with brute force\n",
        "    # (scan sensible regions)\n",
        "    opt1 = 0.0\n",
        "    opt1 = brute(\n",
        "        B96_put_error_function,\n",
        "        (\n",
        "            (0.0, 0.51, 0.1),  # lambda\n",
        "            (-0.5, -0.11, 0.1),  # mu\n",
        "            (0.0, 0.51, 0.25),\n",
        "        ),  # delta\n",
        "        finish=None,\n",
        "    )\n",
        "\n",
        "    # Second, we run with local, convex minimization\n",
        "    # (dig deeper where promising)\n",
        "    opt2 = fmin(\n",
        "        B96_put_error_function,\n",
        "        opt1,\n",
        "        xtol=0.0000001,\n",
        "        ftol=0.0000001,\n",
        "        maxiter=550,\n",
        "        maxfun=750,\n",
        "    )\n",
        "    return opt2\n",
        "#*************************Visualization********************************************************************************\n",
        "#*************************Bates Carr Madan Call & Put**********************************************************\n",
        "def B96_jump_calculate_model_values_carr(p0, is_call=True):\n",
        "    \"\"\"Calculates all model values given parameter vector p0.\"\"\"\n",
        "    lamb, mu, delta = p0\n",
        "    values = []\n",
        "    for row, option in options.iterrows():\n",
        "        T = (option[\"Days to maturity\"]) / 250\n",
        "        r = 0.015\n",
        "        if is_call:\n",
        "            model_value = B96_call_FFT(\n",
        "            S0,\n",
        "            option[\"Strike\"],\n",
        "            T,\n",
        "            r,\n",
        "            kappa_v,\n",
        "            theta_v,\n",
        "            sigma_v,\n",
        "            rho,\n",
        "            v0,\n",
        "            lamb,\n",
        "            mu,\n",
        "            delta,\n",
        "            N,\n",
        "            M,\n",
        "            seed_value\n",
        "        )\n",
        "        else:\n",
        "            model_value = B96_put_FFT(\n",
        "            S0,\n",
        "            option[\"Strike\"],\n",
        "            T,\n",
        "            r,\n",
        "            kappa_v,\n",
        "            theta_v,\n",
        "            sigma_v,\n",
        "            rho,\n",
        "            v0,\n",
        "            lamb,\n",
        "            mu,\n",
        "            delta,\n",
        "            N,\n",
        "            M,\n",
        "            seed_value\n",
        "        )\n",
        "        values.append(model_value)\n",
        "    return np.array(values)\n",
        "\n",
        "def plot_calibration_results_carr(p0, option_type=\"call\"):\n",
        "    if option_type not in [\"call\", \"put\"]:\n",
        "        raise ValueError(\"Invalid option_type. Use 'call' or 'put'.\")\n",
        "\n",
        "    if option_type == \"call\":\n",
        "        model_column = \"Model_Bates_CarrMadan_Call\"\n",
        "        title_prefix = \"Call Options\"\n",
        "        is_call = True\n",
        "    else:\n",
        "        model_column = \"Model_Bates_CarrMadan_Put\"\n",
        "        title_prefix = \"Put Options\"\n",
        "        is_call = False\n",
        "\n",
        "    options[model_column] = B96_jump_calculate_model_values_carr(p0, is_call=is_call)\n",
        "    unique_maturities = options[\"Days to maturity\"].unique()\n",
        "\n",
        "    for i in unique_maturities:\n",
        "        selected_rows = options[options['Days to maturity'] == i]\n",
        "        plt.figure(figsize=(8, 6))\n",
        "        plt.subplot(211)\n",
        "        plt.grid()\n",
        "        plt.title(\"%s - Maturity %s\" % (title_prefix, str(selected_rows[\"Days to maturity\"].iloc[0])[:10] + \" Days\"))\n",
        "        plt.ylabel(\"option values\")\n",
        "        plt.plot(selected_rows.Strike, selected_rows[option_type.capitalize()], \"b\", label=\"market\")\n",
        "        plt.plot(selected_rows.Strike, selected_rows[model_column], \"ro\", label=\"model\")\n",
        "        plt.legend(loc=0)\n",
        "\n",
        "        plt.subplot(212)\n",
        "        plt.grid()\n",
        "        wi = 5.0\n",
        "        diffs = selected_rows[model_column].values - selected_rows[option_type.capitalize()].values\n",
        "        plt.bar(selected_rows.Strike.values - wi / 2, diffs, width=wi)\n",
        "        plt.ylabel(\"difference\")\n",
        "        plt.tight_layout()\n"
      ],
      "metadata": {
        "id": "wwqSZd5pQyHV"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "metadata": {
        "id": "TTAw5I_9zNB0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "872feca9-a22d-4b71-94ee-c1693ffb1779"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/drive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Import Options File\n",
        "google_drive_link = \"https://docs.google.com/spreadsheets/d/1aWg1hoNmdXHnvRFn0LvhbHqNEBWmwmiN/edit?usp=sharing&ouid=111861681755998244691&rtpof=true&sd=true\"\n",
        "local_file_path = \"/content/drive/MyDrive/WQU Stochastic Modelling/options_data.xlsx\"\n",
        "options_df = load_excel_from_google_drive(google_drive_link, local_file_path)\n",
        "\n",
        "# Pivot the DataFrame to have separate columns for call and put prices\n",
        "pivot_df = options_df.pivot_table(index=[\"Days to maturity\", \"Strike\"], columns=\"Type\", values=\"Price\").reset_index()\n",
        "\n",
        "# Rename columns for clarity\n",
        "pivot_df.rename(columns={\"C\": \"Call\", \"P\": \"Put\"}, inplace=True)\n",
        "\n",
        "# Fill any missing values with 0 if necessary\n",
        "pivot_df.fillna(0, inplace=True)\n",
        "pivot_df.head()\n",
        "\n",
        "S0 = 232.90\n",
        "\n",
        "# Option Selection\n",
        "tol = 0.02  # Tolerance level to select ATM options (percent around ITM/OTM options)\n",
        "options = pivot_df[(np.abs(pivot_df[\"Strike\"] - S0) / S0) < tol]\n",
        "\n",
        "for row, option in options.iterrows():\n",
        "    T = (option[\"Days to maturity\"]) / 250 # Convert Days to Maturity to years\n",
        "    options.loc[row, \"T\"] = T\n",
        "    options.loc[row, \"r\"] = 0.015  # Constant short-rate\n"
      ],
      "metadata": {
        "id": "-CIxCWUF21F_",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9d16ed68-3881-4e8f-9b1a-670c8f0d41b7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Downloading...\n",
            "From: https://drive.google.com/uc?id=1aWg1hoNmdXHnvRFn0LvhbHqNEBWmwmiN\n",
            "To: /content/drive/MyDrive/WQU Stochastic Modelling/options_data.xlsx\n",
            "100%|██████████| 9.72k/9.72k [00:00<00:00, 21.4MB/s]\n",
            "<ipython-input-4-85c5a9f2460f>:24: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  options.loc[row, \"T\"] = T\n",
            "<ipython-input-4-85c5a9f2460f>:25: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  options.loc[row, \"r\"] = 0.015  # Constant short-rate\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Step 1 - Team Member A - Model Calibration\n",
        "\n",
        "# Option Parameters\n",
        "S0 = 232.90\n",
        "K = 232.90\n",
        "T = 15/250\n",
        "r = 0.015\n",
        "\n",
        "# Heston(1993) Parameters for Asian Options\n",
        "kappa_v = 1.5     # Mean-reversion factor for variance\n",
        "theta_v = 0.02    # Long-run mean of variance\n",
        "sigma_v = 0.1     # Volatility of variance\n",
        "rho = 0.25        # Correlation between variance and stock/index level\n",
        "v0 = 0.01         # Initial level of variance\n",
        "\n",
        "N = 10\n",
        "M = 100\n",
        "seed_value = 42\n",
        "\n",
        "\n",
        "i = 0\n",
        "min_MSE = 500\n",
        "\n",
        "# Call the calibration function\n",
        "heston_lewis_call_params = H93_calibration_full()\n",
        "\n",
        "#Call the Put Calibration Function\n",
        "i = 0\n",
        "min_MSE = 500\n",
        "heston_lewis_put_params = H93_put_calibration_full()"
      ],
      "metadata": {
        "id": "M6JtPBfRCy0Q",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "41e2ea2f-aac7-4697-e0bc-8b7b70573b5a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "   0 | [ 2.5   0.01  0.05 -0.75  0.01] | 215.202 | 215.202\n",
            "  25 | [ 2.5   0.02  0.05 -0.75  0.02] | 215.202 | 151.495\n",
            "  50 | [ 2.5   0.02  0.25 -0.75  0.03] |  87.384 |  87.384\n",
            "  75 | [ 2.5   0.03  0.15 -0.5   0.01] | 151.495 |  87.384\n",
            " 100 | [ 2.5   0.04  0.05 -0.5   0.02] | 215.202 |  87.384\n",
            " 125 | [ 2.5   0.04  0.25 -0.5   0.03] |  87.384 |  87.384\n",
            " 150 | [ 7.5   0.01  0.15 -0.25  0.01] | 151.495 |  87.384\n",
            " 175 | [ 7.5   0.02  0.05 -0.25  0.02] | 215.202 |  87.384\n",
            " 200 | [ 7.5   0.02  0.25 -0.25  0.03] |  87.384 |  87.384\n",
            " 225 | [7.5  0.03 0.15 0.   0.01] | 151.495 |  87.384\n",
            " 250 | [7.5  0.04 0.05 0.   0.02] | 215.202 |  87.384\n",
            " 275 | [7.5  0.04 0.25 0.   0.03] |  87.384 |  87.384\n",
            " 300 | [ 2.53875874  0.0203974   0.31783046 -0.71726384  0.00843718] |  53.337 |  53.337\n",
            " 325 | [ 3.70052651  0.02584294  0.42786602 -0.6864958   0.00906051] |  16.322 |  16.322\n",
            " 350 | [ 5.13526884  0.0335542   0.56928208 -0.64008384  0.01007824] |   0.908 |   0.908\n",
            " 375 | [ 5.11291918  0.03351454  0.56637566 -0.63947813  0.0101433 ] |   0.875 |   0.865\n",
            " 400 | [ 5.06846977  0.0332342   0.56253917 -0.63879783  0.0100544 ] |   0.863 |   0.862\n",
            " 425 | [ 5.0757943   0.0332608   0.56325633 -0.63875916  0.01005213] |   0.862 |   0.862\n",
            " 450 | [ 5.07565885  0.03326072  0.56323851 -0.63876237  0.01005274] |   0.862 |   0.862\n",
            " 475 | [ 5.07542166  0.03325948  0.56321782 -0.6387585   0.01005239] |   0.862 |   0.862\n",
            " 500 | [ 5.07544422  0.03325958  0.56321976 -0.63875784  0.01005241] |   0.862 |   0.862\n",
            " 525 | [ 5.07543784  0.03325956  0.56321919 -0.6387586   0.01005242] |   0.862 |   0.862\n",
            "Optimization terminated successfully.\n",
            "         Current function value: 0.862270\n",
            "         Iterations: 138\n",
            "         Function evaluations: 269\n",
            "   0 | [ 2.5   0.01  0.05 -0.75  0.01] | 139.295 | 139.295\n",
            "  25 | [ 2.5   0.02  0.05 -0.75  0.02] | 139.295 |  86.954\n",
            "  50 | [ 2.5   0.02  0.25 -0.75  0.03] |  47.905 |  47.905\n",
            "  75 | [ 2.5   0.03  0.15 -0.5   0.01] |  86.954 |  47.905\n",
            " 100 | [ 2.5   0.04  0.05 -0.5   0.02] | 139.295 |  47.905\n",
            " 125 | [ 2.5   0.04  0.25 -0.5   0.03] |  47.905 |  47.905\n",
            " 150 | [ 7.5   0.01  0.15 -0.25  0.01] |  86.954 |  47.905\n",
            " 175 | [ 7.5   0.02  0.05 -0.25  0.02] | 139.295 |  47.905\n",
            " 200 | [ 7.5   0.02  0.25 -0.25  0.03] |  47.905 |  47.905\n",
            " 225 | [7.5  0.03 0.15 0.   0.01] |  86.954 |  47.905\n",
            " 250 | [7.5  0.04 0.05 0.   0.02] | 139.295 |  47.905\n",
            " 275 | [7.5  0.04 0.25 0.   0.03] |  47.905 |  47.905\n",
            " 300 | [ 2.53875874  0.0203974   0.31783046 -0.71726384  0.00843718] |  26.126 |  26.126\n",
            " 325 | [ 3.48805706  0.02385461  0.40231792 -0.62663409  0.00870298] |   9.226 |   9.142\n",
            " 350 | [ 4.65125397  0.03031874  0.50932426 -0.52282638  0.01000609] |   0.543 |   0.498\n",
            " 375 | [ 4.62635602  0.03015521  0.50688233 -0.52604577  0.00998283] |   0.405 |   0.393\n",
            " 400 | [ 4.61155296  0.03003624  0.50531293 -0.52602869  0.00995885] |   0.417 |   0.385\n",
            " 425 | [ 4.60878468  0.03003382  0.50503927 -0.52699458  0.0099646 ] |   0.386 |   0.385\n",
            " 450 | [ 4.60983778  0.03003928  0.50512068 -0.52704984  0.00996679] |   0.418 |   0.385\n",
            " 475 | [ 4.60999799  0.03003757  0.50511262 -0.52713171  0.00996684] |   0.418 |   0.385\n",
            " 500 | [ 4.60991281  0.03003803  0.5051113  -0.52714444  0.00996692] |   0.385 |   0.385\n",
            " 525 | [ 4.60998859  0.03003754  0.50511135 -0.52715743  0.00996689] |   0.385 |   0.385\n",
            " 550 | [ 4.609974    0.03003741  0.50511133 -0.52713334  0.00996674] |   0.385 |   0.385\n",
            " 575 | [ 4.60999105  0.0300374   0.50511135 -0.52714596  0.0099668 ] |   0.418 |   0.385\n",
            " 600 | [ 4.60999214  0.03003737  0.50511135 -0.52714434  0.00996678] |   0.385 |   0.385\n",
            " 625 | [ 4.60999921  0.03003733  0.50511135 -0.52714631  0.00996678] |   0.418 |   0.385\n",
            " 650 | [ 4.60999673  0.03003732  0.50511135 -0.52714376  0.00996677] |   0.385 |   0.385\n",
            " 675 | [ 4.60999954  0.03003731  0.50511135 -0.52714424  0.00996677] |   0.385 |   0.385\n",
            " 700 | [ 4.61000011  0.0300373   0.50511135 -0.52714416  0.00996677] |   0.385 |   0.385\n",
            " 725 | [ 4.6099989   0.03003731  0.50511135 -0.52714415  0.00996677] |   0.418 |   0.385\n",
            "Optimization terminated successfully.\n",
            "         Current function value: 0.384570\n",
            "         Iterations: 253\n",
            "         Function evaluations: 484\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Team Member A - Report - Step 1\n",
        "1. Introduction\n",
        "\n",
        "This report presents the calibration of the Heston (1993) stochastic volatility model for Asian call and put options on SM Energy Company's stock (SM). The client is interested in purchasing an Over-The-Counter (OTC) Asian option, but is uncertain about the maturity she wants to consider for the option. Our task as Team Member A is to calibrate the model to observed market prices for both call and put options, describe the calibration process, and discuss the results.\n",
        "\n",
        "2. Data and Parameters\n",
        "\n",
        "We obtained market data for vanilla call and put options traded on SM stock from the attached Excel file. SM stock is currently trading at $232.90 USD. The parameters used in the Heston (1993) model calibration are as follows:\n",
        "\n",
        "    Initial stock price (S0): $232.90 USD\n",
        "    Strike price (K): $232.90 USD\n",
        "    Time-to-maturity (T): 15 days, converted to a fraction of a year (T = 15/250)\n",
        "    Constant risk-free rate (r): 1.50% per annum\n",
        "    Number of monitoring points for the Asian option (N): 10\n",
        "    Number of Monte Carlo simulations (M): 100\n",
        "    Seed value for random number generator: 42\n",
        "\n",
        "3. Option Selection:\n",
        "\n",
        "    To proceed with calibration, we selected options that were close to the at-the-money (ATM) level. This selection was based on a tolerance level to ensure that the options chosen were sufficiently representative of the market conditions.\n",
        "    The tolerance level was set at 2% (tol = 0.02), meaning options whose strike prices were within 2% of the current stock price (S0) were considered for calibration.\n",
        "\n",
        "4. Selection of Maturities:\n",
        "\n",
        "    We considered multiple maturities for the Asian options to calibrate the model. The client expressed initial interest in a very short maturity of around 15 days. However, we also explored other maturities as part of the calibration process to cover a range of market scenarios.\n",
        "\n",
        "5. Conversion to Annualized Time:\n",
        "\n",
        "    For each selected maturity, we converted the \"Days to maturity\" of the options into years by dividing by 250. This conversion was based on the assumption that there are 250 trading days in a year.\n",
        "\n",
        "6. Risk-Free Rate Assumption:\n",
        "\n",
        "    A constant annual risk-free rate of 1.50% was assumed for all maturities. This rate was converted into a daily rate based on the assumption of 250 trading days in a year.\n",
        "\n",
        "7. Model Selection:\n",
        "\n",
        "    We chose the Heston (1993) model without jumps as the underlying stochastic volatility model for this calibration.\n",
        "\n",
        "8. Parameters to Calibrate:\n",
        "\n",
        "    The model parameters we aimed to calibrate were:\n",
        "        κ (kappa_v): Mean-reversion factor for variance.\n",
        "        θ (theta_v): Long-run mean of variance.\n",
        "        σ (sigma_v): Volatility of variance.\n",
        "        ρ (rho): Correlation between variance and stock/index level.\n",
        "        v0 (v0): Initial level of variance.\n",
        "\n",
        "9. Initial Parameter Guess:\n",
        "\n",
        "    We started with an initial guess for the parameters and used a brute-force method to scan sensible parameter regions for faster convergence.\n",
        "\n",
        "10. Calibration Iteration:\n",
        "\n",
        "    The calibration process involved iteratively adjusting the model parameters to minimize the Mean Squared Error (MSE) error function. Each iteration calculated the MSE, and we updated the parameter values accordingly.\n",
        "    The calibration process continued until the error converged or a maximum number of iterations was reached.\n",
        "\n",
        "11. Calibration Results\n",
        "    \n",
        "    11.1 Asian Call Option Calibration\n",
        "\n",
        "The calibration process for Asian call options involved finding the parameter values that minimized the Mean Squared Error (MSE) between the market quotes and model prices. The final parameter values for Asian call option calibration are as follows:\n",
        "\n",
        "    kappa_v: 5.07543848\n",
        "    theta_v: 0.03325956\n",
        "    sigma_v: 0.56321925\n",
        "    rho: -0.63875854\n",
        "    v0: 0.01005242\n",
        "\n",
        "The resulting MSE for Asian call option calibration is 0.862270.\n",
        "\n",
        "    11.2 Asian Put Option Calibration\n",
        "\n",
        "Similarly, for Asian put options, we calibrated the model parameters to minimize the MSE between market quotes and model prices. The final parameter values for Asian put option calibration are as follows:\n",
        "\n",
        "    kappa_v: 4.60999932\n",
        "    theta_v: 0.03003731\n",
        "    sigma_v: 0.50511135\n",
        "    rho: -0.52714421\n",
        "    v0: 0.00996677\n",
        "\n",
        "The resulting MSE for Asian put option calibration is 0.384570.\n",
        "\n",
        "12. Monte Carlo Simulation:\n",
        "\n",
        "    To calculate the model prices for Asian call options, we employed a Monte Carlo simulation approach.\n",
        "    Specifically, we used a binomial model to simulate the price paths of the underlying stock. In this binomial model, at each time step, the stock price could either go up or down based on the calculated probabilities.\n",
        "    The risk-neutral probabilities for the up and down movements were determined using the constant risk-free rate and the volatility of the underlying stock.\n",
        "    For each simulated price path, the average stock price over the monitoring points was calculated. This average stock price was then used to determine the Asian option's payoff at maturity.\n",
        "    We repeated this Monte Carlo simulation process multiple times (M times) to estimate the option prices. The average of these simulated option prices provided the model's estimate for the Asian call option price.\n",
        "\n",
        "Thus, we successfully calibrated the Heston (1993) model to the market data for Asian call options on SM Energy Company's stock. The calibration process involved option selection, consideration of various maturities, parameter estimation, and Monte Carlo simulations. The resulting parameter values and model quality were reported for further analysis and use by the team."
      ],
      "metadata": {
        "id": "lM-UEu2HxZRu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plot_calibration_results(heston_lewis_call_params, \"call\")"
      ],
      "metadata": {
        "id": "ybY7sZG8I1E7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "bd5194e8-2edd-40bd-b310-39aae4017889"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-2-f3815e05660f>:377: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  options[model_column] = calculate_model_values_heston_lewis(p0, is_call=is_call)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plot_calibration_results(heston_lewis_put_params, \"put\")"
      ],
      "metadata": {
        "id": "43XfC_2m881S",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "f5a9190d-3df1-4077-bb5c-b6df7a17bab3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-2-f3815e05660f>:377: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  options[model_column] = calculate_model_values_heston_lewis(p0, is_call=is_call)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Team Member A - Discussion About Graph - Step 1\n",
        "The slight discrepancies between the model prices and the market prices for both call and put options can be attributed to several factors in the calibration process:\n",
        "\n",
        "    Model Assumptions: The Heston (1993) model used for calibration makes certain simplifying assumptions about the dynamics of volatility and the underlying asset's behavior. These assumptions may not perfectly capture the complexities of real-world markets.\n",
        "\n",
        "    Market Data: Market data can sometimes contain noise or anomalies that may not be fully accounted for in the calibration process. Additionally, the model may not perfectly fit the specific characteristics of the Asian options in the market.\n",
        "\n",
        "    Optimization Process: The calibration involves an optimization process that aims to minimize the mean squared error (MSE) between model prices and market prices. Depending on the optimization algorithm and initial parameter values, the calibration may find local minima instead of the global minimum, leading to some discrepancies.\n",
        "\n",
        "    Model Limitations: The Heston model itself has limitations, such as assuming constant parameters over time, which may not fully capture the time-varying nature of market conditions.\n",
        "\n",
        "    Market Noise: Financial markets are subject to various forms of noise and volatility, which can lead to discrepancies between model prices and market prices.\n",
        "\n",
        "In the graph that compares model prices with market prices for both call and put options, we can observe that while there are some differences, the overall fit is reasonably good. The model prices generally follow the trend of the market prices, especially for options with shorter maturities. However, for longer maturities, the discrepancies become more noticeable.\n",
        "\n",
        "It's important to note that calibration is an iterative process, and achieving a perfect fit between the model and market prices is often challenging. The goal is to find parameter values that provide a reasonable approximation to market data while adhering to the assumptions of the model."
      ],
      "metadata": {
        "id": "rjSO9HMS844y"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Step 2 - Team Member A (Calibration based on 60days maturity and Carr Maden & Bates)\n",
        "i = 0\n",
        "min_MSE = 5000.0\n",
        "local_opt = False\n",
        "N = 10\n",
        "M = 100\n",
        "seed_value = 42\n",
        "#previous calibrated parameters\n",
        "kappa_v, theta_v, sigma_v, rho, v0 = heston_lewis_call_params\n",
        "#New Maturity and change in market data\n",
        "T = 60/250\n",
        "\n",
        "params_carr_call = B96_calibration_short()\n",
        "#Step 2 - Team Member A - Carr Madan Put options calibration\n",
        "i = 0\n",
        "min_MSE = 5000.0\n",
        "local_opt = False\n",
        "N = 10\n",
        "M = 100\n",
        "seed_value = 42\n",
        "kappa_v, theta_v, sigma_v, rho, v0 = heston_lewis_put_params\n",
        "params_carr_put = B96_put_calibration_short()"
      ],
      "metadata": {
        "id": "SaDqyAiQC5XU",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "03f2cfdf-e639-4dea-f130-ea6b79bd0091"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "   0 | [ 0.  -0.5  0. ] |  89.390 |  89.390\n",
            "  25 | [ 0.2  -0.5   0.25] |  45.882 |  44.302\n",
            "  50 | [ 0.4 -0.5  0.5] |  15.722 |  15.722\n",
            "  75 | [ 0.5   -0.5    0.525] |   8.913 |   8.275\n",
            " 100 | [ 0.60709877 -0.44351852  0.55648148] |   7.275 |   7.216\n",
            " 125 | [ 0.6537231  -0.34025292  0.57762927] |   6.956 |   6.953\n",
            " 150 | [ 0.68844354 -0.17516306  0.56906948] |   6.670 |   6.634\n",
            " 175 | [ 0.72503983 -0.06370867  0.53676275] |   6.492 |   6.480\n",
            " 200 | [ 0.8383542  -0.05151979  0.48251605] |   6.240 |   6.240\n",
            " 225 | [ 2.0261441  -0.25806648  0.02453377] |   3.846 |   2.810\n",
            " 250 | [ 1.98170207 -0.22853966  0.03045276] |   1.747 |   1.674\n",
            " 275 | [ 2.05621773e+00 -2.28788130e-01  4.91023060e-04] |   1.548 |   1.546\n",
            " 300 | [ 2.26683935 -0.21494213  0.00292908] |   1.432 |   1.432\n",
            " 325 | [ 2.79175382 -0.19162247  0.01173117] |   1.328 |   1.323\n",
            " 350 | [ 4.0901447  -0.15125377  0.04788311] |   1.242 |   1.230\n",
            " 375 | [ 4.59906878 -0.14997899  0.01812011] |   1.145 |   1.130\n",
            " 400 | [ 5.81934088 -0.1319239   0.00626324] |   1.037 |   1.035\n",
            " 425 | [ 5.82939901e+00 -1.31410878e-01  6.04162179e-04] |   1.032 |   1.032\n",
            " 450 | [ 5.81458757e+00 -1.31605970e-01  1.01189999e-04] |   1.032 |   1.032\n",
            " 475 | [ 5.81187091e+00 -1.31643553e-01  1.18148140e-05] |   1.032 |   1.032\n",
            " 500 | [ 5.81136478e+00 -1.31650088e-01  6.04069655e-07] |   1.032 |   1.032\n",
            " 525 | [ 5.81137341e+00 -1.31649852e-01  5.79719828e-08] |   1.032 |   1.032\n",
            " 550 | [ 5.81137827e+00 -1.31649811e-01  1.94070134e-08] |   1.032 |   1.032\n",
            "Optimization terminated successfully.\n",
            "         Current function value: 1.032252\n",
            "         Iterations: 313\n",
            "         Function evaluations: 573\n",
            "   0 | [ 0.  -0.5  0. ] |  61.042 |  61.042\n",
            "  25 | [ 0.2  -0.5   0.25] |  31.802 |  30.847\n",
            "  50 | [ 0.4 -0.5  0.5] |  17.230 |  17.230\n",
            "  75 | [ 0.5   -0.2    0.525] |  15.222 |  15.222\n",
            " 100 | [ 0.32113245 -0.09190062  0.77284141] |  12.829 |  12.829\n",
            " 125 | [ 0.19638834 -0.01145931  0.95808273] |  12.202 |  12.202\n",
            " 150 | [ 2.18354602e-01 -3.35710904e-04  9.88158276e-01] |  11.023 |  10.370\n",
            " 175 | [ 0.25058963 -0.00160099  1.01624158] |   6.627 |   6.528\n",
            " 200 | [ 2.49454898e-01 -1.98520458e-04  1.01373111e+00] |   6.484 |   6.482\n",
            " 225 | [ 2.51677711e-01 -8.40404670e-05  1.01334871e+00] |   6.430 |   6.430\n",
            " 250 | [ 2.89004343e-01 -4.93758913e-04  1.00162462e+00] |   5.853 |   5.853\n",
            " 275 | [ 2.94353375e-01 -7.40391043e-04  9.99622652e-01] |   5.834 |   5.834\n",
            " 300 | [ 2.94464425e-01 -1.08450177e-04  9.99367581e-01] |   5.833 |   5.833\n",
            " 325 | [ 2.95347290e-01 -3.81498719e-06  9.99101002e-01] |   5.832 |   5.832\n",
            " 350 | [ 2.95413720e-01 -1.01459294e-06  9.99052702e-01] |   5.832 |   5.832\n",
            " 375 | [ 2.95278730e-01 -6.19488253e-08  9.99089524e-01] |   5.832 |   5.832\n",
            " 400 | [ 2.95282295e-01 -2.39776434e-11  9.99088047e-01] |   5.832 |   5.832\n",
            " 425 | [ 2.95283076e-01 -2.87999965e-10  9.99087786e-01] |   5.832 |   5.832\n",
            " 450 | [ 2.95293442e-01 -1.35715326e-09  9.99084035e-01] |   5.832 |   5.832\n",
            " 475 | [ 2.95289178e-01 -9.97947746e-10  9.99085171e-01] |   5.832 |   5.832\n",
            " 500 | [ 2.95289679e-01 -1.03749605e-11  9.99085033e-01] |   5.832 |   5.832\n",
            "Optimization terminated successfully.\n",
            "         Current function value: 5.832370\n",
            "         Iterations: 301\n",
            "         Function evaluations: 541\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Team Member A - Report - Step 2\n",
        "\n",
        "**Introduction**\n",
        "This report presents the calibration of the Carr-Madan (1999) approach to the Bates (1996) stochastic volatility model for Asian call and put options on SM Energy Company's stock (SM) with a 60-day maturity. The client's preference for this extended maturity is addressed. This report details the calibration process using the Carr-Madan approach and presents the results for both call and put options.\n",
        "Data and Parameters\n",
        "\n",
        "Market data for Asian call and put options on SM stock was obtained from the attached Excel file. SM stock's current price is $232.90 USD. The parameters used in the Carr-Madan approach to the Bates model calibration are as follows:\n",
        "\n",
        "    Initial stock price (S0): $232.90 USD\n",
        "    Strike price (K): $232.90 USD\n",
        "    Time-to-maturity (T): 60 days, converted to a fraction of a year (T = 60/250)\n",
        "    Constant risk-free rate (r): 1.50% per annum\n",
        "    Number of monitoring points for the Asian option (N): 10\n",
        "    Number of Monte Carlo simulations (M): 100\n",
        "    Seed value for random number generator: 42\n",
        "\n",
        "Option Selection\n",
        "\n",
        "For calibration, options close to the at-the-money (ATM) level were selected with a tolerance level of 2% (tol = 0.02), ensuring representation of the prevailing market conditions.\n",
        "Selection of Maturities\n",
        "\n",
        "In response to the client's preference for a 60-day maturity, the calibration focused on this specific maturity while retaining the flexibility to explore alternative maturities.\n",
        "Conversion to Annualized Time\n",
        "\n",
        "For the 60-day maturity, the time-to-maturity (T) was converted into years by dividing 60 by 250, based on the assumption of 250 trading days in a year.\n",
        "Risk-Free Rate Assumption\n",
        "\n",
        "The constant annual risk-free rate of 1.50% was retained and converted into a daily rate using the assumption of 250 trading days in a year.\n",
        "Model Selection\n",
        "\n",
        "Consistent with Step 1, the Bates (1996) model without jumps, in conjunction with the Carr-Madan (1999) approach, was chosen as the underlying stochastic volatility model for calibration.\n",
        "Parameters to Calibrate\n",
        "\n",
        "The parameters to be calibrated in the Bates model are:\n",
        "\n",
        "    λ (lambda): Mean reversion rate of volatility.\n",
        "    μ (mu): Long-run mean of volatility.\n",
        "    δ (delta): Volatility of volatility.\n",
        "    ρ (rho): Correlation between volatility and stock/index level.\n",
        "    ν (nu): Initial level of volatility.\n",
        "\n",
        "Initial Parameter Guess\n",
        "\n",
        "As in Step 1, we initiated the calibration process with an initial parameter guess and employed a systematic approach to explore sensible parameter regions, seeking faster convergence.\n",
        "Calibration Iteration\n",
        "\n",
        "The calibration process involved iteratively adjusting the model parameters to minimize the Mean Squared Error (MSE) error function. Each iteration calculated the MSE, and we updated the parameter values accordingly. The process continued until the error converged or a maximum number of iterations was reached.\n",
        "Calibration Results\n",
        "11.1 Asian Call Option Calibration\n",
        "\n",
        "The calibration process for Asian call options resulted in the following parameter values:\n",
        "\n",
        "    λ (lambda): 5.81137837\n",
        "    μ (mu): -0.131649811\n",
        "    δ (delta): 4.44809421e-09\n",
        "\n",
        "The resulting MSE for Asian call option calibration is 1.032252.\n",
        "11.2 Asian Put Option Calibration\n",
        "\n",
        "For Asian put options, the calibration process yielded these parameter values:\n",
        "\n",
        "    λ (lambda): 0.295289572\n",
        "    μ (mu): -2.56361811e-12\n",
        "    δ (delta): 0.999085069\n",
        "\n",
        "The resulting MSE for Asian put option calibration is 5.83237.\n",
        "Conclusion\n",
        "\n",
        "In Step 2, we successfully recalibrated the Bates model using the Carr-Madan approach for Asian call and put options on SM Energy Company's stock with a 60-day maturity, aligning with the client's updated requirements. The calibration process mirrored the approach from Step 1, ensuring consistency in our methodology. The resulting parameter values and model quality are reported for further analysis and use by the team."
      ],
      "metadata": {
        "id": "RU_ZDq9WpzjW"
      }
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "BNdcuAHppTOc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plot_calibration_results_carr(params_carr_call, \"call\")"
      ],
      "metadata": {
        "id": "ltj0kZYEfOlL",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "5926f9ab-60b4-4fcd-e359-8a1c6863f132"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-2-f3815e05660f>:801: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  options[model_column] = B96_jump_calculate_model_values_carr(p0, is_call=is_call)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 2 Axes>"
            ],
            "image/png": 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ftP8za/bs2bpy5Yrd3btmz56t7t27a9y4cerUqZNatWql++67L8N5RNq0aaOiRYtqxowZmjt3rhISEvT000+nW69EiRLq16+ffv75Zx06dEiFCxdOd1YGQM5AqACQLV5++WXlz59fvXv31unTp9M9f+DAAdstT1P/Gm+kuUtPbGyspk6d6rR6nnvuOYWFhWnYsGHpLrm4evWqevbsKcMwNGLEiHSv/fzzz2W1Wm2PJ0+erKSkJLVt29bWlj9//kxN2tagQQOFhYXp008/tTtrsmDBAu3evVvt27e/431Le2tWyZwbo1atWpIyvlwmVZMmTdSyZUvbktEX/Vvp3bu3Ro4cqXHjxt10nYyOrSRNmDAh3br58+eXlD48BAcHq0iRIlqxYoVd+6RJk+6o3ozc6rgVKVJEbdu21bfffqsZM2aoTZs2dndkcoaYmBhFRkbKy8tLv//++03ntKhevbqqVKmizz//3O4MzeTJk2WxWNLNPXEntm7dqiFDhqhQoUJ2d1rz9vZOd9w++uijDM8Q+fj4qEuXLvrhhx80bdo01axZ0/YZlMyzSjde6hYWFqaSJUve8jMKwHNxS1kA2aJ8+fKaOXOmnnjiCVWtWlXdunVTjRo1dO3aNa1Zs0Y//vijevToIUmKjIy0/aX9ueeeU3x8vL744guFhYVleLlHVhQuXFizZ89W+/btVa9ePfXu3VvVqlVTTEyMpk2bpv3792vixIkZ3gL32rVrevDBB9W5c2ft3btXkyZN0n333aeHH37Ytk79+vU1efJkvfnmm6pQoYLCwsLsridP5evrq3fffVc9e/ZU8+bN1aVLF9stZcuWLZvutpyZ0bt3b50/f14PPPCAwsPDdeTIEX300UeqU6eOqlatesfby6wyZcrYzRGRkeDgYDVr1kz//e9/ZbVaVapUKS1atEiHDh1Kt279+vUlSa+//rqefPJJ+fr6qkOHDrZw+s4776h3795q0KCBVqxYoX379jm8D/Xr19fixYv1wQcfqGTJkipXrpzuvvtu2/PdunWzfWEfM2ZMprf7zTff6MiRI0pISJAkrVixQm+++aYk6emnn7adkWrTpo0OHjyol19+WatWrdKqVats2yhWrJhatWple/zee+/p4YcfVmRkpJ588knt2LFDH3/8sXr37p3p47xy5UpdvXpVycnJ+ueff7R69WrNnz9fISEhmjt3rooXL25b96GHHtI333yjkJAQVatWTWvXrtXixYtVuHDhDLfdrVs3ffjhh1q6dKnt1sapLl26pPDwcHXq1Em1a9dWgQIFtHjxYq1fv/6WoRSAB3PvzacA5DX79u0z+vTpY5QtW9bIly+fERQUZDRp0sT46KOPjKtXr9rWmz9/vlGrVi3D39/fKFu2rPHuu+8aU6ZMSXeL0azeUjbt+n369DFKly5t+Pr6GkWKFDEefvhhY+XKlenWTb096vLly41nn33WKFSokFGgQAHjqaeeMv755x+7dWNiYoz27dsbQUFBhiRbjTfeUjbV999/b9StW9fw8/MzQkNDjaeeeso4fvy43Trdu3c38ufPn66uG2+NOnv2bCMyMtIICwsz8uXLZ5QuXdp47rnnjFOnTmWqTzIr9Zayt5LRLWWPHz9uPPLII0bBggWNkJAQ4/HHHzdOnjyZ4a1Wx4wZY5QqVcrw8vKyO/YJCQlGr169jJCQECMoKMjo3LmzcebMmZveUvbs2bPpasvolrJ79uwxmjVrZgQEBBiS0t1eNjEx0ShUqJAREhJidwvg22nevLkhKcMl7WfhZuuk/QylNXfuXKNOnTqGn5+fER4ebvz73/+2u93xzaR+DlMXX19fo2jRokazZs2Mt956yzhz5ky611y4cMHo2bOnUaRIEaNAgQJG69atjT179hhlypTJ8Da8hmHeWtnLyyvdZzkxMdEYNmyYUbt2bSMoKMjInz+/Ubt2bWPSpEm3rR2AZ7IYxk1mAQIA2EmdpG79+vXpJh1D3pCUlKSSJUuqQ4cO+uqrr9xdjserW7euQkNDtWTJEneXAsDFGFMBAEAm/fzzzzp79uwdD2LPizZs2KAtW7bQV0AewZgKAABuY926ddq2bZvGjBmjunXrqnnz5u4uyWPt2LFDGzdu1Lhx41SiRAmX3CELgOfhTAUAALcxefJk9e3bV2FhYZo+fbq7y/Fos2fPVs+ePWW1WjVr1iy7meIB5F6MqQAAAADgEM5UAAAAAHAIoQIAAACAQ/LcQO2UlBSdPHlSQUFBslgs7i4HAAAAcBvDMHTp0iWVLFlSXl5ZP9+Q50LFyZMnFRER4e4yAAAAAI9x7NgxhYeHZ/n1eS5UBAUFSTI7Ljg42C01WK1WLVq0SJGRkfL19XVLDbkR/eoa9Ktr0K+uQb+6Dn3rGvSra9CvmRcXF6eIiAjbd+SsynOhIvWSp+DgYLeGisDAQAUHB/NBdyL61TXoV9egX12DfnUd+tY16FfXoF/vnKPDAhioDQAAAMAhhAoAAAAADiFUAAAAAHBInhtT4XbJybIsX65SK1bIkj+/dP/9kre3u6sCAABwmeTkZFmt1mx7P6vVKh8fH129elXJycnZ9r6eytfXV94u/r5JqMhOc+ZIgwfL5/hxNZCkDz6QwsOliROlRx91d3UAAABOZRiGYmJidPHixWx/3+LFi+vYsWPMS/b/ChYsqOLFi7usPwgV2WXOHKlTJ8kw7NtPnDDbZ88mWAAAgFwlNVCEhYUpMDAw277gp6SkKD4+XgUKFHBoQrfcwDAMJSQk6MyZM5KkEiVKuOR9CBXZITlZGjw4faCQzDaLRRoyROrYkUuhAABArpCcnGwLFIULF87W905JSdG1a9fk7++f50OFJAUEBEiSzpw5o7CwMJdcCkUvZ4eVK6Xjx2/+vGFIx46Z6wEAAOQCqWMoAgMD3VwJpOvHwVVjWzwqVIwdO1YNGzZUUFCQwsLCFBUVpb1792a4rmEYatu2rSwWi37++efsLfROnTqVqdXGDTulN96Q/vc/86qojE5sAAAA5CSMafAMrj4OHnX50/Lly9W/f381bNhQSUlJeu211xQZGaldu3Ypf/78dutOmDAh53xIM3nt2v82lNDyDdcfFy0q1a17falXTypfXuIsHgAAADyJR4WKhQsX2j2eNm2awsLCtHHjRjVr1szWvmXLFo0bN04bNmxw2WATp2ra1LzL001OPxgWixKLhCvqlaYqvVXatEnavVs6e1ZatMhcUgUFSbVrXw8ZdetK1apJzEAPAACQ85QtW1ZDhgzRkCFD3F2KQzwqVNwoNjZWkhQaGmprS0hIUNeuXfXJJ5+oePHi7irtznh7m7eN7dTJHJSdNlhYLLJI8v90goY8en3QzJUr0vbt0ubNZsjYvNl8fOmStGqVuaTKl0+qUcM+aNSqJd1wcgcAAAC5TIsWLVSnTh1NmDDBrXV4bKhISUnRkCFD1KRJE9WoUcPW/sILL+jee+9Vx44dM7WdxMREJSYm2h7HxcVJMgepZOckLOrQQZbvvpP30KGynDhhazZKlVLyuHEyOnSQ0tTj43P9sqdnnjHbkpKkPXukLVsstmXrVotiYy3atMkMH199Za7r5WWoYkWpTh1DdesaqlPHXNLks1wn9Xhm63HNA+hX16BfXYN+dR361jVyc79arVYZhqGUlBSlpKRk63sb//8H3NT390TXrl1Tvnz5JDleZ2Zen5KSIsMwZLVa7e7+5KzPnsUwPHM4cN++fbVgwQKtWrVK4eHhkqT58+frxRdf1ObNm1WgQAFJ5qCTuXPnKioqKsPtjBo1SqNHj07XPnPmTPfcjSA5WYV37ZL/hQu6WqiQ/qlWzaHbyBqGdPp0oA4eDNHBgwV18GCIDh0K0YUL/hmuX7RogsqVi1X58hdVrlys7rorVoULX1VOGZ4CAAByBh8fHxUvXlwRERG2L885xUMPPaRq1arJ29tbs2bNUr58+fT666+rU6dOevnllzV//nwVLVpU7777rlq1aqXk5GQNGTJEK1as0JkzZxQeHq5evXrp+eeft22zX79+io2NVd26dfXVV18pX7582rp1q2rVqqW+ffuqb9++kqTp06frP//5j6ZPn67mzZtr165dGjFihP78808FBgbq/vvv19tvv63ChQurX79+mjVrll3tW7duVenSpdPt07Vr13Ts2DHFxMQoKSnJ1p56FVBsbKyCg4Oz3GceeaZiwIAB+uWXX7RixQpboJCkP/74QwcOHFDBggXt1n/sscfUtGlTLVu2LN22hg8frqFDh9oex8XFKSIiQpGRkQ51nCOsbdooOjparVq1kq+LBkPExFi1ZYtFmzdfP6Nx8KBFZ88G6uzZQP311/WxKEWKXD+TkbpUqJDzBoRbrVaX92teRL+6Bv3qGvSr69C3rpGb+/Xq1as6duyYChQoIH9/84+dhiElJLj+vQ3D0KVLlxQUFCSLxaLAQN3RH1B9fHz03XffadiwYVq3bp1++OEHvfjii1q4cKGioqI0YsQITZgwQX379tXhw4cVEBCgcuXKaeDAgSpcuLDWrFmj559/XmXLllXnzp0lSb6+vlqxYoVCQ0O16P8HzAYHB8vLy0v+/v4KDg7We++9p/fee0+///67GjVqpIsXLyoqKkq9evXShx9+qCtXrujVV19Vnz59tHjxYn3yySc6fPiwqlevbvsjetGiRTOch+Lq1asKCAhQs2bNbMdDun4Vj6M8KlQYhqGBAwdq7ty5WrZsmcqVK2f3/KuvvqrevXvbtdWsWVPjx49Xhw4dMtymn5+f/Pz80rX7+vq6/X9eV9YQEWEuabslNlbasuX6GI3Nm80B4efOWbR4sUWLF19ft0ABc0B46hiN1AHhOeEPDZ5wbHMj+tU16FfXoF9dh751jdzYr8nJybJYLPLy8rJNQHf5spR9f9MtaPuv+Pg7H2tau3Zt/ec//5Ekvfbaa3r33XdVtGhRPffcc5KkkSNH6tNPP9WOHTt0zz336I033rC9tnz58lq3bp1mz56tJ598UpJ5dU3+/PltZynSslgsGj58uL755hstX75c1atXlyRNmjRJdevW1dixY23rTp06VREREdq/f78qVaqkfPnyKX/+/CpZsuQt98fLy0sWiyXdZ81ZnzuPChX9+/fXzJkzNW/ePAUFBSkmJkaSFBISooCAABUvXjzDwdmlS5dOF0CQXkiI1Ly5uaS6ckXascM+aGzbZv7Pt3q1uaTKl0+qXt0+aNSuzYBwAACQ+9SqVcv2397e3ipcuLBq1qxpaytWrJgkc5ZqSfrkk080ZcoUHT16VFeuXNG1a9dUp04du23WrFkzw0vBxo0bp8uXL2vDhg266667bO1bt27V0qVLbZf9p3XgwAFVqlTJoX10Jo8KFZMnT5ZkjmJPa+rUqerRo0f2F5QHBARIDRuaS6qkJGnvXvugsXmzeaYj9b9TWSxSpUr2QaNuXalw4ezfFwAA4NkCA80/XLpaSkqK4uLibJcXZWUY7Y1/wU/9K3/ax6nv9d133+mll17SuHHj1LhxYwUFBem9997TunXr7LZx47xrqZo2bapff/1VP/zwg1599VVbe3x8vDp06KB333033Ws8bVoFjwoVWRkz7qHjzHM0Hx/zjET16tLTT5tthiEdPpw+aJw6ZQaQvXultOOESpe2Dxl165pTdTAgHACAvMtiyZ4rHFJSpORk872yY4zo6tWrde+996pfv362tgMHDmT69Y0aNdKAAQPUpk0b+fj46KWXXpIk1atXTz/99JPKli0rH5+Mv7bny5dPycnJju2AE3hUqIDnslikcuXM5bHHrrfHxNiHjM2bpQMHpKNHzWXevOvrFimSPmhUrJjzBoQDAACkVbFiRU2fPl2///67ypUrp2+++Ubr16+/o8vz7733Xv32229q27atfHx8NGTIEPXv319ffPGFunTpopdfflmhoaHav3+/vvvuO3355Zfy9vZW2bJltW7dOh0+fFgFChRQaGiobQxLdiJUwCHFi0tt25pLqtQB4WmDxq5d0rlzUnS0uaRKHRCeNmhUr54zBoQDAABI0nPPPafNmzfriSeekMViUZcuXdSvXz8tWLDgjrZz33336ddff1W7du3k7e2tgQMHavXq1XrllVcUGRmpxMRElSlTRm3atLEFh5deekndu3dXtWrVdOXKFR06dEhly5Z1wV7eGqECTnerAeFpg8bWrRkPCPf1vT5DeNoB4RmMUQIAAHC6jKYpOHz4cLq2tJfhT506VVOnTrV7Pu1dm6ZNm5bhe9243WbNmik+zcCTihUras6cOTettVKlSlq7du1Nn88uhApki1sNCL/x8qmLF28+IPzGy6eKFMn2XQEAAMANCBVwm7QDwv/1L7MtdUB42pCxaZP9gPDvvru+jYiI6wGjZk2LLlzwF2P3AQAAshehAh4l7YDwRx+93n76dPqgceCAdOyYucyfL5kf59Z69VXDFjRSb3XLgHAAAADXIVQgRyhWTGrTxlxSxcaa4zJSg8bGjYZ27TL0zz9eWrxYdjOE589/fUB4atBgQDgAAIBzECqQY4WESM2amYskWa1J+vnnhYqIaKvt231sZzS2bZMuX5bWrDGXVL6+ZrBIGzQYEA4AAHDnCBXIVfLlS1H9+obuued6W1KStG+f/aVTqQPCt2wxl9SbNVgs5qVSaYMGA8IBAABujVCBXM/HR6pWzVyeespsMwzpyJH0QePkSTOA7Nsnff/99W2Eh6cPGhERzBAOAAAgESqQR1ksUtmy5vLII9fbz5xJHzT275eOHzeX//3v+rqFC0t16tgHjYoVJW/vbN4ZAAAANyNUAGmEhUmtW5tLqri46wPCU4PGrl3SP/9IS5aYS6q0A8LTzhDu55f9+wIAAJBdCBXAbQQHS02bmkuqq1elnTuvh4zUGcJvNyA87QzhQUHZvy8AAMBztGjRQnXq1NGECRMytf60adM0ZMgQXbx40aV1ZQWhAsgCf3+pfn1zSZWcbI7FSBs0Nm+WLly49YDwtEvRou7YGwAAPFhysrRypTkTbokS5l/5uNbY4xAqACfx9paqVjWXtAPCjx5NHzROnLj1gPC0k/cxIBwAkGfNmSMNHmwObEwVHi5NnGg/Sy7cjjmGAReyWKQyZczB4G+8YQ70Pn7cnCF84UJp7Fipc2fzrIV0fTD4G2+YrylTxrydbcuW0rBh0syZ0p495h9tAADI1ebMkTp1sg8UkvmXuU6dzOddpEWLFho4cKCGDBmiQoUKqVixYvriiy90+fJl9ezZU0FBQapQoYIWLFhge83y5cvVqFEj+fn5qUSJEnr11VeVlJRke/7y5cvq1q2bChQooBIlSmjcuHHp3jcxMVEvvfSSSpUqpfz58+vuu+/WsmXLXLafzkSoANwgdUD4q6+aZyr27TNnCF+xwvzjS48e5rgLHx/p/HlzMPj775tnQKpWNcd53Huv1L+/9OWX5pmQxER37xUAAE6SnGyeoTCM9M+ltg0Z4tK/sn399dcqUqSI/vrrLw0cOFB9+/bV448/rnvvvVebNm1SZGSknn76aSUkJOjEiRNq166dGjZsqK1bt2ry5Mn66quv9Oabb9q2N2zYMC1fvlzz5s3TokWLtGzZMm3atMnuPQcMGKC1a9fqu+++07Zt2/T444+rTZs2+vvvv122n87C5U+Ah8hoQHhiorRjh/2lU1u3SgkJ0tq15pLKx8d+QHi9egwIBwDkUCtXpj9DkZZhSMeOmeu1aOGSEmrXrq1///vfkqThw4frnXfeUZEiRdSnTx9J0ogRIzR58mRt27ZN//vf/xQREaGPP/5YFotFVapU0cmTJ/XKK69oxIgRSkhI0FdffaVvv/1WDz74oCQztISHh9ve7+jRo5o6daqOHj2qkiVLSpJeeuklLVy4UFOnTtXbb7/tkv10FkIF4MH8/G4+IDxt0Ni82TyjsXWruUybZq5rsUgVKtgHDQaEAwA83qlTzl0vC2rVqmX7b29vbxUuXFg1a9a0tRUrVkySdObMGe3evVuNGzeWJc0gyCZNmig+Pl7Hjx/XhQsXdO3aNd19992250NDQ1W5cmXb4+3btys5OVmVKlWyqyMxMVGFCxd2+v45G6ECyGHSDgjv2tVsSx0QfmPQOH5c+vtvc/nhh+vbKFUq/QzhpUszIBwA4CFKlHDuelng6+tr99hisdi1pQaIlJQUp7xffHy8vL29tXHjRnnfcHerAgUKOOU9XIlQAeQCqQPCy5SRoqKut589mz5o7NtnjnE7cUL65Zfr64aGpp8h/IY/lgAAkD2aNjXv8nTiRMbjKiwW8/m01wy7UdWqVfXTTz/JMAxb2Fi9erWCgoIUHh6u0NBQ+fr6at26dSpdurQk6cKFC9q3b5+aN28uSapbt66Sk5N15swZNfWQ/boThAogFytaVIqMNJdUly5dnyE8ddmxw7x86o8/zCVVYKBUs6a3QkNrKSbGogYNpBo1mCEcAOBi3t7mnUs6dTIDRNpgkXpafcIEj5mvol+/fpowYYIGDhyoAQMGaO/evRo5cqSGDh0qLy8vFShQQL169dKwYcNUuHBhhYWF6fXXX5eX1/V7JlWqVElPPfWUunXrpnHjxqlu3bo6e/aslixZolq1aql9+/Zu3MPbI1QAeUxQkHTffeaSKjHRnCE8NWRs2nR9QPi6dV6Syin1rnk+PlK1avZnNGrXNgeaAwDgNI8+Ks2enfE8FRMmeNQ8FaVKldJvv/2mYcOGqXbt2goNDVWvXr1sA70l6b333lN8fLw6dOigoKAgvfjii4qNjbXbztSpU/Xmm2/qxRdf1IkTJ1SkSBHdc889euihh7J7l+6YxTAyOqeUe8XFxSkkJESxsbEKdtO3IKvVqt9++03t2rVLd70eso5+da7kZHMsxvr1SZoz55Di4spryxYvnT+f8foVKtgHjbp1zVvnImN8Xl2DfnUd+tY1cnO/Xr16VYcOHVK5cuXk7++f9Q1lYUbtlJQUxcXFKTg42O5sQF52s+PhrO/GnKkAkCFvb6lKFal8eUPBwbvUrl1Z+fh46dgx+zMaqQPC9+83l7QDwkuWTB80ypRhQDgA4A54e7vstrFwHo8KFWPHjtWcOXO0Z88eBQQE6N5779W7775rd7ut5557TosXL9bJkydVoEAB2zpVqlRxY+VA3mCxmHeJKl1a6tjxevvZs9KWLfZB4++/pZMnzSXtgPBChexDRt26UuXKHnNZLAAAyAKPChXLly9X//791bBhQyUlJem1115TZGSkdu3apfz580uS6tevr6eeekqlS5fW+fPnNWrUKEVGRurQoUPpbr8FIHsULSq1amUuqS5dkrZtsw8aO3dKFy5kPCC8Vi37oFGjhuTI2XIAAJB9PCpULFy40O7xtGnTFBYWpo0bN6pZs2aSpGeffdb2fNmyZfXmm2+qdu3aOnz4sMqXL5+t9QK4uaAgqUkTc0mVmCjt2mUfNLZulS5flv7801xSpQ4ITxs06tRhQDgAAJ7Io0LFjVJHxIeGhmb4/OXLlzV16lSVK1dOERER2VkagCzw87seEJ55xmxLTjbHYqSGjNTln3/MMx3btklff319G2lnCE9d/n9SUwAA4CYeGypSUlI0ZMgQNWnSRDVq1LB7btKkSXr55Zd1+fJlVa5cWdHR0cqXL1+G20lMTFRiYqLtcVxcnCTzbgtWq9V1O3ALqe/rrvfPrehX18iOfr3rLnPp1Ml8bBjm4O/Nmy3assVctm616Ngxi21A+I8/Xn99yZKG6tQxVLu2obp1DdWvbyg83LMHhPN5dQ361XXoW9fIzf2alJQkwzCUlJTktFmnMyv15qaGYWT7e3uqtMcj7efNWZ89j72lbN++fbVgwQKtWrVK4eHhds/FxsbqzJkzOnXqlN5//32dOHFCq1evzvB2ZaNGjdLo0aPTtc+cOVOBgYEuqx+A88XF5dPBgyE6eDBEhw6Z/548WUCGYZGXktVUK1VCp3RKJbQ9pKHuqnhJ5ctfVIUKF1Wx4kUVLJh4+zcBADhNsWLFVKBAAYWGhsrHx2P/lp3rJSUl6fz584qPj9fp06ftnktISFDXrl0dvqWsR4aKAQMGaN68eVqxYoXKlSt3y3WvXbumQoUK6csvv1SXLl3SPZ/RmYqIiAidO3fOrfNUREdHq1WrVrnuntTuRL+6hqf3a3y8dPLjn1X6g6EKunh9cqRjCtdgTdRcXZ8cKTzcUL165pmM1KVwYXdU7fn9mlPRr65D37pGbu9Xq9Wq06dP68qVK9n6voZh6OrVq/L395fFk09bZ6OAgAAVK1Ys3ecsLi5ORYoUyV3zVBiGoYEDB2ru3LlatmzZbQNF6msMw7ALDmn5+fnJz88vXbuvr6/b/+f1hBpyI/rVNTy1XwstnaNCI58wr5lKI1wn9JM66aPms/XZ2Ue1e7d0/LhFx49bNH/+9fXKlZMaNLi+1K8vhYRkX/2e2q85Hf3qOvSta+TWfvX19VXZsmWVlJSk5OTkbHtfq9WqFStWqFmzZrmyX++Ut7e3fHx8MgxYzuofjwoV/fv318yZMzVv3jwFBQUpJiZGkhQSEqKAgAAdPHhQ33//vSIjI1W0aFEdP35c77zzjgICAtSuXTs3Vw8g2yUnS4MHpwsUkmSRIVksGnRwiAYd6qj4K97avFnasEFav9789++/pUOHzCXtGI1KleyDRt26UoEC2bhfAJCLWCyWbA9N3t7eSkpKkr+/P6Eim3hUqJg8ebIkqcUNsyZOnTpVPXr0kL+/v1auXKkJEybowoULKlasmJo1a6Y1a9YoLCzMDRUDcKuVK80R3TdjGNKxY9LKlSrQooWaNpWaNr3+9MWL5l2n0gaNw4elffvMZeZMcz0vL6lqVfugUbu2FBDgyp0DACDn8KhQcbvhHSVLltRvv/2WTdUA8HinTjm0XsGC0gMPmEuqc+ekjRvNgJEaNk6cMCfu27nz+u1tfXzMCfrSBo2aNaWb3IgOAIBczaNCBQDckRIlnLuepCJFpNatzSXVqVPXg8b69eZy9qy0ZYu5fPmluV6+fOYZjLRBo1o1M4AAAJCb8asOQM7VtKkUHm6eSsjoTKfFYj6f9pqnLChRQnroIXORrs+jkXo2IzVsXLhwPXSkCggwx2SkDRqVKztUDgAAHodQASDn8vaWJk40Z82zWOyDReodLiZMMNdzIotFiogwl0ceMdsMwxzwnTZkbNwoXbokrVljLqkKFJDq1fNWoULVdemSRffcI5Uv79mT9QEAcCuECgA526OPSrNnm3eBSjtoOzzcDBSPPnrTlzqTxXJ9ZvDOnc22lBTzDlNpz2hs2mTOrbFihZekCpo3z1y3YEH7sxkNGkilSxM0AAA5A6ECQM736KNSx47m3aBOnTKvV2ra1OlnKO6Ul5d5qVPlytJTT5ltSUnSnj3SunVJmjPnqM6eLatt27x08aK0eLG5pCpaNH3QKFnSLbsCAMAtESoA5A7e3tINt6P2RKl3japc2VCRItvVrl2EDMNLO3faXzq1fbs5GHzBAnNJVbJk+qBRtKj79gcAAIlQAQBuly+fOZi7bl2pTx+z7epVads2+6Cxa5d08qQ0f77sZgUvUyb9rOCFCrlnXwAAeROhAgA8kL+/1KiRuaS6fNm8hW3aoLF3r3TkiLn89NP1dStUsA8a9epJQUHZvhsAgDyCUAEAOUT+/FKTJuaSKi7u+qzgqUHj4EFp/35z+e47cz2LRapSxT5o1KkjBQa6ZVcAALkMoQIAcrDgYHMoSdrhJOfPp58V/Ngxafduc/nmG3M9b2+penX7oFGrluTn5449AQDkZIQKAMhlQkOlVq3MJdXp0+mDRkyMOW5j2zZpyhRzPV9fM1ikDRrVq5vtAADcDKECAPKAYsWkdu3MRTIn6zt5Mv2s4P/8Y4aPjRulzz4z1/X3Ny+VShs0qlRx+x17AQAehFABAHmQxSKVKmUuHTuabYZhDvhOGzQ2bJBiY6U//zSXVPnzm4O/0waNChXMuTkAAHkPoQIAIMkMGmXLmkunTmZbSop04IB9yNi40bwT1cqV5pIqJMS8nW3aoFG2LLOCA0BeQKgAANyUl5dUsaK5dOlitiUnm7eyTRs0Nm82z2j88Ye5pCpcOP1kfaVKETQAILchVAAA7oi3t1Stmrl062a2Wa3m5Hxpg8bWreYYjd9/N5dUxYunDxrFirlnXwAAzkGoAAA4zNdXql3bXHr1MtsSE6Xt2+2Dxo4d5l2nfvnFXFKFh0sNG9rPCl64sHv2BQBw5xwOFQsXLlSBAgV03333SZI++eQTffHFF6pWrZo++eQTFSpUyOEiAQA5j5/f9ZCQKiHBPIORNmjs3i0dP24uc+deX7dcOfugUa+eOW4DAOB5HA4Vw4YN07vvvitJ2r59u1588UUNHTpUS5cu1dChQzV16lSHiwQA5A6BgVLjxuaS6tIlc0xG2qDx99/SoUPm8sMP19etVMk+aNSta96JCgDgXg6HikOHDqlatWqSpJ9++kkPPfSQ3n77bW3atEntUm+IDgDATQQFSc2amUuqCxekTZvsg8bhw9K+feYyY4a5npeXVLXq9aBRp45F165xX1sAyG4Oh4p8+fIpISFBkrR48WJ1+/9Re6GhoYqLi3N08wCAPKhQIenBB80l1dmz9rOCb9ggnTgh7dxpLtOmSZKPvL3bq2ZNi90ZjRo1pHz53LQzAJAHOBwq7rvvPg0dOlRNmjTRX3/9pe+//16StG/fPoWHhztcIAAAklS0qNSmjbmkOnnSPmisX2/o7FkvbdkibdkiffGFuV6+fOYg8rRBo2pVyYfblQCAUzj84/Tjjz9Wv379NHv2bE2ePFmlSpWSJC1YsEBt0v7kBwDAyUqWNJcOHczH164lafr0pQoOfkBbtvjYwsaFC9L69eaSKjDQHJOR9ta2lSoxKzgAZIXDoaJ06dL6Je19Af/f+PHjHd00AAB3xGKRiha9onbtDHXubLYZhnTwYPpZwS9dklavNpdUQUHmXabSntG46y4m6wOA23HKid8DBw5o6tSpOnDggCZOnKiwsDAtWLBApUuXVvXq1Z3xFgAAZInFIpUvby5PPGG2paSYA77TBo1Nm8ygsXy5uaQqVCj9ZH0REQQNAEjL4ZO8y5cvV82aNbVu3TrNmTNH8fHxkqStW7dq5MiRd7StsWPHqmHDhgoKClJYWJiioqK0d+9e2/Pnz5/XwIEDVblyZQUEBKh06dIaNGiQYmNjHd0NAEAe4uUlVaki/etf0oQJ0qpVUlyctG2bNGWK1K+f1KiRORbjwgUpOloaO1Z67DGpTBlzBvB27aSRI6X//U86dcrdewQA7uXwmYpXX31Vb775poYOHaqgoCBb+wMPPKCPP/74jra1fPly9e/fXw0bNlRSUpJee+01RUZGateuXcqfP79OnjypkydP6v3331e1atV05MgRPf/88zp58qRmz57t6K4AAPIwHx+pZk1z6dnTbLt2zZwFPO0Zje3bzTtRLVhgLqlKlkw/K3jRou7ZFwDIbg6Hiu3bt2vmzJnp2sPCwnTu3Lk72tbChQvtHk+bNk1hYWHauHGjmjVrpho1auinn36yPV++fHm99dZb+te//qWkpCT5cBsPAIAT5ctnjrGoV0969lmz7erV9LOC79pl3olq3jxzSVWmjBkwUsNG/fpSwYJu2RUAcCmHv4UXLFhQp06dUrly5ezaN2/ebLsTVFalXtYUGhp6y3WCg4MJFACAbOHvL919t7mkio83b2GbNmjs3SsdOWIuaf4epgoV0s8KnuZEPwDkSA5/E3/yySf1yiuv6Mcff5TFYlFKSopWr16tl156yTYRXlakpKRoyJAhatKkiWrUqJHhOufOndOYMWP0bOqfjzKQmJioxMRE2+PUCfmsVqusVmuW63NE6vu66/1zK/rVNehX16BfXcNd/ernlz5oxMZKmzdbtHGjuWzaZNHBgxbt3y/t3y/NmmWuZ7EYqlxZql/fUIMGhurXN1SrlqHAwGzdhdviM+sa9Ktr0K+Z56w+shiGYTiygWvXrql///6aNm2akpOT5ePjo+TkZHXt2lXTpk2Tt7d3lrbbt29fLViwQKtWrcpwEr24uDi1atVKoaGhmj9/vnx9fTPczqhRozR69Oh07TNnzlSgp/3EBgDkanFxvjpwoKD27y9o+/fcufS/i7y8UlS69CVVqHDRtpQpEydf3xQ3VA0gN0tISFDXrl1tV/9klcOhItXRo0e1Y8cOxcfHq27duqpYsWKWtzVgwADNmzdPK1asSHdZlSRdunRJrVu3VmBgoH755Rf5+/vfdFsZnamIiIjQuXPnHOo4R1itVkVHR6tVq1Y3DUO4c/Sra9CvrkG/ukZO7NfTp2U7m5G6nD6d/n61vr6Gata8fjajXj1D1apJ2bWbObFvcwL61TXo18yLi4tTkSJFHA4VThuIULp0aZUuXdqhbRiGoYEDB2ru3LlatmxZhoEiLi5OrVu3lp+fn+bPn3/LQCFJfn5+8vPzS9fu6+vr9g+ZJ9SQG9GvrkG/ugb96ho5qV/Dw82lY0fzsWFIJ07Yj89Yv146f968hGrTpuuv9feX6tSxH6NRubKUxYsEMiUn9W1OQr+6Bv16e87qH4dDxTPPPHPL56dMmZLpbfXv318zZ87UvHnzFBQUpJiYGElSSEiIAgICFBcXp8jISCUkJOjbb79VXFycbYxE0aJFs3ypFQAAnsJiuR40oqLMNsOQDh+2DxobNphza/z5p7mkyp8//azg5cubc3MAgKs4HCouXLhg99hqtWrHjh26ePGiHnjggTva1uTJkyVJLVq0sGufOnWqevTooU2bNmndunWSpAoVKtitc+jQIZUtW/bOigcAIAewWKRy5czl8cfNtpQUc8D3jbOCX74srVxpLqlCQszb2aYNGmXKMCs4AOdxOFTMnTs3XVtKSor69u2r8uXL39G2bje8o0WLFrddBwCAvMDLS6pUyVy6djXbkpOlPXvsg8aWLeadqP74w1xSFS5sP4dGgwbmBH4EDQBZ4ZLJHby8vDR06FC1aNFCL7/8siveAgAA3MDbW6pe3Vy6dzfbrFZp5077oLFtm/TPP9Lvv5tLquLF0weNsDD37AuAnMVlM8YdOHBASUlJrto8AADIBF9fczB3nTpS795mW2KiGSzSBo2dO6WYGOmXX8wlVUSEGS7q1fNS8eK3vjkKgLzL4VAxdOhQu8eGYejUqVP69ddf1T31zyQAAMBj+PmZZyMaNrzelpCQflbwPXukY8ekE8eSdX7uSpXxPav861eo08QW8vXn5igArnM4VGzevNnusZeXl4oWLapx48bd9s5QAADAMwQGSvfeay6pLl2Sjk6Yo9LjBiso9rhklfS5FDM1XLGjJ6ry8EfdVi8Az+JwqFi6dKkz6gAAAB4mKHqOqo/sZN7TNo0w6wmFvdZJk/+YrSe+f1ShoW4qEIDH4K7VAAAgveRkafDgdIFCkrxktrVfPETVKidr+vQMVwOQh2TpTEXdunVlyeQ95zalnfoTAADkDCtXSseP3/RpLxkqrWOqcm6lundvoalTpUmTpKpVs7FGAB4jS6EiKnWKTwAAkDudOpWp1YY+eUp/zZOWLZNq15Zefll6/XUpIMC15QHwLFkKFSNHjnR2HQAAwJOUKJGp1R5+roR2jZUGDJB+/VV66y1p5kzpk0+ktm1dXCMAj8GYCgAAkF7TplJ4+M2n2LZYzEksmjZV2bLS//4nzZljvuTQIaldO+nxx6UTJ7K1agBu4nCoSE5O1vvvv69GjRqpePHiCg0NtVsAAEAO5O0tTZxo/veNwSL18YQJ5nr/3/TII9KuXdLQoWbz7NlSlSrmZpgPF8jdHA4Vo0eP1gcffKAnnnhCsbGxGjp0qB599FF5eXlp1KhRTigRAAC4xaOPmsmgVCn79vBws/3R9PNUBAVJ48aZk+fdfbcUHy8NGSI1aiT99Vf2lA0g+zkcKmbMmKEvvvhCL774onx8fNSlSxd9+eWXGjFihP78809n1AgAANzl0Uelw4eVFB2tDUOHKik62ry+KYNAkVadOtKaNdKnn0oFC0qbN0v33CP17y9dvJgdhQPITg6HipiYGNWsWVOSVKBAAcXGxkqSHnroIf3666+Obh4AALibt7eM5s11olkzGc2b2y55uh0vL+m556Q9e6Snnzbnspg0ybwkatYs5rYAchOHQ0V4eLhO/f9t58qXL69FixZJktavXy8/Pz9HNw8AAHK4YsWk6dOlJUukypWl06elrl2lyEjp77/dXR0AZ3A4VDzyyCNasmSJJGngwIH6z3/+o4oVK6pbt2565plnHC4QAADkDg88IG3dKo0ZI/n5SYsXSzVqSKNGSVevurs6AI7I0jwVab3zzju2/37iiSdUpkwZrVmzRhUrVlSHDh0c3TwAAMhF/Pykf/9b6tLFHF/x++/S6NHSjBnmpVGtWrm7QgBZ4fCZiqs3/Gnhnnvu0dChQwkUAADgpsqXlxYskH74wZxnb/9+83Korl2lmBh3VwfgTjkcKsLCwtS9e3dFR0crJSXFGTUBAIA8wGIxJ8jbs0caNMgc2D1rljmQe9IkKTnZ3RUCyCyHQ8XXX3+thIQEdezYUaVKldKQIUO0YcMGZ9QGAADygOBgc4K8v/6SGjSQYmPNS6MaN5Y2bXJ3dQAywykDtX/88UedPn1ab7/9tnbt2qV77rlHlSpV0htvvOGMGgEAQB5Qv77055/Sxx+bQWP9eqlhQ2nwYCkuzt3VAbgVh0NFqqCgIPXs2VOLFi3Stm3blD9/fo0ePdpZmwcAAHmAt7d5lmLPHunJJ6WUFOnDD81Lon78kbktAE/ltFBx9epV/fDDD4qKilK9evV0/vx5DRs2zFmbBwAAeUiJEub4it9/Nwd1nzolde4stWsnHTjg7uoA3MjhUPH777+re/fuKlasmPr27atixYpp0aJFOnLkiN3tZgEAAO5UZKS0Y4c0cqSUL5+0cKE5t8Vbb0mJie6uDkAqp4ypuHLliqZPn66YmBh99tlnatasmTNqAwAAkL+/OUHe9u3Sgw+aE+X9+99SnTrSsmVuLg6AJCeEitOnT+uHH35Qx44d5evr69C2xo4dq4YNGyooKEhhYWGKiorS3r177db5/PPP1aJFCwUHB8tisejixYsOvScAAMgZKlWSoqPNifLCwsxxF/ffL3XrJp054+7qgLzN4VARFBTkjDokScuXL1f//v31559/Kjo6WlarVZGRkbp8+bJtnYSEBLVp00avvfaa094XAADkDBaLOUHenj1S377m42++MQdyf/65ObAbQPbzcXcBaS1cuNDu8bRp0xQWFqaNGzfaLqkaMmSIJGkZ5zsBAMizChUyJ8jr0UN67jlpyxbz32nTpMmTpdq13VwgkMc47e5PrhAbGytJCg0NdXMlAADAEzVqZM5nMWGCVKCAtHatOd/FSy9J8fHurg7IOzzqTEVaKSkpGjJkiJo0aaIaNWpkeTuJiYlKTHN7iLj/nz3HarXKarU6XGdWpL6vu94/t6JfXYN+dQ361TXoV9fx9L7t10/q2FF68UVvzZnjpXHjpO+/NzR+fLIeftiQxeLuCjPm6f2aU9GvmeesPrIYhmdOI9O3b18tWLBAq1atUnh4eLrnly1bpvvvv18XLlxQwYIFb7qdUaNGZTgJ38yZMxUYGOjMkgEAgAfYsCFMX3xRS6dP55ckNWx4Sn36bFdY2BU3VwZ4noSEBHXt2lWxsbEKDg7O8nYcDhWXL1/WO++8oyVLlujMmTNKuWGE1MGDB+94mwMGDNC8efO0YsUKlStXLsN1MhsqMjpTERERoXPnzjnUcY6wWq2Kjo5Wq1atHL5jFq6jX12DfnUN+tU16FfXyWl9m5AgjR3rpQ8+8JLValFgoKHXX0/RkCEp8qTyc1q/5hT0a+bFxcWpSJEiDocKhy9/6t27t5YvX66nn35aJUqUkMWB84uGYWjgwIGaO3euli1bdtNAcSf8/Pzk5+eXrt3X19ftHzJPqCE3ol9dg351DfrVNehX18kpfRsSIr3zjnm72b59pRUrLHr9dW/NnOmtyZOlpk3dXaG9nNKvOQ39envO6h+HQ8WCBQv066+/qkmTJg4X079/f82cOVPz5s1TUFCQYmJiJEkhISEKCAiQJMXExCgmJkb79++XJG3fvl1BQUEqXbo0A7oBAICdatXMCfKmTzcHb+/cKTVrJj3zjPTuu1KRIu6uEMgdHL77U6FChZz2ZX7y5MmKjY1VixYtVKJECdvy/fff29b59NNPVbduXfXp00eS1KxZM9WtW1fz5893Sg0AACB3sVik7t3NuS3+/+uDpkwx57aYOpW5LQBncDhUjBkzRiNGjFBCQoLDxRiGkeHSo0cP2zqjRo267ToAAAA3KlzYnCBv1SqpZk3pn3/MMxYtWphnMABkncOXP40bN04HDhxQsWLFVLZs2XTXZW3atMnRtwAAAHCaJk2kjRuliROlkSOllSulOnWkF1+U/vMfKX9+d1cI5DwOh4qoqCgnlAEAAJB9fH3NMRadO0uDBknz5pljLL77Tvr4Y+mhh9xdIZCzOBwqRo4c6Yw6AAAAsl3p0tLPP0vz50sDB0pHjkgdOkiPPGKeyYiIcHeFQM7g8JiKVBs3btS3336rb7/9Vps3b3bWZgEAAFzu4YelXbukl1+WfHykuXOlqlWlDz6QkpLcXR3g+RwOFWfOnNEDDzyghg0batCgQRo0aJDq16+vBx98UGfPnnVGjQAAAC6XP795CdSmTea4i8uXzXEWDRpIf/7p7uoAz+ZwqBg4cKAuXbqknTt36vz58zp//rx27NihuLg4DRo0yBk1AgAAZJuaNaUVK6Qvv5RCQ6WtW6V775Wef166cMHd1QGeyeFQsXDhQk2aNElVq1a1tVWrVk2ffPKJFixY4OjmAQAAsp2Xl9Srlzm3RY8ekmFIn30mVa4sffut+RjAdQ6HipSUlAyn9/b19VUKs8kAAIAcrGhRc4K8ZcvMMRZnz0pPPy09+KAZOACYHA4VDzzwgAYPHqyTJ0/a2k6cOKEXXnhBDz74oKObBwAAcLvmzaUtW6SxY6WAAGnpUqlWLXNeiytX3F0d4H4Oh4qPP/5YcXFxKlu2rMqXL6/y5curXLlyiouL00cffeSMGgEAANwuXz7p1VfN2bfbtZOsVunNN6UaNaSFC91dHXKk5GTzNNisWea/ycnurijLHJ6nIiIiQps2bdLixYu15//PA1atWlUtW7Z0uDgAAABPU66c9Msv5m1nBw2SDh6U2raVHn9cmjBBKlnS3RUiR5gzRxo8WDp+/HpbeLg5Qcqjj7qvrixyyjwVFotFrVq10sCBAzVw4EACBQAAyNUsFvN73+7d0gsvmAO7f/xRqlJF+vDDHP0HZ2SHOXOkTp3sA4UknThhts+Z4566HJClMxUffvihnn32Wfn7++vDDz+85brcVhYAAORWQUHmBHlPPy317SutW2f+8fnrr6VPP5UaNnR3hfA4ycnmhySjW4gZhplYhwyROnaUvL2zvbysylKoGD9+vJ566in5+/tr/PjxN13PYrEQKgAAQK5Xt660Zo30xRfmuItNm6S775b69ZPeeksKCXF3hfAYK1emP0ORlmFIx46Z67VokW1lOSpLoeLQoUMZ/jcAAEBe5eUlPfecFBUlvfSSOZ/FJ59IP/0kjR8vPfGE+Udo5HGnTjl3PQ/h8JiKN954QwkJCenar1y5ojfeeMPRzQMAAOQoxYpJ33wjLVkiVaokxcRIXbpIrVtLf//t7urgdiVKOHc9D+FwqBg9erTi4+PTtSckJGj06NGObh4AACBHeuABads26Y03JD8/KTpaqlnTfJyY6O7q4DZNm5p3ebrZaSuLRYqIMNfLQRwOFYZhyJJBp2zdulWhoaGObh4AACDH8vMzJ8jbsUOKjDTDxMiR5sR5S5a4uzq4hbe3edtYKX2wSH08YUKOGqQtORAqChUqpNDQUFksFlWqVEmhoaG2JSQkRK1atVLnzp2dWSsAAECOVKGCOUHed99JxYtL+/ZJLVtK3bp568IFP3eXh+z26KPS7NlSqVL27eHhZnsOnKciy5PfTZgwQYZh6JlnntHo0aMVkua2Bvny5VPZsmXVuHFjpxQJAACQ01ks5mDtNm3Msxcffyx9952X5s9/UPHxXurbN8f9cRqOePRR87axK1eag7JLlDAvecqhH4Ish4ru3btLksqVK6d7771Xvr6+TisKAAAgtwoJMSfI69ZNeu65FG3a5KuBA83B3Z9+at6eFnmEt3eOum3srWQ5VKRq3ry5kpOTNXv2bO3evVuSVK1aNXXs2FE+Pg5vHgAAIFdq0EBavTpZgwbt0Hff1dRff1nUoIE0cKA5mDs42N0VApnn8EDtnTt3qlKlSurevbvmzp2ruXPnqnv37qpYsaJ27NjhjBoBAAByJW9vqX37Q9q+PUlPPCGlpJhjeKtWNS+tz2jSZcATORwqevfurerVq+v48ePatGmTNm3apGPHjqlWrVp69tlnnVEjAABArlaypDmIe+FCqXx56eRJ6fHHpfbtpYMH3V0dcHsOh4otW7Zo7NixKlSokK2tUKFCeuutt7R582ZHNw8AAJBntG4tbd9uDuTOl09asECqXl16+23p2jV3VwfcnMOholKlSjp9+nS69jNnzqhChQp3tK2xY8eqYcOGCgoKUlhYmKKiorR37167da5evar+/furcOHCKlCggB577LEM3x8AACAnCggwx1Rs22ZOoHf1qvT661KdOtLy5e6uDsiYw6Fi7NixGjRokGbPnq3jx4/r+PHjmj17toYMGaJ3331XcXFxtuV2li9frv79++vPP/9UdHS0rFarIiMjdfnyZds6L7zwgv73v//pxx9/1PLly3Xy5Ek9mgPv5QsAAHArlStLixdL334rhYVJu3ebNwrq0UM6e9bd1QH2HL4900MPPSRJ6ty5s21mbeP/RxV16NDB9thisSg5OfmW21q4cKHd42nTpiksLEwbN25Us2bNFBsbq6+++kozZ87UAw88IEmaOnWqqlatqj///FP33HOPo7sDAADgMSwW6amnpHbtpNdekz77TPr6a2n+fOm//5WeeUbycvhPxIDjHA4VS5cudUYdGYqNjZUkhYaGSpI2btwoq9Wqli1b2tapUqWKSpcurbVr1xIqAABArlSokDR5stS9u/T889LWrVKfPtKUKebcFrVqubtC5HVOmafCFVJSUjRkyBA1adJENWrUkCTFxMQoX758KliwoN26xYoVU0xMTIbbSUxMVGJiou1x6mVYVqtVVqvVJbXfTur7uuv9cyv61TXoV9egX12DfnUd+tY17rRf69eX1q6VJk3y0qhRXlq71qJ69QwNHpyif/87RQUKuLLanIPPa+Y5q48shuH4HZAvXryor776yjb5XfXq1fXMM88oJCQky9vs27evFixYoFWrVik8PFySNHPmTPXs2dMuJEhSo0aNdP/99+vdd99Nt51Ro0Zp9OjR6dpnzpypwMDALNcHAADgTufO+eurr2pq7dqSkqQiRRLUp8923X13xn9oBTKSkJCgrl27KjY2VsEOzLjocKjYsGGDWrdurYCAADVq1EiStH79el25ckWLFi1SvXr17nibAwYM0Lx587RixQqVK1fO1v7HH3/owQcf1IULF+zOVpQpU0ZDhgzRCy+8kG5bGZ2piIiI0Llz5xzqOEdYrVZFR0erVatW8vX1dUsNuRH96hr0q2vQr65Bv7oOfesazujX336zaMgQbx0+bI5tbd8+RRMmJKtMGWdWmrPwec28uLg4FSlSxOFQ4fDlTy+88IIefvhhffHFF/LxMTeXlJSk3r17a8iQIVqxYkWmt2UYhgYOHKi5c+dq2bJldoFCkurXry9fX18tWbJEjz32mCRp7969Onr0qBo3bpzhNv38/OTn55eu3dfX1+0fMk+oITeiX12DfnUN+tU16FfXoW9dw5F+7dhRatVKevNN6b33pF9/9dLSpV4aOVJ64QUpLx8uPq+356z+cfh+ARs2bNArr7xiCxSS5OPjo5dfflkbNmy4o231799f3377rWbOnKmgoCDFxMQoJiZGV65ckSSFhISoV69eGjp0qJYuXaqNGzeqZ8+eaty4MYO0AQBAnhUYaE6Qt2WL1LSplJAgvfKKVK+etGqVu6tDXuBwqAgODtbRo0fTtR87dkxBQUF3tK3JkycrNjZWLVq0UIkSJWzL999/b1tn/Pjxeuihh/TYY4+pWbNmKl68uObMmePobgAAAOR41aubE+RNnSoVLizt2GGGjN69pX/+cXd1yM0cDhVPPPGEevXqpe+//17Hjh3TsWPH9N1336l3797q0qXLHW3LMIwMlx49etjW8ff31yeffKLz58/r8uXLmjNnjooXL+7obgAAAOQKFos5Qd7evWaYkKSvvjIn05s2TXL8Fj1Aeg6PqXj//fdlsVjUrVs3JSUlSTKvzerbt6/eeecdhwsEAADAnStcWPriCzNgPP+8edaiZ0/zLMbkyVK1au6uELmJw2cq8uXLp4kTJ+rChQvasmWLtmzZovPnz2v8+PEZDpAGAABA9mnSRNq0yZyBOzBQWrFCql3bnKE7IcHd1SG3cNrE7oGBgapZs6Zq1qzJ/A8AAAAexNdXGjZM2rVLevhhKSlJGjvWHIPx66/urg65gdNCBQAAADxbmTLSvHnSzz9LERHS4cPSQw9Jjz0mHT/u7uqQkxEqAAAA8piOHc2zFsOGSd7e0pw5UtWq0vjx5lkM4E4RKgAAAPKgAgXMcRabNkn33ivFx0tDh0oNGkjr1rm7OuQ0hAoAAIA8rFYtaeVK805RhQpJW7dKjRtLfftKFy64uzrkFIQKAACAPM7Ly5zTYu9eqXt3cy6LTz+VqlSRvv2WuS1we4QKAAAASJKKFjUnyFu61AwUZ85ITz8tPfigGTiAmyFUAAAAwE6LFuZlUG+9Jfn7myGjVi1pxAjpyhV3VwdPRKgAAABAOvnymRPk7dwptW0rXbsmjRkj1awp/f67u6uDpyFUAAAA4KbuusucIG/2bKlkSenAAalNG+nJJ6WTJ91dHTwFoQIAAAC3ZLGYE+Tt2SMNGWIO7P7+e3Nui48/lpKT3V0h3I1QAQAAgEwJCjInyNuwQWrUSIqLkwYOlO6+22xD3kWoAAAAwB2pW1das0aaPFkKCZE2bjRDxsCBUmysu6uDOxAqAAAAcMe8vaXnnzcviXrqKXMui48/Nm9F+/33zG2R1xAqAAAAkGXFi5sT5C1eLFWsKMXEmIO427SR9u93d3XILoQKAAAAOOzBB6Vt26TRoyU/P2nRIqlGDfM2tImJ7q4OrkaoAAAAgFP4+5sT5G3fLrVqZYaJESPMifP++MPd1cGVCBUAAABwqooVzQnyZs0yL4/at888k/Gvf0mnT7u7OrgCoQIAAABOZ7GYYyt275b69zcfz5ghVa4sffqplJLi7grhTIQKAAAAuEzBguZdodatk+rVM28527evdO+90pYt7q4OzkKoAAAAgMs1bCj99Zf04YfmJHrr1kn160tDh0qXLrm7OjiKUAEAAIBs4e1tTpC3Z4/UubN5CdT48VLVqtJPPzG3RU5GqAAAAEC2KlnSnCBv4ULprrukEyekTp2khx6SDh1yd3XICo8KFStWrFCHDh1UsmRJWSwW/fzzz3bPnz59Wj169FDJkiUVGBioNm3a6O+//3ZPsQAAAHBI69bSjh3Sf/4j+fpKv/0mVa8ujR0rXbvm7upwJzwqVFy+fFm1a9fWJ598ku45wzAUFRWlgwcPat68edq8ebPKlCmjli1b6vLly26oFgAAAI4KCJDeeMOcOO/++6UrV6TXXpPq1JFWrHB3dcgsjwoVbdu21ZtvvqlHHnkk3XN///23/vzzT02ePFkNGzZU5cqVNXnyZF25ckWzZs1yQ7UAAABwlipVpCVLpG++kYoWNW9F27y51LOndPasu6vD7XhUqLiVxP+f393f39/W5uXlJT8/P61atcpdZQEAAMBJLBZzgry9e6XnnjPbpk0zA8dXXzG3hSfzcXcBmVWlShWVLl1aw4cP12effab8+fNr/PjxOn78uE6dOnXT1yUmJtoCiSTFxcVJkqxWq6xWq8vrzkjq+7rr/XMr+tU16FfXoF9dg351HfrWNejXjBUoIH30kfTUUxb17++t7dst6t1bmjIlRR99lKyaNW/9evo185zVRxbD8Mybd1ksFs2dO1dRUVG2to0bN6pXr17aunWrvL291bJlS3l5eckwDC1YsCDD7YwaNUqjR49O1z5z5kwFBga6qnwAAAA4QXKyRb/8cpdmzaqiq1d95O2dog4dDujJJ/fK3z/Z3eXleAkJCeratatiY2MVHByc5e3kqFCRKjY2VteuXVPRokV19913q0GDBhkO7pYyPlMRERGhc+fOOdRxjrBarYqOjlarVq3k6+vrlhpyI/rVNehX16BfXYN+dR361jXo18w7dkx68UVv/fyzefV+6dKGxo9PVocO6b/K0q+ZFxcXpyJFijgcKnLM5U9phYSESDIHb2/YsEFjxoy56bp+fn7y8/NL1+7r6+v2D5kn1JAb0a+uQb+6Bv3qGvSr69C3rkG/3t5dd0lz50q//CINGCAdOWLRY4/5qGNHc5bu0qXTv4Z+vT1n9Y9HDdSOj4/Xli1btGXLFknSoUOHtGXLFh09elSS9OOPP2rZsmW228q2atVKUVFRioyMdGPVAAAAyC4PPSTt3Cm9+qrk4yPNm2fOyP3eexJDKNzHo0LFhg0bVLduXdWtW1eSNHToUNWtW1cjRoyQJJ06dUpPP/20qlSpokGDBunpp5/mdrIAAAB5TP785gR5W7ZITZtKCQnSyy9L9epJq1e7u7q8yaMuf2rRooVuNcRj0KBBGjRoUDZWBAAAAE9Vvbq0fLn09dfSSy+Zs3Pfd5/0zDPeatGCy56yk0edqQAAAADuhMUi9ehhzm3Rq5fZNmWKlwYMeFDTp1vkmbckyn0IFQAAAMjxCheWvvxSWrlSqlbNUFycn3r39tH995uzc8O1CBUAAADINe67T1q/Pknduu1UQICh5cul2rWl1183x17ANQgVAAAAyFV8faVHH92vrVuT9NBD5l2h3n5bqlFD+u03d1eXOxEqAAAAkCuVLSvNn2/ObxEeLh06JLVvLz3+uHTihLury10IFQAAAMi1LBYpKsocV/Hii5K3tzR7tlSlijRhgpSU5O4KcwdCBQAAAHK9AgWk99+XNm2SGjeW4uOlF16QGjaU1q1zd3U5H6ECAAAAeUatWtKqVdLnn0uFCpkT6DVuLPXrJ1286O7qci5CBQAAAPIULy+pTx9pzx6pWzfJMKTJk6XKlaUZM8TcFllAqAAAAECeFBZmzsa9dKk5xuLMGelf/5JatjQn00PmESoAAACQp7VoIW3dKr31luTvL/3xh3mZ1MiR0tWr7q4uZyBUAAAAIM/Ll0967TVp506pTRvp2jXpjTekmjWlRYvcXZ3nI1QAAAAA/++uu8wJ8n78USpZUtq/X2rdWurSRTp1yt3VeS5CBQAAAJCGxSJ16mTObTF4sDmw+7vvzHEXn3wiJSe7u0LPQ6gAAAAAMhAcbE6Qt369OZ9FXJw0YIB0zz3Sxo3urs6zECoAAACAW6hXT1q71jxLERwsbdggNWokDRokxca6uzrPQKgAAAAAbsPb25wgb+9eqWtXKSVF+ugjqWpV6YcfmNuCUAEAAABkUvHi5gR50dFSxYrm4O0nnpDatpUOHHB3de5DqAAAAADuUMuW0rZt0qhR5u1of/9dql5dGjNGSkx0d3XZj1ABAAAAZIG/vzlB3vbtZshITJRGjJBq1zYn0MtLCBUAAACAAypVMifImzVLKlbMHHfx4IPS009Lp0+7u7rsQagAAAAAHGSxSE8+Ke3ZI/Xvbz7+9ltzbovPPjMHdudmhAoAAADASQoWlD7+WFq3TqpbV7p4UXr+ealJE2nrVndX5zqECgAAAMDJGjaU/vpLmjhRCgqS/vxTql9fevFF6dIld1fnfIQKAAAAwAV8fMwJ8nbvlh5/XEpOlj74QKpWTZo7N3fNbeFRoWLFihXq0KGDSpYsKYvFop9//tnu+fj4eA0YMEDh4eEKCAhQtWrV9Omnn7qnWAAAACATSpUyJ8j77TepXDnp+HHp0Uelhx+WDh92d3XO4VGh4vLly6pdu7Y++eSTDJ8fOnSoFi5cqG+//Va7d+/WkCFDNGDAAM2fPz+bKwUAAADuTNu20s6d0uuvS76+0i+/mGct3nlHunbN3dU5xqNCRdu2bfXmm2/qkUceyfD5NWvWqHv37mrRooXKli2rZ599VrVr19Zff/2VzZUCAAAAdy4gQHrzTXPQdosW0pUr0vDh0v/+5+7KHONRoeJ27r33Xs2fP18nTpyQYRhaunSp9u3bp8jISHeXBgAAAGRa1armBHnTp0tPPGFeDpWT+bi7gDvx0Ucf6dlnn1V4eLh8fHzk5eWlL774Qs2aNbvpaxITE5WYZq70uLg4SZLVapXVanV5zRlJfV93vX9uRb+6Bv3qGvSra9CvrkPfugb96ho5qV+ffNJckpLc8/7O6iOLYXjmuHOLxaK5c+cqKirK1vb+++/riy++0Pvvv68yZcpoxYoVGj58uObOnauWLVtmuJ1Ro0Zp9OjR6dpnzpypwMBAV5UPAAAAeLyEhAR17dpVsbGxCg4OzvJ2ckyouHLlikJCQjR37ly1b9/etl7v3r11/PhxLVy4MMPtZHSmIiIiQufOnXOo4xxhtVoVHR2tVq1aydfX1y015Eb0q2vQr65Bv7oG/eo69K1r0K+uQb9mXlxcnIoUKeJwqMgxlz+lXq7k5WU/DMTb21spt5j33M/PT35+funafX193f4h84QaciP61TXoV9egX12DfnUd+tY16FfXoF9vz1n941GhIj4+Xvv377c9PnTokLZs2aLQ0FCVLl1azZs317BhwxQQEKAyZcpo+fLlmj59uj744AM3Vg0AAADkbR4VKjZs2KD777/f9njo0KGSpO7du2vatGn67rvvNHz4cD311FM6f/68ypQpo7feekvPP/+8u0oGAAAA8jyPChUtWrTQrYZ4FC9eXFOnTs3GigAAAADcTo6apwIAAACA5/GoMxXZIfVMSOp8Fe5gtVqVkJCguLg4Bg85Ef3qGvSra9CvrkG/ug596xr0q2vQr5mX+p3Y0RvC5rlQcenSJUlSRESEmysBAAAAPMOlS5cUEhKS5dd77DwVrpKSkqKTJ08qKChIFovFLTWkzpVx7Ngxt82VkRvRr65Bv7oG/eoa9Kvr0LeuQb+6Bv2aeYZh6NKlSypZsmS6qRvuRJ47U+Hl5aXw8HB3lyFJCg4O5oPuAvSra9CvrkG/ugb96jr0rWvQr65Bv2aOI2coUjFQGwAAAIBDCBUAAAAAHEKocAM/Pz+NHDlSfn5+7i4lV6FfXYN+dQ361TXoV9ehb12DfnUN+jX75bmB2gAAAACcizMVAAAAABxCqAAAAADgEEIFAAAAAIcQKgAAAAA4hFDhBGPHjlXDhg0VFBSksLAwRUVFae/evXbrPPfccypfvrwCAgJUtGhRdezYUXv27LFb5+jRo2rfvr0CAwMVFhamYcOGKSkpKTt3xeM4q28HDRqk+vXry8/PT3Xq1MnGPfBMzujXrVu3qkuXLoqIiFBAQICqVq2qiRMnZveueBRn9Os///yjNm3aqGTJkvLz81NERIQGDBiguLi47N4dj+GsnwOp/vnnH4WHh8tisejixYvZsAeeyVn9arFY0i3fffdddu6Kx3HmZ3batGmqVauW/P39FRYWpv79+2fXbngcZ/TrtGnTMvzMWiwWnTlzJrt3KVchVDjB8uXL1b9/f/3555+Kjo6W1WpVZGSkLl++bFunfv36mjp1qnbv3q3ff/9dhmEoMjJSycnJkqTk5GS1b99e165d05o1a/T1119r2rRpGjFihLt2yyM4o29TPfPMM3riiSeyexc8kjP6dePGjQoLC9O3336rnTt36vXXX9fw4cP18ccfu2u33M4Z/erl5aWOHTtq/vz52rdvn6ZNm6bFixfr+eefd9duuZ0zfw5IUq9evVSrVq3s3AWP5Mx+nTp1qk6dOmVboqKisnlvPIuz+vaDDz7Q66+/rldffVU7d+7U4sWL1bp1a3fskkdwRr8+8cQTdp/VU6dOqXXr1mrevLnCwsLctWu5gwGnO3PmjCHJWL58+U3X2bp1qyHJ2L9/v2EYhvHbb78ZXl5eRkxMjG2dyZMnG8HBwUZiYqLLa84pstK3aY0cOdKoXbu2CyvMmRzt11T9+vUz7r//fleUmCM5q18nTpxohIeHu6LEHMmRfp00aZLRvHlzY8mSJYYk48KFCy6uNufIar9KMubOnZsNFeZcWenb8+fPGwEBAcbixYuzq8wcxxk/Y8+cOWP4+voa06dPd1WZeQZnKlwgNjZWkhQaGprh85cvX9bUqVNVrlw5RURESJLWrl2rmjVrqlixYrb1Wrdurbi4OO3cudP1RecQWelb3J6z+jU2Nvam28iLnNGvJ0+e1Jw5c9S8eXOX1ZnTZLVfd+3apTfeeEPTp0+Xlxe//m7kyOe1f//+KlKkiBo1aqQpU6bIYAosO1np2+joaKWkpOjEiROqWrWqwsPD1blzZx07dizb6vZ0zvgZO336dAUGBqpTp04uqzPPcHeqyW2Sk5ON9u3bG02aNEn33CeffGLkz5/fkGRUrlzZLjX36dPHiIyMtFv/8uXLhiTjt99+c3ndOUFW+zYtzlSk54x+NQzDWL16teHj42P8/vvvriw3x3C0X5988kkjICDAkGR06NDBuHLlSnaU7fGy2q9Xr141atWqZXzzzTeGYRjG0qVLOVORhiOf1zfeeMNYtWqVsWnTJuOdd94x/Pz8jIkTJ2ZX6R4vq307duxYw9fX16hcubKxcOFCY+3atcaDDz5oVK5cmSsYDOf97qpatarRt29fV5aaZxAqnOz55583ypQpYxw7dizdcxcvXjT27dtnLF++3OjQoYNRr1492xcFQsXtZbVv0yJUpOeMft2+fbtRpEgRY8yYMdlRco7gaL+eOnXK2L17tzFv3jyjWrVq/NL7f1nt1xdeeMF44oknbOsSKuw54+dAqv/85z9crpdGVvv2rbfeMiTZ/aHmzJkzhpeXl7Fw4cJsq99TOeMzu2bNGkOSsWHDhuwoOdcjVDhR//79jfDwcOPgwYO3XTcxMdEIDAw0Zs6caRiG+UP4xi+7Bw8eNCQZmzZtckW5OYojfZsWocKeM/p1586dRlhYmPHaa6+5qswcx1mf11QrV640JBknT550Zpk5jiP9Wrt2bcPLy8vw9vY2vL29DS8vL0OS4e3tbYwYMcLVpXs0Z39ef/nlF0OScfXqVWeWmSM50rdTpkwxJKX70hwWFmZ8/vnnLqk3p3DWZ/aZZ54x6tSp44oS8ySf7L3YKncyDEMDBw7U3LlztWzZMpUrVy5TrzEMQ4mJiZKkxo0b66233tKZM2dsdx+Ijo5WcHCwqlWr5tL6PZkz+hbpOatfd+7cqQceeEDdu3fXW2+95cqScwRXfV5TUlIkKc9+pp3Rrz/99JOuXLlie379+vV65plntHLlSpUvX95ltXsyV31et2zZokKFCsnPz8+Z5eYozujbJk2aSJL27t2r8PBwSdL58+d17tw5lSlTxnXFezBnfmbj4+P1ww8/aOzYsa4qN+/JvvySe/Xt29cICQkxli1bZpw6dcq2JCQkGIZhGAcOHDDefvttY8OGDcaRI0eM1atXGx06dDBCQ0ON06dPG4ZhGElJSUaNGjWMyMhIY8uWLcbChQuNokWLGsOHD3fnrrmdM/rWMAzj77//NjZv3mw899xzRqVKlYzNmzcbmzdvzrPXpTqjX7dv324ULVrU+Ne//mW3jTNnzrhz19zKGf3666+/GlOmTDG2b99uHDp0yPjll1+MqlWrZnjdcF7hrJ8DaXH5k3P6df78+cYXX3xhbN++3fj777+NSZMmGYGBgXn+7I+zPrMdO3Y0qlevbqxevdrYvn278dBDDxnVqlUzrl275q5dcytn/iz48ssvDX9//zz9M8DZCBVOICnDZerUqYZhGMaJEyeMtm3bGmFhYYavr68RHh5udO3a1dizZ4/ddg4fPmy0bdvWCAgIMIoUKWK8+OKLhtVqdcMeeQ5n9W3z5s0z3M6hQ4eyf6c8gDP6deTIkRluo0yZMu7ZKQ/gjH79448/jMaNGxshISGGv7+/UbFiReOVV17J07/4nPVzIC1ChXP6dcGCBUadOnWMAgUKGPnz5zdq165tfPrpp0ZycrKb9sozOOszGxsbazzzzDNGwYIFjdDQUOORRx4xjh496oY98gzO/FnQuHFjo2vXrtm8B7mbxTC47xsAAACArONG3QAAAAAcQqgAAAAA4BBCBQAAAACHECoAAAAAOIRQAQAAAMAhhAoAAAAADiFUAAAAAHAIoQIAAACAQwgVAAAAABxCqAAAAADgEEIFAAAAAIcQKgAAAAA4hFABAAAAwCGECgAAAAAOIVQAAAAAcAihAgAAAIBDCBUAAAAAHEKoAAAAAOAQt4aKsWPHqmHDhgoKClJYWJiioqK0d+/eW75m2rRpslgsdou/v382VQwAAADgRm4NFcuXL1f//v31559/Kjo6WlarVZGRkbp8+fItXxccHKxTp07ZliNHjmRTxQAAAABu5OPON1+4cKHd42nTpiksLEwbN25Us2bNbvo6i8Wi4sWLu7o8AAAAAJng1lBxo9jYWElSaGjoLdeLj49XmTJllJKSonr16untt99W9erVM/UeKSkpOnnypIKCgmSxWByuGQAAAMipDMPQpUuXVLJkSXl5Zf0iJothGIYT68qylJQUPfzww7p48aJWrVp10/XWrl2rv//+W7Vq1VJsbKzef/99rVixQjt37lR4eHi69RMTE5WYmGh7fOLECVWrVs0l+wAAAADkRMeOHcvwu3RmeUyo6Nu3rxYsWKBVq1bd0Q5ZrVZVrVpVXbp00ZgxY9I9P2rUKI0ePTpd+5dffqnAwECHagYAAABysoSEBPXu3VsXL15USEhIlrfjEaFiwIABmjdvnlasWKFy5crd8esff/xx+fj4aNasWemeu/FMRVxcnCIiInTu3DkFBwc7VDfMUBcdHa1WrVrJ19fX3eXgBhwfz8Wx8WwcH8/FsfFsHB/PdbNjExcXpyJFiig2Ntah78ZuHVNhGIYGDhyouXPnatmyZVkKFMnJydq+fbvatWuX4fN+fn7y8/NL1+7r68uH3YnoT8/G8fFcHBvPxvHxXBwbz8bx8Vw3HhtnHSe3hor+/ftr5syZmjdvnoKCghQTEyNJCgkJUUBAgCSpW7duKlWqlMaOHStJeuONN3TPPfeoQoUKunjxot577z0dOXJEvXv3dtt+AAAAAHmZW0PF5MmTJUktWrSwa586dap69OghSTp69KjdSPQLFy6oT58+iomJUaFChVS/fn2tWbOGwdcAAACAm7j98qfbWbZsmd3j8ePHa/z48S6qCAAAAMCdcuuM2gAAAAByPkIFAAAAAIcQKgAAAAA4hFABAAAAwCFuHagNAEBeV/bVX91dQo7i523ov42kGqN+V2Kyxd3l4AYcn6w5/E57d5fgMM5UAAAAAHAIoQIAAACAQwgVAAAAABxCqAAAAADgEEIFAAAAAIcQKgAAAAA4hFABAAAAwCGECgAAAAAOIVQAAAAAcAihAgAAAIBDCBUAAAAAHEKoAAAAAOAQQgUAAAAAhxAqAAAAADiEUAEAAADAIYQKAAAAAA4hVAAAAABwCKECAAAAgEMIFQAAAAAcQqgAAAAA4BBCBQAAAACHECoAAAAAOIRQAQAAAMAhhAoAAAAADiFUAAAAAHAIoQIAAACAQwgVAAAAABxCqAAAAADgELeGirFjx6phw4YKCgpSWFiYoqKitHfv3tu+7scff1SVKlXk7++vmjVr6rfffsuGagEAAABkxK2hYvny5erfv7/+/PNPRUdHy2q1KjIyUpcvX77pa9asWaMuXbqoV69e2rx5s6KiohQVFaUdO3ZkY+UAAAAAUvm4880XLlxo93jatGkKCwvTxo0b1axZswxfM3HiRLVp00bDhg2TJI0ZM0bR0dH6+OOP9emnn7q8ZgAAAAD23BoqbhQbGytJCg0Nvek6a9eu1dChQ+3aWrdurZ9//jnD9RMTE5WYmGh7HBcXJ0myWq2yWq0OVozUPqQvPRPHx3NxbDxbdh4fP2/D5e+Rm/h5GXb/wrNwfLImO37W3OznmrPe22IYhkcc9ZSUFD388MO6ePGiVq1addP18uXLp6+//lpdunSxtU2aNEmjR4/W6dOn060/atQojR49Ol37zJkzFRgY6JziAQAAgBwoISFBXbt2VWxsrIKDg7O8HY85U9G/f3/t2LHjloEiK4YPH253ZiMuLk4RERGKjIx0qONgslqtio6OVqtWreTr6+vucnADjo/n4th4tuw8PjVG/e7S7ec2fl6GxjRI0X82eCkxxeLucnADjk/W7BjV2uXvcbOfa6lX8TjKI0LFgAED9Msvv2jFihUKDw+/5brFixdPd0bi9OnTKl68eIbr+/n5yc/PL127r68vv8idiP70bBwfz8Wx8WzZcXwSk/nilRWJKRb6zoNxfO5Mdv4euPHnmrPe2613fzIMQwMGDNDcuXP1xx9/qFy5crd9TePGjbVkyRK7tujoaDVu3NhVZQIAAAC4Bbeeqejfv79mzpypefPmKSgoSDExMZKkkJAQBQQESJK6deumUqVKaezYsZKkwYMHq3nz5ho3bpzat2+v7777Ths2bNDnn3/utv0AAAAA8jK3nqmYPHmyYmNj1aJFC5UoUcK2fP/997Z1jh49qlOnTtke33vvvZo5c6Y+//xz1a5dW7Nnz9bPP/+sGjVquGMXAAAAgDzPrWcqMnPjqWXLlqVre/zxx/X444+7oCIAAAAAd8qtZyoAAAAA5HyECgAAAAAOIVQAAAAAcAihAgAAAIBDCBUAAAAAHEKoAAAAAOAQQgUAAAAAhxAqAAAAADiEUAEAAADAIYQKAAAAAA4hVAAAAABwCKECAAAAgEMIFQAAAAAcQqgAAAAA4BBCBQAAAACHECoAAAAAOIRQAQAAAMAhhAoAAAAADiFUAAAAAHAIoQIAAACAQwgVAAAAABxCqAAAAADgEEIFAAAAAIcQKgAAAAA4hFABAAAAwCGECgAAAAAOIVQAAAAAcAihAgAAAIBDCBUAAAAAHEKoAAAAAOAQQgUAAAAAhxAqAAAAADjEraFixYoV6tChg0qWLCmLxaKff/75lusvW7ZMFosl3RITE5M9BQMAAABIx62h4vLly6pdu7Y++eSTO3rd3r17derUKdsSFhbmogoBAAAA3I6PO9+8bdu2atu27R2/LiwsTAULFnR+QQAAAADuWI4cU1GnTh2VKFFCrVq10urVq91dDgAAAJCnZflMRVJSkpYtW6YDBw6oa9euCgoK0smTJxUcHKwCBQo4s0abEiVK6NNPP1WDBg2UmJioL7/8Ui1atNC6detUr169DF+TmJioxMRE2+O4uDhJktVqldVqdUmdeUlqH9KXnonj47k4Np4tO4+Pn7fh8vfITfy8DLt/4Vk4PlmTHT9rbvZzzVnvbTEM446P+pEjR9SmTRsdPXpUiYmJ2rdvn+666y4NHjxYiYmJ+vTTT++8EItFc+fOVVRU1B29rnnz5ipdurS++eabDJ8fNWqURo8ena595syZCgwMvOM6AQAAgNwiISFBXbt2VWxsrIKDg7O8nSydqRg8eLAaNGigrVu3qnDhwrb2Rx55RH369MlyMVnRqFEjrVq16qbPDx8+XEOHDrU9jouLU0REhCIjIx3qOJisVquio6PVqlUr+fr6ursc3IDj47k4Np4tO49PjVG/u3T7uY2fl6ExDVL0nw1eSkyxuLsc3IDjkzU7RrV2+Xvc7Oda6lU8jspSqFi5cqXWrFmjfPny2bWXLVtWJ06ccEphmbVlyxaVKFHips/7+fnJz88vXbuvry+/yJ2I/vRsHB/PxbHxbNlxfBKT+eKVFYkpFvrOg3F87kx2/h648eeas947S6EiJSVFycnJ6dqPHz+uoKCgTG8nPj5e+/fvtz0+dOiQtmzZotDQUJUuXVrDhw/XiRMnNH36dEnShAkTVK5cOVWvXl1Xr17Vl19+qT/++EOLFi3Kym4AAAAAcIIs3f0pMjJSEyZMsD22WCyKj4/XyJEj1a5du0xvZ8OGDapbt67q1q0rSRo6dKjq1q2rESNGSJJOnTqlo0eP2ta/du2aXnzxRdWsWVPNmzfX1q1btXjxYj344INZ2Q0AAAAATpClMxXjxo1T69atVa1aNV29elVdu3bV33//rSJFimjWrFmZ3k6LFi10q3Hi06ZNs3v88ssv6+WXX85KyQAAAABcJEuhIjw8XFu3btX333+vrVu3Kj4+Xr169dJTTz2lgIAAZ9cIAAAAwINleZ4KHx8fPfXUU3rqqaecWQ8AAACAHCZLYyrGjh2rKVOmpGufMmWK3n33XYeLAgAAAJBzZClUfPbZZ6pSpUq69urVq2dp4jsAAAAAOVeWQkVMTEyGc0MULVpUp06dcrgoAAAAADlHlkJFRESEVq9ena599erVKlmypMNFAQAAAMg5sjRQu0+fPhoyZIisVqseeOABSdKSJUv08ssv68UXX3RqgQAAAAA8W5ZCxbBhw/TPP/+oX79+unbtmiTJ399fr7zyioYPH+7UAgEAAAB4tiyFCovFonfffVf/+c9/tHv3bgUEBKhixYry8/Nzdn0AAAAAPFyW56mQpAIFCqhhw4bOqgUAAABADpSlUHH58mW98847WrJkic6cOaOUlBS75w8ePOiU4gAAAAB4viyFit69e2v58uV6+umnVaJECVksFmfXBQAAACCHyFKoWLBggX799Vc1adLE2fUAAAAAyGGyNE9FoUKFFBoa6uxaAAAAAORAWQoVY8aM0YgRI5SQkODsegAAAADkMFm6/GncuHE6cOCAihUrprJly8rX19fu+U2bNjmlOAAAAACeL0uhIioqysllAAAAAMipshQqRo4c6ew6AAAAAORQWRpTIUkXL17Ul19+qeHDh+v8+fOSzMueTpw44bTiAAAAAHi+LJ2p2LZtm1q2bKmQkBAdPnxYffr0UWhoqObMmaOjR49q+vTpzq4TAAAAgIfK0pmKoUOHqkePHvr777/l7+9va2/Xrp1WrFjhtOIAAAAAeL4shYr169frueeeS9deqlQpxcTEOFwUAAAAgJwjS6HCz89PcXFx6dr37dunokWLOlwUAAAAgJwjS6Hi4Ycf1htvvCGr1SpJslgsOnr0qF555RU99thjTi0QAAAAgGfLUqgYN26c4uPjFRYWpitXrqh58+aqUKGCgoKC9NZbbzm7RgAAAAAeLEt3fwoJCVF0dLRWr16trVu3Kj4+XvXq1VPLli2dXR8AAAAAD3fHocJqtSogIEBbtmxRkyZN1KRJE1fUBQAAACCHuOPLn3x9fVW6dGklJye7oh4AAAAAOUyWxlS8/vrreu2112wzaQMAAADIu7I0puLjjz/W/v37VbJkSZUpU0b58+e3e37Tpk1OKQ4AAACA58tSqIiKinJyGQAAAAByqiyFipEjRzq7DgAAAAA5VJbGVEjSxYsX9eWXX2r48OG2sRWbNm3SiRMnnFYcAAAAAM+XpVCxbds2VapUSe+++67ef/99Xbx4UZI0Z84cDR8+PNPbWbFihTp06KCSJUvKYrHo559/vu1rli1bpnr16snPz08VKlTQtGnTsrILAAAAAJwkS6Fi6NCh6tGjh/7++2/5+/vb2tu1a6cVK1ZkejuXL19W7dq19cknn2Rq/UOHDql9+/a6//77tWXLFg0ZMkS9e/fW77//fsf7AAAAAMA5sjSmYv369frss8/StZcqVUoxMTGZ3k7btm3Vtm3bTK//6aefqly5cho3bpwkqWrVqlq1apXGjx+v1q1bZ3o7AAAAAJwnS6HCz89PcXFx6dr37dunokWLOlzUzaxdu1YtW7a0a2vdurWGDBly09ckJiYqMTHR9ji1bqvVKqvV6pI685LUPqQvPRPHx3NxbDxbdh4fP2/D5e+Rm/h5GXb/wrNwfLImO37W3OznmrPeO0uh4uGHH9Ybb7yhH374QZJksVh09OhRvfLKK3rsscecUlhGYmJiVKxYMbu2YsWKKS4uTleuXFFAQEC614wdO1ajR49O175o0SIFBga6rNa8Jjo62t0l4BY4Pp6LY+PZsuP4/LeRy98iVxrTIMXdJeAWOD535rfffsu297rx51pCQoJTtpulUDFu3Dh16tRJYWFhunLlipo3b66YmBg1btxYb731llMKc5bhw4dr6NChtsdxcXGKiIhQZGSkgoOD3VhZ7mC1WhUdHa1WrVrJ19fX3eXgBhwfz8Wx8WzZeXxqjGJc4J3w8zI0pkGK/rPBS4kpFneXgxtwfLJmxyjXX8Z/s59rGV19lBVZChUhISGKjo7W6tWrtXXrVsXHx6tevXrpLk1ytuLFi+v06dN2badPn1ZwcHCGZykk81ItPz+/dO2+vr78Inci+tOzcXw8F8fGs2XH8UlM5otXViSmWOg7D8bxuTPZ+Xvgxp9rznrvTIeK0NBQ7du3T0WKFNEzzzyjiRMnqkmTJmrSpIlTCsmMxo0bpzs9FB0drcaNG2dbDQAAAADsZfqWsteuXbOdHvn666919epVh988Pj5eW7Zs0ZYtWySZt4zdsmWLjh49Ksm8dKlbt2629Z9//nkdPHhQL7/8svbs2aNJkybphx9+0AsvvOBwLQAAAACyJtNnKho3bqyoqCjVr19fhmFo0KBBN73kaMqUKZna5oYNG3T//ffbHqeOfejevbumTZumU6dO2QKGJJUrV06//vqrXnjhBU2cOFHh4eH68ssvuZ0sAAAA4EaZDhXffvutxo8frwMHDkiSYmNjHT5b0aJFCxnGzW85ltFs2S1atNDmzZsdel8AAAAAzpPpUFGsWDG98847kswzBt98840KFy7sssIAAAAA5AyZHlMRGhqqc+fOSZLuv/9+5cuXz2VFAQAAAMg53DpQGwAAAEDO59aB2gAAAAByviwN1LZYLE4ZqA0AAAAg52OgNgAAAACHZDpUpHXo0CFn1wEAAAAgh8p0qPjwww/17LPPyt/fXx9++OEt1x00aJDDhQEAAADIGTIdKsaPH6+nnnpK/v7+Gj9+/E3Xs1gshAoAAAAgD8l0qEh7yROXPwEAAABIlelQMXTo0EytZ7FYNG7cuCwXBAAAACBnyXSo2Lx5s93jTZs2KSkpSZUrV5Yk7du3T97e3qpfv75zKwQAAADg0TIdKpYuXWr77w8++EBBQUH6+uuvVahQIUnShQsX1LNnTzVt2tT5VQIAAADwWF5ZedG4ceM0duxYW6CQpEKFCunNN9/k0icAAAAgj8lSqIiLi9PZs2fTtZ89e1aXLl1yuCgAAAAAOUeWQsUjjzyinj17as6cOTp+/LiOHz+un376Sb169dKjjz7q7BoBAAAAeLAszaj96aef6qWXXlLXrl1ltVrNDfn4qFevXnrvvfecWiAAAAAAz5alUBEYGKhJkybpvffe04EDByRJ5cuXV/78+Z1aHAAAAADPl6VQkSp//vyqVauWs2oBAAAAkANlaUwFAAAAAKQiVAAAAABwCKECAAAAgEMIFQAAAAAcQqgAAAAA4BBCBQAAAACHECoAAAAAOIRQAQAAAMAhhAoAAAAADiFUAAAAAHAIoQIAAACAQwgVAAAAABxCqAAAAADgEI8IFZ988onKli0rf39/3X333frrr79uuu60adNksVjsFn9//2ysFgAAAEBabg8V33//vYYOHaqRI0dq06ZNql27tlq3bq0zZ87c9DXBwcE6deqUbTly5Eg2VgwAAAAgLbeHig8++EB9+vRRz549Va1aNX366acKDAzUlClTbvoai8Wi4sWL25ZixYplY8UAAAAA0nJrqLh27Zo2btyoli1b2tq8vLzUsmVLrV279qavi4+PV5kyZRQREaGOHTtq586d2VEuAAAAgAz4uPPNz507p+Tk5HRnGooVK6Y9e/Zk+JrKlStrypQpqlWrlmJjY/X+++/r3nvv1c6dOxUeHp5u/cTERCUmJtoex8XFSZKsVqusVqsT9yZvSu1D+tIzcXw8F8fGs2Xn8fHzNlz+HrmJn5dh9y88C8cna7LjZ83Nfq45670thmG47aifPHlSpUqV0po1a9S4cWNb+8svv6zly5dr3bp1t92G1WpV1apV1aVLF40ZMybd86NGjdLo0aPTtc+cOVOBgYGO7QAAAACQgyUkJKhr166KjY1VcHBwlrfj1jMVRYoUkbe3t06fPm3Xfvr0aRUvXjxT2/D19VXdunW1f//+DJ8fPny4hg4danscFxeniIgIRUZGOtRxMFmtVkVHR6tVq1by9fV1dzm4AcfHc3FsPFt2Hp8ao3536fZzGz8vQ2MapOg/G7yUmGJxdzm4Accna3aMau3y97jZz7XUq3gc5dZQkS9fPtWvX19LlixRVFSUJCklJUVLlizRgAEDMrWN5ORkbd++Xe3atcvweT8/P/n5+aVr9/X15Re5E9Gfno3j47k4Np4tO45PYjJfvLIiMcVC33kwjs+dyc7fAzf+XHPWe7s1VEjS0KFD1b17dzVo0ECNGjXShAkTdPnyZfXs2VOS1K1bN5UqVUpjx46VJL3xxhu65557VKFCBV28eFHvvfeejhw5ot69e7tzNwAAAIA8y+2h4oknntDZs2c1YsQIxcTEqE6dOlq4cKFt8PbRo0fl5XX9JlUXLlxQnz59FBMTo0KFCql+/fpas2aNqlWr5q5dAAAAAPI0t4cKSRowYMBNL3datmyZ3ePx48dr/Pjx2VAVAAAAgMxw++R3AAAAAHI2QgUAAAAAhxAqAAAAADiEUAEAAADAIYQKAAAAAA4hVAAAAABwCKECAAAAgEMIFQAAAAAcQqgAAAAA4BBCBQAAAACHECoAAAAAOIRQAQAAAMAhhAoAAAAADiFUAAAAAHAIoQIAAACAQwgVAAAAABxCqAAAAADgEEIFAAAAAIcQKgAAAAA4hFABAAAAwCGECgAAAAAOIVQAAAAAcAihAgAAAIBDCBUAAAAAHEKoAAAAAOAQQgUAAAAAhxAqAAAAADiEUAEAAADAIYQKAAAAAA4hVAAAAABwCKECAAAAgEMIFQAAAAAcQqgAAAAA4BCPCBWffPKJypYtK39/f919993666+/brn+jz/+qCpVqsjf3181a9bUb7/9lk2VAgAAALiR20PF999/r6FDh2rkyJHatGmTateurdatW+vMmTMZrr9mzRp16dJFvXr10ubNmxUVFaWoqCjt2LEjmysHAAAAIHlAqPjggw/Up08f9ezZU9WqVdOnn36qwMBATZkyJcP1J06cqDZt2mjYsGGqWrWqxowZo3r16unjjz/O5soBAAAASJKPO9/82rVr2rhxo4YPH25r8/LyUsuWLbV27doMX7N27VoNHTrUrq1169b6+eefM1w/MTFRiYmJtsdxcXGSJKvVKqvV6uAeILUP6UvPxPHxXBwbz5adx8fP23D5e+Qmfl6G3b/wLByfrMmOnzU3+7nmrPd2a6g4d+6ckpOTVaxYMbv2YsWKac+ePRm+JiYmJsP1Y2JiMlx/7NixGj16dLr2RYsWKTAwMIuV40bR0dHuLgG3wPHxXBwbz5Ydx+e/jVz+FrnSmAYp7i4Bt8DxuTPZOT74xp9rCQkJTtmuW0NFdhg+fLjdmY24uDhFREQoMjJSwcHBbqwsd7BarYqOjlarVq3k6+vr7nJylBqjfnf5e/h5GRrTIEX/2eClxBSLy98Pmcex8WwcH8+VG4/NjlGt3V2C0/C9wHPd7NikXsXjKLeGiiJFisjb21unT5+2az99+rSKFy+e4WuKFy9+R+v7+fnJz88vXbuvry8fdieiP+9cYnL2/TJMTLFk6/sh8zg2no3j47ly07HJjb8/+V7guW48Ns46Tm4dqJ0vXz7Vr19fS5YssbWlpKRoyZIlaty4cYavady4sd36knka52brAwAAAHAtt1/+NHToUHXv3l0NGjRQo0aNNGHCBF2+fFk9e/aUJHXr1k2lSpXS2LFjJUmDBw9W8+bNNW7cOLVv317fffedNmzYoM8//9yduwEAAADkWW4PFU888YTOnj2rESNGKCYmRnXq1NHChQttg7GPHj0qL6/rJ1TuvfdezZw5U//+97/12muvqWLFivr5559Vo0YNd+0CAAAAkKe5PVRI0oABAzRgwIAMn1u2bFm6tscff1yPP/64i6sCAAAAkBlun/wOAAAAQM5GqAAAAADgEEIFAAAAAIcQKgAAAAA4xCMGagN50eF32rv8PaxWq3777TftGNWaSYg8DMfGs3F8PBfHBvBMnKkAAAAA4BBCBQAAAACHECoAAAAAOIRQAQAAAMAhhAoAAAAADiFUAAAAAHAIoQIAAACAQwgVAAAAABxCqAAAAADgkDw3o7ZhGJKkuLg4N1eSO1itViUkJCguLo6ZTT0Qx8dzcWw8G8fHc3FsPBvHx3Pd7NikfidO/Y6cVXkuVFy6dEmSFBER4eZKAAAAAM9w6dIlhYSEZPn1FsPRWJLDpKSk6OTJkwoKCpLFYnF3OTleXFycIiL+r517C4mq78IA/ri1V8dwTMsdxKiFF4OZCkVGeBEpOImJRVAUUZBEmRhEBB0ooTBvIgg6QGTagYIggi7CTpSUWVmR6aiVmSVaWZlaap5a78X7OV+mZc3ee5xmnh/MRbP/bda/pxnXcu+ZcDQ2NsJsNo91OfQD5uO+mI17Yz7ui9m4N+bjvn6WjYjg8+fPmDJlChTF+U9GeN2VCkVRYLFYxroMj2M2m/nm4caYj/tiNu6N+bgvZuPemI/7GikbLVcoBvGD2kREREREpAmHCiIiIiIi0oRDBWni7++P3Nxc+Pv7j3UpNALm476YjXtjPu6L2bg35uO+jM7G6z6oTURERERE+uKVCiIiIiIi0oRDBRERERERacKhgoiIiIiINOFQQUREREREmnCooGHy8/Mxe/ZsBAUFQVVVLFq0CE+fPnUcb21tRU5ODqxWK0wmEyIiIrBx40a0t7cPO1dRURHi4uIQEBAAVVWRnZ3tyq14JL3yKS8vR3JyMiZMmICQkBDYbDZUVFS4ejseZbRsAGDdunWIioqCyWRCWFgYMjIyUFtbO2TN69evkZaWhsDAQKiqii1btqC/v9+VW/FIeuRTUVGB5cuXIzw8HCaTCdHR0Thw4ICrt+Jx9HrtDPr48SMsFgt8fHzQ1tbmgh14Lj2zYU+gP73y0aMn4FBBw5SUlCA7Oxt3797F1atX0dfXh5SUFHR2dgIAmpub0dzcjH379qGqqgpFRUUoLi5GZmbmkPPs378fO3bswNatW2G323Ht2jXYbLax2JJH0SOfL1++YMGCBYiIiMC9e/dw+/ZtBAUFwWazoa+vb6y29tcbLRsAmDVrFgoLC1FTU4PLly9DRJCSkoKBgQEAwMDAANLS0tDb24s7d+7gxIkTKCoqwq5du8ZqWx5Dj3wePnwIVVVx+vRp2O127NixA9u2bcPBgwfHalseQY9svpeZmYm4uDhXbsFj6ZUNewJj6JGPbj2BEI2ipaVFAEhJSclP15w7d07++ecf6evrExGR1tZWMZlMcu3aNVeV6bWcyae8vFwAyOvXrx1rnjx5IgDk+fPnhtfsLX4nm4qKCgEgdXV1IiJy6dIlURRF3r5961hz5MgRMZvN0tPTY3jN3sSZfEayYcMGmT9/vhElei0t2Rw+fFjmzZsn169fFwDy6dMng6v1Ls5kw57AdZzJR6+egFcqaFSDt82Ehob+co3ZbIafnx8A4OrVq/j27RuampoQHR0Ni8WCpUuXorGx0SU1exNn8rFarZg4cSIKCgrQ29uL7u5uFBQUIDo6GlOnTnVF2V5htGw6OztRWFiIadOmITw8HABQVlaG2NhYTJ482bHOZrOho6MDdrvd+KK9iDP5/Ow8v3r90Z9zNpvq6mrs3r0bJ0+ehKKwxTGCM9mwJ3AdZ/LRrSdwfhYibzAwMCBpaWmSmJj40zXv37+XiIgI2b59u+O5/Px8GTdunFitVikuLpaysjJJTk4Wq9XK37bqyNl8REQqKyslKipKFEURRVHEarVKQ0OD0SV7jV9lc+jQIRk/frwAEKvVOuQ3rWvXrpWUlJQh6zs7OwWAXLp0yfC6vYWz+fyotLRU/Pz85PLly0aW61Wczebr168SFxcnp06dEhGRGzdu8EqFzpzNhj2Ba2h5X9OjJ+BQQb+0fv16iYyMlMbGxhGPt7e3S0JCgixYsEB6e3sdz+fl5QmAIT9oW1paRFEUKS4uNrxub+FsPl1dXZKQkCCrVq2S+/fvS1lZmSxZskRiYmKkq6vLVeV7tF9l09bWJs+ePZOSkhJJT0+XmTNnSnd3t4hwqHAVZ/P5XmVlpUyaNEn27NnjipK9hrPZbNq0SZYtW+ZYy6FCf85mw57ANZzNR6+egEMF/VR2drZYLBapr68f8XhHR4fMnTtXkpOTh/3APX78uAAY9h9bVVU5evSoYTV7Ey35HDt2TFRVlYGBAcdzPT09EhgYKGfPnjW0bm8wWjbfG/x3P3PmjIiI7Ny5U+Lj44esqa+vFwDy6NEjI8r1OlryGWS320VV1WFXAEkbLdnEx8eLoiji6+srvr6+oiiKABBfX1/ZtWuX0aV7PC3ZsCcwnpZ89OoJ/P74Zi3yeCKCnJwcXLhwATdv3sS0adOGreno6IDNZoO/vz8uXryIgICAIccTExMBAE+fPoXFYgHw31edfvjwAZGRkcZvwoPpkU9XVxcURYGPj4/jucE/f/v2zfA9eKrfyWakvyMi6OnpAQDMnTsXeXl5aGlpgaqqAP67H9lsNmP69OmG1u/p9MgHAOx2O5KSkrB69Wrk5eUZWbLX0COb8+fPo7u723G8vLwca9aswa1btxAVFWVY7Z5Oj2zYExhHj3x06wl+e/wgr5GVlSXBwcFy8+ZNefPmjeMxeAmsvb1d5syZI7GxsVJXVzdkTX9/v+M8GRkZEhMTI6WlpVJZWSkLFy6U6dOnD7kNh/6cHvnU1NSIv7+/ZGVlSXV1tVRVVcnKlSslODhYmpubx3J7f7XRsnnx4oXs3btXHjx4IK9evZLS0lJJT0+X0NBQeffunYiI9Pf3y4wZMyQlJUUeP34sxcXFEhYWJtu2bRvLrXkEPfKprKyUsLAwWbly5ZBztLS0jOXW/np6ZPMj3v6kD72yYU9gDD3y0asn4FBBwwAY8VFYWCgi/3+jHunx8uVLx3na29tlzZo1MmHCBAkNDZXFixcP+boyco5e+Vy5ckUSExMlODhYQkJCJCkpScrKysZmUx5itGyampokNTVVVFWVcePGicVikRUrVkhtbe2Q8zQ0NEhqaqqYTCaZNGmSbN682fF1wOQ8PfLJzc0d8RyRkZFjsykPoddr53scKvShVzbsCYyhVz569AQ+/yuIiIiIiIjIKfwSZyIiIiIi0oRDBRERERERacKhgoiIiIiINOFQQUREREREmnCoICIiIiIiTThUEBERERGRJhwqiIiIiIhIEw4VRERERESkCYcKIiIiIiLShEMFERERERFpwqGCiIiIiIg04VBBRERERESa/AsqfWRE1mVt8AAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plot_calibration_results_carr(params_carr_put, \"put\")"
      ],
      "metadata": {
        "id": "uTj8zBtpC7Sb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "eb279bfa-25d7-47d7-ca62-302025cc0d9b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-2-f3815e05660f>:801: SettingWithCopyWarning: \n",
            "A value is trying to be set on a copy of a slice from a DataFrame.\n",
            "Try using .loc[row_indexer,col_indexer] = value instead\n",
            "\n",
            "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
            "  options[model_column] = B96_jump_calculate_model_values_carr(p0, is_call=is_call)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 2 Axes>"
            ],
            "image/png": 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vverYsaNuu+22HP98du7cWREREZo9e7bmzZunlJQUPfjgg9mOK1++vB577DF99913OnDggMqUKZOtlwdAwULxAaBAq169un7//XenGY62bt2abQXy4OBgSdm/kObm4YcfVmRkpEaNGpXtUY9Lly6pf//+MgxDL7zwQrb3fvjhh7Lb7Y7X06ZN0+XLlxUbG+vYVrx48WuK5aabblJkZKTef/99p16YhQsXateuXerates13c+VrpyyVjLXFsmc+etqPT0tW7ZUhw4dHD85FQRXM2jQII0ZM0aTJk3K9ZjMnhvjLzNOvfXWW9mOLV68uKTsbRoaGqrw8HCtWrXKaft7772Xp3hzcrV2Cw8PV2xsrP7zn/9o9uzZ6ty5s9MMVK5w7NgxxcTEyMfHR4sXL851TZB69eqpdu3a+vDDD516fKZNmyabzZZt7Y682Lp1q0aMGKHSpUtr6NChju2+vr7Z2u2dd97JscfJz89PvXv31pdffqmZM2eqfv36TrPPpaenZ3vELjIyUhUqVLjqZxSA92OqXQAF2oABA/Tmm2+qU6dOGjhwoE6cOKH3339f9erVcxoIHhQUpLp16+qLL75QzZo1FRYWphtvvFE33nhjjuctU6aMvv76a3Xt2lVNmjTRoEGDVLduXR07dkwzZ87U3r17NWXKlBwXGExLS1P79u3Vs2dP7d69W++9955uu+02de/e3XFM06ZNNW3aNL344ou64YYbFBkZ6fS8eyZ/f3+9+uqr6t+/v9q0aaPevXs7ptqtUqVKtulKr8WgQYN05swZ3X777YqKitKff/6pd955R40aNVKdOnXyfL5rVbly5auurSKZhUPr1q312muvyW63q2LFilqyZIljXZcrNW3aVJL07LPP6v7775e/v7+6deum4sWLa9CgQXrllVc0aNAg3XTTTVq1apX27Nlz3ffQtGlTLV26VG+++aYqVKigqlWr6pZbbnHs79u3r+OL/YQJE675vJ999pn+/PNPpaSkSJJWrVqlF198UZL04IMPOnq4OnfurP379+tf//qXfvrpJ/3000+Oc5QtW1YdO3Z0vH799dfVvXt3xcTE6P7779eOHTs0depUDRo06JrbefXq1bp06ZLS09N1+vRprVmzRj/88INKliypefPmqVy5co5j77jjDn322WcqWbKk6tatq3Xr1mnp0qW5Tovdt29fvf3221q+fLljyudMFy5cUFRUlO699141bNhQJUqU0NKlS7Vhw4arFq8ACgAPz7YFADnKaQrW3PznP/8xqlWrZhQrVsxo1KiRsXjx4mxT7RqGYaxdu9Zo2rSpUaxYsWuezvTAgQPG4MGDjUqVKhn+/v5GeHi40b17d2P16tW5xrxy5UpjyJAhRunSpY0SJUoYDzzwgHH69GmnY48dO2Z07drVCAkJMSQ5pt3961S7mb744gujcePGRkBAgBEWFmY88MADjumGM/Xr188oXrx4trj+OmXs119/bcTExBiRkZFGsWLFjEqVKhkPP/ywkZCQ8Lf5yIvMqXavJqd2Pnz4sHHXXXcZpUqVMkqWLGncd999xtGjR3NsswkTJhgVK1Y0fHx8nKbdTUlJMQYOHGiULFnSCAkJMXr27GmcOHEi16l2T548mS22nKba/f33343WrVsbQUFBhqRs0+6mpqYapUuXNkqWLOk0NfLfadOmjSEpx58rPwu5HXPlZ+hK8+bNMxo1amQEBAQYUVFRxnPPPec0DXRuMj+HmT/+/v5GRESE0bp1a+Oll14yTpw4ke09Z8+eNfr372+Eh4cbJUqUMDp16mT8/vvvRuXKlXOcntgwzCmnfXx8sn2WU1NTjVGjRhkNGzY0QkJCjOLFixsNGzY03nvvvb+NHYB3sxlGLqspAQDyJHMxwA0bNmRb3A1Fw+XLl1WhQgV169ZNn3zyiafD8XqNGzdWWFiYli1b5ulQALgJYz4AAHCR7777TidPnszzYPyiaOPGjdqyZQu5AooYxnwAAHCdfv75Z23btk0TJkxQ48aN1aZNG0+H5LV27NihX3/9VZMmTVL58uUtmREMgPei5wMAgOs0bdo0Pfroo4qMjNSsWbM8HY5X+/rrr9W/f3/Z7XZ9/vnnCgwM9HRIANyIMR8AAAAA3IKeDwAAAABuQfEBAAAAwC0YcJ6DjIwMHT16VCEhIbLZbJ4OBwAAAPA4wzB04cIFVahQQT4++evDoPjIwdGjRxUdHe3pMAAAAACvc+jQIUVFReXrvRQfOQgJCZFkJjY0NNQjMdjtdi1ZskQxMTHy9/f3SAyFEXm1Bnm1Drm1Bnm1Bnm1Drm1BnnNm8TEREVHRzu+K+cHxUcOMh+1Cg0N9WjxERwcrNDQUP4wuBB5tQZ5tQ65tQZ5tQZ5tQ65tQZ5zZ/rGZbAgHMAAAAAbkHxAQAAAMAtKD4AAAAAuAVjPq5Denq67Ha7Jee22+3y8/PTpUuXlJ6ebsk1Cjp/f3/5+vp6OgwAAABcI4qPfDAMQ8eOHdO5c+csvUa5cuV06NAh1hq5ilKlSqlcuXLkCAAAoACg+MiHzMIjMjJSwcHBlnzxzcjIUFJSkkqUKJHvRVwKM8MwlJKSohMnTkiSypcv7+GIAAAA8HcoPvIoPT3dUXiUKVPGsutkZGQoLS1NgYGBFB+5CAoKkiSdOHFCkZGRPIIFAAAKPcOQCvIDH3yrzaPMMR7BwcEejgRSVjtYNfYGAADAky5elBYtkoYPl2rUkObP93RE14eej3xijIF3oB0AAEBhs3+/tHChtGCBtHy5WYBkWrBAuuMOz8V2vSg+AAAAAA9KTZVWrcoqOHbvdt4fFSV16WL+3H67Z2J0FYoPWKJKlSoaMWKERowY4elQAAAAvM6ff2YVGz/+KCUnZ+3z85Nuu02KjTULjnr1CvY4jytRfMArtW3bVo0aNdJbb73l6VAAAACuW1qatGaNWWwsWCD99pvz/vLlzUIjNlbq0EEqWdIzcVqN4gMulZaWpmLFink6DAAAAI87ciSrdyMuTkpKytrn6ys1b571OFWDBoWnd+NqmO2qCGnbtq0ef/xxjRgxQqVLl1bZsmX10UcfKTk5Wf3791dISIhuuOEGLVy4UJI5rfDAgQNVtWpVBQUFqVatWpoyZYrTOR966CH16NFDL730kipUqKBatWrleO2PP/5YpUqV0rJlyyRJO3bsUGxsrEqUKKGyZcvqwQcf1KlTpxznXLlypaZMmSKbzSabzaaDBw9alxgAAAAXsNvNsRvPPCM1bGiO1Rg8WJo3zyw8ypaV+vWTvvhCOnlSWr1aGj3aPLYoFB4SPR8uYRhSSoprz5mRYT775+sr5bbMR3Bw3j+on376qf71r3/pl19+0RdffKFHH31U8+bN01133aV///vfmjx5sh588EHFx8fL399fUVFR+uqrr1SmTBmtXbtWQ4YMUfny5dWzZ0/HOZctW6bQ0FDFxcXleM3XXntNr732mpYsWaKbb75Z586d0+23365BgwZp8uTJunjxop5++mn17NlTP/74o6ZMmaI9e/boxhtv1Pjx4yVJERERebtRAAAAN0hIMKfCXbBAWrJESkzM2mezSbfemjV2o3Hj3L/XFRUUHy6QkiKVKOHqs/pIKnXVI5KSpOLF83bWhg0b6rnnnpMkjR49Wq+88orCw8M1ePBgSdILL7ygadOmadu2bbr11ls1btw4x3urVq2qdevW6csvv3QqPooXL66PP/44x8etnn76aX322WdauXKl6tWrJ0maOnWqGjdurJdfftlx3PTp0xUdHa09e/aoZs2aKlasmIKDg1WuXLm83SAAAICFLl+Wfv4563GqzZud94eHS507m8VGTIxk4ZrUBRLFRxHToEEDx//7+vqqTJkyql+/vmNb2bJlJZmrhkvSu+++q+nTpys+Pl4XL15UWlqaGjVq5HTO+vXr51h4TJo0ScnJydq4caOqVavm2L5161YtX75cJXKo2Pbt26eaNWte1z0CAAC40okTzr0bZ89m7bPZpJtuyhq70bSp+eQKckbx4QLBwc4DiFwhIyNDiYmJCg0NlU8u/XP5WWTd39/f6bXNZnPalrloX0ZGhubOnaunnnpKkyZNUvPmzRUSEqLXX39dP//8s9M5iufS/dKqVSvNnz9fX375pZ555hnH9qSkJHXr1k2vvvpqtveUL18+7zcFAADgQunp0saNWTNTbdzovL90aalTJ7PY6NRJioz0TJwFkUeLj1WrVun111/Xr7/+qoSEBM2bN089evRw7D9+/LiefvppLVmyROfOnVPr1q31zjvvqEaNGrmec+bMmerfv7/TtoCAAF26dMmq25DNlvfHn/5ORob5wS9e3HPPBq5Zs0YtWrTQY4895ti2b9++a37/zTffrGHDhqlz587y8/PTU089JUlq0qSJvvnmG1WpUkV+fjl/BIsVK6b09PTruwEAAIBrdOqUtHix+TjVokXS6dPO+5s0yZoK9+abzbU4kHceHfKSnJyshg0b6t133822zzAM9ejRQ/v379f333+vzZs3q3LlyurQoYOSr1yFJQehoaFKSEhw/Pz5559W3UKhVqNGDW3cuFGLFy/Wnj179Pzzz2vDhg15OkeLFi20YMECjRs3zrFmx9ChQ3XmzBn17t1bGzZs0L59+7R48WL179/fUXBUqVJFP//8sw4ePKhTp04pIyPD1bcHAACKsIwM6ddfbfrii5pq1cpXkZHSP/4hzZ5tFh4lS0r33SfNmGEOKv/1V2nCBKlFCwqP6+HR1MXGxio2NjbHfX/88YfWr1+vHTt2OAYqT5s2TeXKldPnn3+uQYMG5Xpem83GQGUXePjhh7V582b16tVLNptNvXv31mOPPeaYivda3XbbbZo/f766dOkiX19fPf7441qzZo2efvppxcTEKDU1VZUrV1bnzp0dj5g99dRT6tevn+rWrauLFy/qwIEDqlKligV3CQAAioqzZ80xGwsWmL0bJ074Sarj2N+wYdbMVM2bU2RYwWtTmpqaKkkKDAx0bPPx8VFAQIB++umnqxYfSUlJqly5sjIyMtSkSRO9/PLLjgKmKFuxYkW2bTmtn2EYhuP/Z8yYoRkzZjjtnzhxouP/Z86cmeO1/nre1q1bK+mKgTE1atTQt99+m2usNWvW1Lp163LdDwAA8HcMQ9qyJWtmqnXrzB6PTCEhhurVS1D//pHq2tVPFSt6LNQiw2uLj9q1a6tSpUoaPXq0PvjgAxUvXlyTJ0/W4cOHlZCQkOv7atWqpenTp6tBgwY6f/683njjDbVo0UI7d+5UVFRUju9JTU11FDuSlPi/CZrtdrvsdrvTsXa7XYZhKCMjw9JHgTILgMxrIWcZGRkyDEN2u12+1zC1RGZ7/rVdcX3Iq3XIrTXIqzXIq3XI7bU7f15autSmxYt9tHixTQkJzoui1a1rqHPnDMXGGrrppjStXLlBHTt2lL+/IdJ7da74/NmMK/+Z24NsNlu2Aee//vqrBg4cqK1bt8rX11cdOnSQj4+PDMO45kd/7Ha76tSpo969e2vChAk5HjN27Fin9SwyzZkzR8F/mVLKz89P5cqVU3R0dI7Ty8K90tLSdOjQIR07dkyXL1/2dDgAAMDNDEP6889QbdoUqV9/Lavffw9TenrWsObAwMtq0OCkmjY9riZNTigi4qIHoy3YUlJS1KdPH50/f16hoaH5OofX9nxIUtOmTbVlyxadP39eaWlpioiI0C233KKbbrrpms/h7++vxo0ba+/evbkeM3r0aI0cOdLxOjExUdHR0YqJicmW2EuXLunQoUMqUaKE0yNhrmYYhi5cuKCQkBDH9LfI7tKlSwoKClLr1q2vqT3sdrvi4uL+9y8c/n97PK4NebUOubUGebUGebUOuXV24YK0bJnZu7FokU1Hjjh/V6pVy1BsbIY6dTJ0222GAgLCJYVLcn4Mn7zmTeKVy7fnk1cXH5lKliwpyRyEvnHjxlx7MHKSnp6u7du3q0uXLrkeExAQoICAgGzb/f39s30Q09PTZbPZ5OPjk+v6G66Q+ahV5rWQMx8fH8daJXn5pZHX43FtyKt1yK01yKs1yKt1impuDUPatcsct7FwobR6tZwekQoKkm6/PWsq3KpVbZKufaW/oprXvHJFjjxafCQlJTn1SBw4cEBbtmxRWFiYKlWqpK+++koRERGqVKmStm/frieeeEI9evRQTEyM4z19+/ZVxYoVHYOgx48fr1tvvVU33HCDzp07p9dff11//vnnVQeoAwAAwLskJ0s//phVcPx15YQaNbJmpmrd2ixA4P08Wnxs3LhR7dq1c7zOfPSpX79+mjlzphISEjRy5EgdP35c5cuXV9++ffX88887nSM+Pt6pZ+Ds2bMaPHiwjh07ptKlS6tp06Zau3at6tat656bAgAAQJ4ZhrRnT9bMVCtXSmlpWfsDAqR27cyCIzbWLD5Q8Hi0+Gjbtq2uNt59+PDhGj58+FXP8dfpYydPnqzJkye7IjwAAABYKCVFWrEiq+DYv995f9WqZs9Gly5S27bSX+YBQgFUIMZ8AAAAoHDYuzer2FixQrp0KWtfsWLmI1SZBUfNmhLz7hQuFB8AAACwzKVL5iNUmQXHH384769UKWvsxu23SyVKeCZOuAfFB1yubdu2atSokd56661rOn7mzJkaMWKEzp07Z2lcAADAPQ4ezBoo/uOP5uNVmfz8pFatsmamqluX3o2ihOLDk9LTzbniEhKk8uXNP4nXsEo3AACAN0lNlX76Kavg2LXLeX+FClmPUrVvL+VzfToUAhQfnvLtt9ITT0iHD2dti4qSpkyR7r7bc3EBAABcg0OHsh6lWrZMSkrK2ufrK7VokVVw1K9P7wZMrF7nCd9+K917r3PhIUlHjpjbv/3Wksu2bdtWjz/+uEaMGKHSpUurbNmy+uijj5ScnKz+/fsrJCREN9xwgxYuXOh4z8qVK3XzzTcrICBA5cuX1zPPPKPLly879icnJ6tv374qUaKEypcvr0mTJmW7bmpqqp566ilVrFhRxYsX1y233JJtljIAAODd7HZzgPjTT5vFRKVK0sMPS99/bxYe5cpJ/ftLX34pnTolrVolPfOM1KABhQeyUHy4W3q62eOR0xTDmdtGjDCPs8Cnn36q8PBw/fLLL3r88cf16KOP6r777lOLFi20adMmxcTE6MEHH1RKSoqOHDmiLl26qFmzZtq6daumTZumTz75RC+++KLjfKNGjdLKlSv1/fffa8mSJVqxYoU2bdrkdM1hw4Zp3bp1mjt3rrZt26b77rtPnTt31h9/HXEGAAC8ytGj0iefSPfcI4WHm+tsvPaatGOH5ONj9m68+KK0aZP5b6jTp0v33SeVKuXpyOGteOzK3Vavzt7jcSXDMPsxV6+WmjRx+eUbNmyo5557TpI0evRovfLKKwoPD9fgwYMlSS+88IKmTZumbdu26f/+7/8UHR2tqVOnymazqXbt2jp69KiefvppvfDCC0pJSdEnn3yi//znP2rfvr0ks7iJiopyXC8+Pl4zZsxQfHy8KlSoIEl66qmntGjRIs2YMUMvv/yyy+8RAADkz+XL0rp1WY9Tbd3qvD8iQurc2XyUKiZGCgvzTJwouCg+3C0hwbXH5VGDBg0c/+/r66syZcqofv36jm1ly5aVJJ04cUK7du1S8+bNZbuir7Rly5ZKSkrS4cOHdfbsWaWlpemWW25x7A8LC1OtWrUcr7dv36709HTVrFnTKY7U1FSVKVPG5fcHAADy5tgxadEis+BYskS6cvJJm026+easqXCbNjV7PID8ovhwt/LlXXtcHvn7+zu9ttlsTtsyC42MjAyXXC8pKUm+vr769ddf5fuXmbxKMJE3AABul54u/fJL1sxUv/7qvD8szLl3IyLCM3GicKL4cLdWrcxZrY4cyXnch81m7m/VSkpOdn98V6hTp46++eYbGYbhKErWrFmjkJAQRUVFKSwsTP7+/vr5559VqVIlSdLZs2e1Z88etWnTRpLUuHFjpaen68SJE2rVqpXH7gUAgKLs5Elp8WKz4Fi8WDpzxnl/06ZZM1M1a8bM/7AOxYe7+fqa0+nee69ZaFxZgGQ+3vTWW17xp/6xxx7TW2+9pccff1zDhg3T7t27NWbMGI0cOVI+Pj4qUaKEBg4cqFGjRqlMmTKKjIzUs88+K58r+mNr1qypBx54QH379tWkSZPUuHFjnTx5UsuWLVODBg3UtWtXD94hAACFU0aGtHFjVu/Ghg3OXzlKlTJ7Nbp0MXs5/vfUNWA5ig9PuPtu6euvc17n4623zP0ueuzpelSsWFELFizQqFGj1LBhQ4WFhWngwIGOAeuS9PrrryspKUndunVTSEiInnzySZ0/f97pPDNmzNCLL76oJ598UkeOHFF4eLhuvfVW3XHHHe6+JQAACq3Tp80xG5m9GydPOu9v1ChrVfFbbzVXGgfcjY+dp9x9t3TnnW5d4TyntTUOHjyYbZtxxT+NtGnTRr/88kuu5yxRooQ+++wzffbZZ45to0aNcjrG399f48aN07hx43I8x0MPPaSHHnro6sEDAAAnGRnSli1msbFggfTzz87/dhkaKnXsmNW78b9JJwGPovjwJF9fqW1bT0cBAAAKiHPnpOXLzUepFi6Ujh933l+/ftbMVC1aSH+ZZwbwOIoPAAAAL2UY0rZt0v/9n48+/7yldu/2c1qHuEQJqUMHs+CIjZWioz0XK3AtKD4AAAC8SGKitHRp1mDxo0clyVdSuCSpTp2smaluu00qVsyT0QJ5Q/EBAADgQYYh7dyZtar4Tz+ZK41nCg6W2rbNUHT0dj35ZF3VqMGzVCi4KD4AAADcLClJWrYsq3fj0CHn/TVrZo3daN1a8vVN14IFB1WlSl3PBAy4CMVHPrlqBXBcH9oBAFAQGIa0e3fWzFSrV0tpaVn7AwOldu2ypsKtXt35/Xa7e+MFrELxkUfFihWTj4+Pjh49qoiICBUrVsyx+rcrZWRkKC0tTZcuXXJatA8mwzCUlpamkydPysfHR8V44BUA4GVSUsyZqTILjr/Obl+tWtbYjbZtpaAgT0QJuJdHi49Vq1bp9ddf16+//qqEhATNmzdPPXr0cOw/fvy4nn76aS1ZskTnzp1T69at9c4776hGjRpXPe9XX32l559/XgcPHlSNGjX06quvqkuXLi6J2cfHR1WrVlVCQoKOmiPALGEYhi5evKigoCBLipvCIjg4WJUqVaJAAwB4hT/+yHqUasUKKTU1a1+xYmaRkfk4VY0aEn/Fo6jxaPGRnJyshg0basCAAbr77rud9hmGoR49esjf31/ff/+9QkND9eabb6pDhw767bffVLx48RzPuXbtWvXu3VsTJ07UHXfcoTlz5qhHjx7atGmTbrzxRpfEXaxYMVWqVEmXL19W+pXz3bmQ3W7XqlWr1Lp1a/kzSXeOfH195efnR3EGAPCYixellSuzejf27XPeX7lyVu9Gu3ZSLl9fgCLDo8VHbGysYmNjc9z3xx9/aP369dqxY4fq1asnSZo2bZrKlSunzz//XIMGDcrxfVOmTFHnzp0dq2xPmDBBcXFxmjp1qt5//32XxW6z2eTv729ZYeDr66vLly8rMDCQ4gMAAC+yf3/WzFTLl5sFSCZ/f6lVq6yCo3ZtejeAK3ntmI/U//VTBgYGOrb5+PgoICBAP/30U67Fx7p16zRy5EinbZ06ddJ333131WulXtEvmpiYKMnsfbB7aIRX5nU9df3Cirxag7xah9xag7xao7DmNTVVWr3apsWLbVq40Ed79jhXE1FRhjp1MtS5c4Zuv91QSEjWviunzL0ehTW3nkZe88YVefLa4qN27dqqVKmSRo8erQ8++EDFixfX5MmTdfjwYSUkJOT6vmPHjqls2bJO28qWLatjx47l+p6JEydq3Lhx2bYvWbJEwcHB+b8JF4iLi/Po9Qsr8moN8modcmsN8mqNwpDXEyeCtGlTWf36a6S2b4/QpUtZX5l8fDJUp84ZNW16XE2aHFflyhccvRurV1sbV2HIrTcir9cmJSXlus/htcWHv7+/vv32Ww0cOFBhYWHy9fVVhw4dFBsbK8MwXHqt0aNHO/WWJCYmKjo6WjExMQoNDXXpta6V3W5XXFycOnbsyGNXLkRerUFerUNurUFerVGQ85qWJq1Zk9W7sWuXc+9G+fJZvRvt2xsqWbKkpJKSarolvoKcW29GXvMm8+mg6+G1xYckNW3aVFu2bNH58+eVlpamiIgI3XLLLbrppptyfU+5cuV0/Phxp23Hjx9XuXLlcn1PQECAAgICsm23ckzHtfKGGAoj8moN8modcmsN8mqNgpLXw4fNsRsLF0pxcebCf5l8fKTmzbPGbjRsaPvfBCeenV2xoOS2oCGv18YVOfLq4iOT+a8L5iD0jRs3asKECbke27x5cy1btkwjRoxwbIuLi1Pz5s2tDhMAAHgxu11aty5rZqrt2533R0aa0+DGxkodO0phYZ6JEyjMPFp8JCUlae/evY7XBw4c0JYtWxQWFqZKlSrpq6++UkREhCpVqqTt27friSeeUI8ePRQTE+N4T9++fVWxYkVNnDhRkvTEE0+oTZs2mjRpkrp27aq5c+dq48aN+vDDD91+fwAAwLMSEqRFi8xiY8kS6cqnRmw26ZZbslYVb9LE7PEAYB2PFh8bN25Uu3btHK8zx13069dPM2fOVEJCgkaOHKnjx4+rfPny6tu3r55//nmnc8THxzstMNeiRQvNmTNHzz33nP7973+rRo0a+u6771y2xgcAAPBely9LP/+cNRXu5s3O+8PDpU6dzIIjJsZ8DcB9PFp8tG3b9qqDx4cPH67hw4df9RwrVqzItu2+++7Tfffdd73hAQCAAuDECefejbNnnfc3a5a1qvhNN0m+vp6JE0ABGfMBAACQKT1d2rAhq3dj40bn/aVLZ/VudOpkjuUA4B0oPgAAgNc7dUpavNgsOBYtkk6fdt7fuHHWzFQ33yz58Q0H8Er80QQAAF4nI0PatMns2Vi40BzHceWT2iVLmjNSdekide4slS/vuVgBXDuKDwAA4BXOnjXHbCxYYPZunDjhvL9Bg6yZqZo3l1iWASh4KD4AAIBHGIa0ZUvW2I1168wej0wlSjj3bkRFeSxUAC5C8QEAANzm/HlzNfHM3o2EBOf9detmjd1o2VIqVswzcQKwBsUHAACwjGGYK4ln9m6sWWPOVpUpOFjq0CFrZfHKlT0XKwDrUXwAAACXunBBWrkyq+A4csR5f61aWb0brVpJAQGeiROA+1F8AACA65aWJs2ZY9Obb7bQ77/7yW7P2hcUJLVrlzVYvFo1z8UJwLMoPgAAQL6dPi198IE0daqUkOAnKUKSVL16Vu9GmzZmAQIAFB8AACDPfv9deustadYs6eJFc1u5cobatftdzz13g+rWZR5cANn55PUNixYt0k8//eR4/e6776pRo0bq06ePzp4969LgAACA9zAMc6aqLl2kOnXMHo+LF6VGjaRPP5X++OOyevXaoxo1PB0pAG+V5+Jj1KhRSkxMlCRt375dTz75pLp06aIDBw5o5MiRLg8QAAB41qVL0iefmIv8xcSYA8ltNql7d2n5cnMl8r59GTgO4O/l+bGrAwcOqG7dupKkb775RnfccYdefvllbdq0SV26dHF5gAAAwDOOH5fee0+aNk06edLcVry41L+/9MQT0g03eDY+AAVPnouPYsWKKSUlRZK0dOlS9e3bV5IUFhbm6BEBAAAF17Zt0uTJ0pw55ixWkhQdLT3+uDR4sFSqlEfDA1CA5bn4uO222zRy5Ei1bNlSv/zyi7744gtJ0p49exQVFeXyAAEAgPUyMsw1OSZPln78MWv7LbdI//yndPfdkj9jyAFcpzyP+Zg6dar8/Pz09ddfa9q0aapYsaIkaeHChercubPLAwQAANZJTjYfrapTR+rWzSw8fHyk++6T1q6V1q+XevWi8ADgGnnu+ahUqZL++9//Zts+efJklwQEAACsd/iwuTbHhx9KmZNVhoaaj1U9/rhUubJn4wNQOOVrnY99+/ZpxowZ2rdvn6ZMmaLIyEgtXLhQlSpVUr169VwdIwAAcJENG8xHq776Srp82dxWrZo5gLx/fykkxLPxASjc8vzY1cqVK1W/fn39/PPP+vbbb5WUlCRJ2rp1q8aMGePyAAEAwPVJT5e+/VZq1Uq6+Wbp88/NwqN1a2nePGnPHmn4cAoPANbLc/HxzDPP6MUXX1RcXJyKFSvm2H777bdr/fr1eTrXqlWr1K1bN1WoUEE2m03fffed0/6kpCQNGzZMUVFRCgoKUt26dfX+++9f9ZwzZ86UzWZz+gkMDMxTXAAAFAaJieYq5DVqSPfcI/30k+TnJ/3jH9LGjdLKlVKPHpKvr6cjBVBU5Pmxq+3bt2vOnDnZtkdGRurUqVN5OldycrIaNmyoAQMG6O677862f+TIkfrxxx/1n//8R1WqVNGSJUv02GOPqUKFCurevXuu5w0NDdXu3bsdr202W57iAgCgIDt4UHr7benjj6ULF8xtYWHSI49IQ4dKFSp4NDwARViei49SpUopISFBVatWddq+efNmx8xX1yo2NlaxsbG57l+7dq369euntm3bSpKGDBmiDz74QL/88stViw+bzaZy5crlKRYAAAoywzBnp5o82XyUKiPD3F67tjRihPTgg1JwsEdDBIC8Fx/333+/nn76aX311Vey2WzKyMjQmjVr9NRTTzkWHHSVFi1a6IcfftCAAQNUoUIFrVixQnv27PnbmbWSkpJUuXJlZWRkqEmTJnr55ZevOhA+NTVVqampjteZiyXa7XbZ7XbX3EweZV7XU9cvrMirNcirdcitNQpTXu126ZtvbHr7bR9t3Jj1NHWHDhkaPjxDMTGGfHyyjrU2lsKTV29Dbq1BXvPGFXmyGYZh5OUNaWlpGjp0qGbOnKn09HT5+fkpPT1dffr00cyZM+WbzwdHbTab5s2bpx49eji2paamasiQIZo1a5b8/Pzk4+Ojjz766KpFzrp16/THH3+oQYMGOn/+vN544w2tWrVKO3fuzHURxLFjx2rcuHHZts+ZM0fB/DMRAMALJSX5a8mSypo/v5pOnw6SJPn7p6t168Pq1m2fqlS54OEIARQ2KSkp6tOnj86fP6/Q0NB8nSPPxUem+Ph47dixQ0lJSWrcuLFq1KiRrwAcgeRQfLzxxhv66KOP9MYbb6hy5cpatWqVRo8erXnz5qlDhw7XdF673a46deqod+/emjBhQo7H5NTzER0drVOnTuU7sdfLbrcrLi5OHTt2lD8rO7kMebUGebUOubVGQc7rnj3S1Kk+mjXLRykp5pjGyEhDDz+coYcfzlBkpOdiK8h59Xbk1hrkNW8SExMVHh5+XcVHvtb5kMzFBitVqpTft/+tixcv6t///rfmzZunrl27SpIaNGigLVu26I033rjm4sPf31+NGzfW3r17cz0mICBAAQEBOb7X0x9Eb4ihMCKv1iCv1iG31igoeTUMaflyczzH/Pnma0mqX1/65z+l3r1tCgz0leQd01YVlLwWROTWGuT12rgiR3kuPgYMGHDV/dOnT893MFfKHG/h4+M8G7Cvr68yMkfRXYP09HRt375dXbp0cUlcAAC4S2qquSbHW29JW7dmbe/a1Sw6br9dYkJHAAVJnouPs2fPOr222+3asWOHzp07p9tvvz1P50pKSnLqkThw4IC2bNmisLAwVapUSW3atNGoUaMUFBSkypUra+XKlZo1a5befPNNx3v69u2rihUrauLEiZKk8ePH69Zbb9UNN9ygc+fO6fXXX9eff/6pQYMG5fVWAQDwiJMnpWnTpPfek44fN7cFBUkPPWSuRF6rlkfDA4B8y3PxMW/evGzbMjIy9Oijj6p69ep5OtfGjRvVrl07x+uRI0dKkvr166eZM2dq7ty5Gj16tB544AGdOXNGlStX1ksvvaRHHnnE8Z74+Hin3pGzZ89q8ODBOnbsmEqXLq2mTZtq7dq1qlu3bl5vFQAAt9q50+zl+Owzs9dDkipWlIYNk4YMMdfqAICCLN9jPq7k4+OjkSNHqm3btvrXv/51ze9r27atrjbevVy5cpoxY8ZVz7FixQqn15MnT/7bqXgBAPAWGRnSkiXmeI4lS7K233ST+WjVffdJPIoOoLBwSfEhSfv27dPly5dddToAAAq1lBSzh2PKFGnXLnObj4/Uo4dZdLRsyXgOAIVPnouPzEejMhmGoYSEBM2fP1/9+vVzWWAAABRGCQnSu+9K778vnT5tbgsJkQYOlIYPl6pW9Wx8AGClPBcfmzdvdnrt4+OjiIgITZo06W9nwgIAoKjavNl8tGru3KyVxqtUMQuOAQOkkiU9Gh4AuEWei4/ly5dbEQcAAIVOerr03/+aRcfKlVnbW7Y0H626807Jz2UPQAOA9+NXHgAALpaUJM2YYY7n2LfP3ObrK/XsKY0YId18s0fDAwCPuabio3HjxrJd46i3TZs2XVdAAAAUVPHx0jvvSB99JJ0/b24rVcqcJnfYMCk62qPhAYDHXVPx0aNHD4vDAACg4Fq/3ny06ptvzEetJKlGDXNBwH79pBIlPBsfAHiLayo+xowZY3UcAAAUKJcvS99+axYd69dnbW/XzhzP0bWrOXUuACALYz4AAMiDc+ekjz82H6+Kjze3FSsm9e5tjudo1MiDwQGAl8tz8ZGenq7Jkyfryy+/VHx8vNLS0pz2nzlzxmXBAQDgLfbtMweQz5hhDiiXpPBw6dFHpccek8qV82x8AFAQ5LlDeNy4cXrzzTfVq1cvnT9/XiNHjtTdd98tHx8fjR071oIQAQDwDMOQVq0yVx2vUcPs7UhKkurWNQeVx8dL48dTeADAtcpzz8fs2bP10UcfqWvXrho7dqx69+6t6tWrq0GDBlq/fr2GDx9uRZwAALhNWpr05ZfmeI4rJ3Hs3Nkcz9Gxo3SNk0ACAK6Q5+Lj2LFjql+/viSpRIkSOv+/uQTvuOMOPf/8866NDgAANzp9WvrgA2nqVCkhwdwWGCj17WvOXFW3rmfjA4CCLs/FR1RUlBISElSpUiVVr15dS5YsUZMmTbRhwwYFBARYESMAAJb6/XfprbekWbOkixfNbeXLS0OHSg8/bI7tAABcvzwXH3fddZeWLVumW265RY8//rj+8Y9/6JNPPlF8fLz++c9/WhEjAAAuZxjS0qU2vfOOtHBh1vbGjc1Hq3r1MmexAgC4Tp6Lj1deecXx/7169VLlypW1du1a1ahRQ926dXNpcAAAuNqlS9KsWTa99FI7xcebfw3abFK3bmbR0aYN4zkAwCp5Lj4uXbqkwMBAx+tbb71Vt956q0uDKvLS02VbuVIVV62SrXhxc8UqX19PRwUABdrx49J770nTpkknT/pJClXx4ob697fpiSekG27wdIQAUPjleardyMhI9evXT3FxccrIyLAipqLt22+lKlXk17GjbnrzTfl17ChVqWJuBwDk2bZtUv/+UqVK5rS4J09K0dGG+vXbqQMHLuuddyg8AMBd8lx8fPrpp0pJSdGdd96pihUrasSIEdq4caMVsRU9334r3XuvdPiw8/YjR8ztFCAAcE0yMqT//ldq315q2FCaOdOcPveWW6S5c6Xduy/rrrv2qlQpT0cKAEVLnouPu+66S1999ZWOHz+ul19+Wb/99ptuvfVW1axZU+PHj7cixqIhPd2cx9Ewsu/L3DZihHkcACBHycnmo1V16phjOH78UfLxke67T1q7Vlq/3hxI7pfnh44BAK6Q5+IjU0hIiPr3768lS5Zo27ZtKl68uMaNG5enc6xatUrdunVThQoVZLPZ9N133zntT0pK0rBhwxQVFaWgoCDVrVtX77///t+e96uvvlLt2rUVGBio+vXra8GCBXmKyyNWr87e43Elw5AOHTKPAwA4OXxYeuYZKTranB53zx4pNFR68klp/35zwcDmzT0dJQAg38XHpUuX9OWXX6pHjx5q0qSJzpw5o1GjRuXpHMnJyWrYsKHefffdHPePHDlSixYt0n/+8x/t2rVLI0aM0LBhw/TDDz/kes61a9eqd+/eGjhwoDZv3qwePXqoR48e2rFjR55ic7vM1axcdRwAFAEbNkh9+khVq0qvviqdPStVqyZNmWIWJG+8IVWu7OkoAQCZ8tzxvHjxYs2ZM0ffffed/Pz8dO+992rJkiVq3bp1ni8eGxur2NjYXPevXbtW/fr1U9u2bSVJQ4YM0QcffKBffvlF3bt3z/E9U6ZMUefOnR2F0IQJExQXF6epU6deU6+Jx5Qv79rjAKCQSk+Xvv9emjxZ+umnrO2tW5tT5XbrxgSBAOCt8jXm4+LFi5o1a5aOHTumDz74IF+Fx7Vo0aKFfvjhBx05ckSGYWj58uXas2ePYmJicn3PunXr1KFDB6dtnTp10rp16yyJ0WVatZKionKfXN5mM58naNXKvXEBgJdITDRXIa9RQ7rnHrPw8POT/vEP6ddfpZUrpR49KDwAwJvluefj+PHjCgkJsSKWbN555x0NGTJEUVFR8vPzk4+Pjz766KOrFjvHjh1T2bJlnbaVLVtWx44dy/U9qampSk1NdbxOTEyUJNntdtnt9uu8i2tnmzRJvvffL9lssl0x8Nz4X0GS/sYbMjIyzGlckC+Z7enOdi0KyKt1yK108KD07rs+mj7dRxcumL8Pw8IMDR6coUcfzVCFCuZxeUkRebUGebUOubUGec0bV+Qpz8WHuwoPySw+1q9frx9++EGVK1fWqlWrNHToUFWoUCFb78b1mDhxYo6D5ZcsWaLg4GCXXedvBQSo/L/+pfoff6yg06cdmy+WKaMdAwcqISBAKgiD5wuAuLg4T4dQKJFX6xS13BqG9PvvYfrhh+r6+efyysgwi46oqAvq1m2f2rY9rICAdG3ZIm3Zkv/rFLW8ugt5tQ65tQZ5vTYpKSnXfQ6bYeQ0t6v72Ww2zZs3Tz169JAkXbx4USVLltS8efPUtWtXx3GDBg3S4cOHtWjRohzPU6lSJY0cOVIjRoxwbBszZoy+++47bd26Ncf35NTzER0drVOnTik0NPT6by6v0tOVvmKFdsTF6caOHeXbti3PEbiI3W5XXFycOnbsKH9/f0+HU2iQV+sUtdza7dI339j09ts+2rgx68ngDh0yNHx4hmJiDPnke6qUK69TtPLqLuTVOuTWGuQ1bxITExUeHq7z58/n+zuy1850nvnIk89f/pbx9fW96srqzZs317Jly5yKj7i4ODW/yhyLAQEBCggIyLbd39/fMx9Ef3+pfXsdSU1Vw/bt+cNgAY+1bSFHXq1T2HN79qz04YfS1KlZs44HBJjjOUaMkG680UfXMUFjrgp7Xj2FvFqH3FqDvF4bV+TIo8VHUlKS9u7d63h94MABbdmyRWFhYapUqZLatGmjUaNGKSgoSJUrV9bKlSs1a9Ysvfnmm4739O3bVxUrVtTEiRMlSU888YTatGmjSZMmqWvXrpo7d642btyoDz/80O33B8ALpaeb6+UkJJizx7VqRc+iB+3ZY06LO3OmlNmbHxlprtXxyCPm/wMACg+PFh8bN25Uu3btHK9HjhwpSerXr59mzpypuXPnavTo0XrggQd05swZVa5cWS+99JIeeeQRx3vi4+OdekdatGihOXPm6LnnntO///1v1ahRQ999951uvPFG990YAO/07bfSE084L+gZFWV++737bs/FVcQYhrR8uTlV7vz55mtJql/fnCq3d28pMNCzMQIArJHn4iM5OVmvvPKKli1bphMnTmR7BGr//v3XfK62bdvqakNOypUrpxkzZlz1HCtWrMi27b777tN99913zXEAKAK+/Va6996sb7qZjhwxt3/9NQWIxVJTpc8/N6fLvXIIXteuZtFx++25zzYOACgc8lx8DBo0SCtXrtSDDz6o8uXLy8bfFAC8XXq62eOR0z92GIb5jXfECOnOO3kEywInT0rTpknvvScdP25uCw6W+vUzm6VWLc/GBwBwnzwXHwsXLtT8+fPVsmVLK+IBANdbvdr5Uau/Mgzp0CHzuLZt3RZWYbdzp9nL8dlnZq+HJFWsKA0bJg0ZIoWFeTQ8AIAH5Ln4KF26tML4GwNAQZKQ4NrjkKuMDGnJEnM8x5IlWdtvusl8tOq++8wJ/QAARVOe5y2cMGGCXnjhBZcsMgIAblG+vGuPQzYpKdIHH0g33ijFxpqFh4+POYxm9Wrpl1+kPn0oPACgqMtzz8ekSZO0b98+lS1bVlWqVMk23++mTZtcFhwAuESrVuasVkeO5Dzuw2Yz97dq5f7YCriEBOndd6X335dOnza3hYRIAwdKw4dLVat6Nj4AgHfJc/GRuQI5ABQYvr7mdLr33msWGlcWIJmTZrz1FoPN82DzZvPRqrlzzVXJJalKFbPgGDhQyufCtyjI0tNlW7lSFVetkq14caldO/5MAcgmz8XHmDFjrIgDAKx1993mdLo5rfPx1ltMs3sN0tOl//7XLDpWrsza3rKlOZ7jzjslP4+uHgWP+d8aOn6HD+smSXrzTdbQAZCjfP818euvv2rXrl2SpHr16qlx48YuCwoALHH33eY3ZFY4z5OkJGnGDPN75L595jZfX6lnT3OG4ptv9mh48DTW0AGQB3kuPk6cOKH7779fK1asUKlSpSRJ586dU7t27TR37lxFRES4OkYAcB1fX6bTvUbx8dI770gffSSdP29uK1VKevhhc7rcqCiPhgdvwBo6APIoz7NdPf7447pw4YJ27typM2fO6MyZM9qxY4cSExM1fPhwK2IEALjR+vVSr15StWrSG2+YhUeNGubA8sOHpVdeofDA/+RlDR0A+ZeeLq1YIX3+ufnf9HRPR5Rvee75WLRokZYuXao6deo4ttWtW1fvvvuuYmJiXBocAMA9Ll82n56ZPNksPjK1ayeNHCl16WJOnQs4YQ0dwHr/G1OVbbxiAR1TlefiIyMjI9v0upLk7++vjIwMlwQFAHCPc+ekjz82H6+Kjze3FSsm9e5tPi3TqJEHg4P3Yw0dwFqFcExVnv8d6/bbb9cTTzyho0ePOrYdOXJE//znP9W+fXuXBgcAsMa+fea0uNHR0qhRZuERHi49/7z055/SzJkUHrgGmWvoZE5Z/Vc2m/khYw0dIO/+bkyVZP4rUQF7BCvPxcfUqVOVmJioKlWqqHr16qpevbqqVq2qxMREvfPOO1bECABwAcOQVq2SevQwx3C88445k1W9euag8vh4afx4qVw5T0eKAiNzDR0pewHCGjrA9SmkY6ry/NhVdHS0Nm3apKVLl+r333+XJNWpU0cdOnRweXAAgOuXliZ9+aU5nmPTpqztnTub63N07Jj7P1wDf4s1dABrFNIxVfla58Nms6ljx47q2LGjq+MBALjI6dPSBx9IU6dm/d0UGCj17Wt+T6xb17PxoRD53xo6l5cv15aFC9UoNlZ+rHAOXJ9COqbqmoqPt99+W0OGDFFgYKDefvvtqx7LdLsA4Fm//27+g/OsWdLFi+a28uWloUPNNTrCwz0aHgorX18ZbdroSHKyGrZpQ+EBXK/MMVVHjuQ87sNmM/cXsDFV11R8TJ48WQ888IACAwM1efLkXI+z2WwUHwDgAYYhLV1qPlq1cGHW9saNzUerevUyZ7ECABQQmWOq7r3XLDSuLEAK8Jiqayo+Dhw4kOP/AwA869IlafZs8++fHTvMbTab1L27WXS0bs14DgAosArhmKo8z3Y1fvx4paSkZNt+8eJFjR8/3iVBAQCu7vhxacwYqVIladAgs/AoXlx6/HFpzx7pu++kNm0oPACgwLv7bungQWn5cmnOHPO/Bw4UyMJDykfxMW7cOCUlJWXbnpKSonHjxrkkKABAzrZtk/r3N4uO8eOlkyfNZRRee838R7G335ZuuMHTUQIAXMrXV2rb1lwBtm3bAveo1ZXyXHwYhiFbDv+UtnXrVoWFheXpXKtWrVK3bt1UoUIF2Ww2fffdd077bTZbjj+vv/56ruccO3ZstuNr166dp7gAwJtkZEjz59vUvr3UsKG5AGBamnTLLdLcudL+/eZCgaVKeTpSAACu7pqn2i1durTjy3zNmjWdCpD09HQlJSXpkUceydPFk5OT1bBhQw0YMEB359B1lPCXeYsXLlyogQMH6p577rnqeevVq6elS5c6Xvv55WtGYQDwqORkafp0H73ySnsdPWr+HvP1le65xxzPceutHg4QAIA8uuZv5W+99ZYMw9CAAQM0btw4lSxZ0rGvWLFiqlKlipo3b56ni8fGxio2NjbX/eX+sszu999/r3bt2qlatWpXPa+fn1+29wJAQXH4sLk2x4cfSmfP+koqodBQQ4MH2/T441Llyp6OEACA/Lnm4qNfv36SpKpVq6pFixby9/e3LKicHD9+XPPnz9enn376t8f+8ccfqlChggIDA9W8eXNNnDhRlSpVyvX41NRUpaamOl4nJiZKkux2u+x2+/UHnw+Z1/XU9Qsr8moN8uoaGzfaNGWKj775xqbLl83e5apVM9S+/U69+GJ1hYWZv3dJ8/XjM2sN8modcmsN8po3rsiTzTByWrXk6tLT0zVv3jzt2rVLklS3bl3deeed1/V4k81m07x589SjR48c97/22mt65ZVXdPToUQUGBuZ6noULFyopKUm1atVSQkKCxo0bpyNHjmjHjh0KCQnJ8T1jx47NcbD8nDlzFBwcnK/7AYBrkZ4u/fxzef3f/1XXrl1lHNvr1Tulbt32qVmzYwV5XCEAoBBJSUlRnz59dP78eYWGhubrHHkuPnbu3Knu3bvr2LFjqlWrliRpz549ioiI0P/93//pxhtvzF8gf1N81K5dWx07dtQ777yTp/OeO3dOlStX1ptvvqmBAwfmeExOPR/R0dE6depUvhN7vex2u+Li4tSxY0e39zIVZuTVGuQ17xITpZkzfTR1qo8OHjR7Ofz8DPXsaeiJJ9LVuLF5HLm1Bnm1Bnm1Drm1BnnNm8TERIWHh19X8ZHnropBgwapXr162rhxo0qXLi1JOnv2rB566CENGTJEa9euzVcgV7N69Wrt3r1bX3zxRZ7fW6pUKdWsWVN79+7N9ZiAgAAFBARk2+7v7+/xD6I3xFAYkVdrkNe/d/CgOR3uxx9LFy6Y28LCpEcekYYOtalCBZtymoiQ3FqDvFqDvFqH3FqDvF4bV+Qoz8XHli1bnAoPyZwJ66WXXlKzZs2uO6CcfPLJJ2ratKkaNmyY5/cmJSVp3759evDBBy2IDAD+nmFIa9dKkydL8+aZU+dKUu3a0ogR0oMPSjzhCQAoCvK8zkfNmjV1/PjxbNtPnDihG/K4slVSUpK2bNmiLVu2SJIOHDigLVu2KD4+3nFMYmKivvrqKw0aNCjHc7Rv315Tp051vH7qqae0cuVKHTx4UGvXrtVdd90lX19f9e7dO0+xAcD1stulzz831+O47Tbpm2/MwqNjR2nBAmnnTunhhyk8AABFR557PiZOnKjhw4dr7NixuvV/k8yvX79e48eP16uvvuqYKUrS3z4LtnHjRrVr187xeuTIkZLMmbVmzpwpSZo7d64Mw8i1eNi3b59OnTrleH348GH17t1bp0+fVkREhG677TatX79eEREReb1VAMiXs2fNaXKnTjWnzZWkgADpH/8wezryOTQOAIACL8/Fxx133CFJ6tmzp2Ohwcwx6926dXO8ttlsSk9Pv+q52rZtq78b7z5kyBANGTIk1/0HDx50ej137tyrng8ArLJnjzRlirkCeUqKuS0yUho61BzTERnp0fAAAPC4PBcfy5cvtyIOACiQDENavtwczzF/vvlakho0MFch793b7PUAAAD5KD7atGljRRwAUKCkpprjOd56S9q6NWt7165m0XH77dL/OocBAMD/5GtVwHPnzumTTz5xLDJYr149DRgwQCVLlnRpcADgbU6elKZNk957T8qceyM4WOrXT3riCel/yx8BAIAc5Hm2q40bN6p69eqaPHmyzpw5ozNnzujNN99U9erVtWnTJitiBACP27lTGjxYio6WxowxC4+KFaWJE6VDh8xihMIDAICry3PPxz//+U91795dH330kfz8zLdfvnxZgwYN0ogRI7Rq1SqXBwkAnpCRIS1ZYo7nWLIka/tNN5mPVt13n8SaVAAAXLs8Fx8bN250Kjwkyc/PT//617900003uTQ4APCElBTps8/Mmav+93SpfHykHj3MoqNlS8ZzAACQH3kuPkJDQxUfH6/atWs7bT906JBCQkJcFhgAuFtCgvTuu9L770unT5vbQkKkgQOl4cOlqlU9Gx8AAAVdnouPXr16aeDAgXrjjTfUokULSdKaNWs0atQoVhEHUCBt3mw+WjV3rrkquSRVqWIWHAMHSn+zXioAALhGeS4+3njjDdlsNvXt21eXL1+WJPn7++vRRx/VK6+84vIAAcAK6enSf/9rFh0rV2Ztb9nSfLTqzjslv3zNBwgAAHKT579aixUrpilTpmjixInat2+fJKl69eoKDg52eXAA4GrHjklffWWO5/jfrzD5+ko9e5pFR7Nmno0PAIDCLN//rhccHKz69eu7MhYAcDm7XVq3Tlq0yPzZvDlrX6lS0sMPS8OGSVFRHgsRAIAig4cKABQ68fFZxcbSpdKFC877mzaVBgwwFwYsXtwzMQIAUBRRfAAo8C5dklavzio4fvvNeX+ZMlKnTlJsrNSxo1S2rGfiBACgqKP4AFAg7d0rLVxoFhvLl0sXL2bt8/GRbr1V6tzZ/GnSxBzXAQAAPIviA0CBkJxsFhmZvRuZg8UzlS9vFhqxsVKHDlLp0p6JEwAA5I7iA4BXMgzz8anM3o3Vq6W0tKz9/v7Sbbdl9W7Ur8+q4wAAeDuKDwBe49w5admyrN6Nw4ed91epktW70a6dufo4AAAoOCg+AHhMRoa0ZUtW78a6debif5kCA6W2bbN6N2rWpHcDAICCjOIDgFudPCnFxZnFxuLF0okTzvtr1TJ7Njp3llq3loKCPBMnAABwPYoPAJa6fFn65ZesR6k2bjTHc2QqUUJq394sNjp1kqpW9VysAADAWj6evPiqVavUrVs3VahQQTabTd99953TfpvNluPP66+/ftXzvvvuu6pSpYoCAwN1yy236JdffrHwLgD81dGj0owZUq9eUmSk1LKlNGGCtGGDWXg0aCA9/bQ5e9Xp09J330mPPELhAQBAYefRno/k5GQ1bNhQAwYM0N13351tf0JCgtPrhQsXauDAgbrnnntyPecXX3yhkSNH6v3339ctt9yit956S506ddLu3bsVGRnp8nsAYM5CtX17uFav9lFcnLRtm/P+UqWkmJis3o0KFTwSJgAA8DCPFh+xsbGKjY3NdX+5cuWcXn///fdq166dqlWrlut73nzzTQ0ePFj9+/eXJL3//vuaP3++pk+frmeeecY1gQPQwYNZj1ItW+anpKSWjn02m9SsWdZA8WbNJD8e8gQAoMgrMF8Hjh8/rvnz5+vTTz/N9Zi0tDT9+uuvGj16tGObj4+POnTooHXr1rkjTKDQunhRWrkyq+DYvfvKvTaVLHlJd9xRTF26+KhjRykiwlORAgAAb1Vgio9PP/1UISEhOT6elenUqVNKT09X2bJlnbaXLVtWv//+e67vS01NVWpqquN1YmKiJMlut8tut19n5PmTeV1PXb+wIq/XzjCkPXukJUt8tGSJTStX2nTpUtY8t76+hpo3NxQTY+j229N04sQSderUUf7+/pIkUuwafGatQV6tQV6tQ26tQV7zxhV5KjDFx/Tp0/XAAw8oMDDQ5eeeOHGixo0bl237kiVLFBwc7PLr5UVcXJxHr19YkdecXbzop23bwrV5c6Q2bYrUiRPFnfaXKXNRTZocV+PGJ9SgwUmVKHFZknTqlOTjQ16tRG6tQV6tQV6tQ26tQV6vTUpKynWfo0AUH6tXr9bu3bv1xRdfXPW48PBw+fr66vjx407bjx8/nm38yJVGjx6tkSNHOl4nJiYqOjpaMTExCg0Nvb7g88lutysuLk4dO2b9SzKuH3l1ZhjS9u1ZvRtr1thkt2f1bhQrZqhVK7N3IyYmQ3Xr+slmqyipotN5yKt1yK01yKs1yKt1yK01yGveZD4ddD0KRPHxySefqGnTpmrYsOFVjytWrJiaNm2qZcuWqUePHpKkjIwMLVu2TMOGDcv1fQEBAQoICMi23d/f3+MfRG+IoTAqynk9ezZrkb9Fi6S/TCqnatWyFvlr186m4sUzixHfvz13Uc6r1citNcirNcirdcitNcjrtXFFjjxafCQlJWnv3r2O1wcOHNCWLVsUFhamSpUqSTIrrK+++kqTJk3K8Rzt27fXXXfd5SguRo4cqX79+ummm27SzTffrLfeekvJycmO2a+AoiYjQ/r116xiY/16c1umoCDp9tuzZqa64QbPxQoAAAo3jxYfGzduVLt27RyvMx996tevn2bOnClJmjt3rgzDUO/evXM8x759+3Tq1CnH6169eunkyZN64YUXdOzYMTVq1EiLFi3KNggdKMyOH5eWLDGLjSVLzDEZV6pbN6vYaNVKsmAoFQAAQDYeLT7atm0rwzCuesyQIUM0ZMiQXPcfPHgw27Zhw4Zd9TEroLC5fNns0cjs3fj1V+f9oaFShw5Zi/z9r2MRAADArQrEmA8A2R0+nFVsLF0qnT/vvL9x46zejebNJR5lBQAAnkbxARQQqanSTz9lFRw7djjvL1NGiokxi42YGOkqE7wBAAB4BMUH4MX27csqNn78Ubpyem0fH+nmm7NmpmraVPL9+wmpAAAAPIbiA/AiKSnSihVmsbFwoXTFZHCSzN6MzEepOnQwezsAAAAKCooPwIMMQ9q1K6t3Y9Uq8/GqTH5+UsuWWb0bDRpINlvu5wMAAPBmFB+AmyUmSsuWZRUc8fHO+ytVyio2br/dnKkKAACgMKD4ACyWkSFt3ZpVbKxda06NmykgQGrTJqvgqFWL3g0AAFA4UXwAFjh9WoqLM8dtLF5sLvp3pZo1s8ZutGkjBQd7Jk4AAAB3ovgAXCA9XdqwIat345dfzPEcmYoXl9q3z1rkr1o1z8UKAADgKRQfQD4lJEhLlpi9G3Fx0pkzzvvr18/q3WjZ0ny8CgAAoCij+ACukd1ujtfI7N3YssV5f8mSWYv8deokVazokTABAAC8FsUHcBV//mmO2Vi40Jyh6sIF5/033ZTVu3HLLebUuAAAAMgZX5WAK1y6ZK61kdm7sWuX8/6ICLNXo3NnqWNHKTLSM3ECAAAURBQfKNIMw1xFfOFCs9hYsUK6eDFrv4+P1Ly5WWzExkqNG5vbAAAAkHcUHyhyLl701X//a9PSpWbBsX+/8/6KFbMepWrfXipd2jNxAgAAFDYUHyj0DEPaudPs3Vi40FerV3fR5ctZ3Rf+/lKrVlm9G/XqscgfAACAFSg+UCidOydHz8aiRdKRI5l7zKKjalVDsbE2de4stWsnlSjhqUgBAACKDooPFAoZGdKmTVnFxvr15sJ/mQIDzSKjY8d0BQYu18CBbVSsmL/nAgYAACiCKD5QYJ08aS7yt2iROR3uyZPO++vUyRq70aqVFBQk2e0ZWrAgmceqAAAAPIDiAwXG5cvSzz9n9W78+qs5niNTiRJShw7muI1OnaTKlT0XKwAAALLz6KShq1atUrdu3VShQgXZbDZ999132Y7ZtWuXunfvrpIlS6p48eJq1qyZ4uPjcz3nzJkzZbPZnH4CAwMtvAtY6cgRafp0qWdPc42N226TXnxR2rjRLDwaNZKeecacIvf0aWnePGnIEAoPAAAAb+TRno/k5GQ1bNhQAwYM0N13351t/759+3Tbbbdp4MCBGjdunEJDQ7Vz586/LSZCQ0O1e/dux2sbz9gUGKmp0po1Wb0b27c77y9dWoqJMXs3YmKk8uU9EycAAADyzqPFR2xsrGJjY3Pd/+yzz6pLly567bXXHNuqV6/+t+e12WwqV66cS2KE9Q4cyCo2li2TkpOz9tls0s03Z43daNZM8vX1XKwAAADIP68d85GRkaH58+frX//6lzp16qTNmzeratWqGj16tHr06HHV9yYlJaly5crKyMhQkyZN9PLLL6tevXruCRx/KyVFWrkyq+DYs8d5f9myWcVGx45SmTKeiRMAAACu5bXFx4kTJ5SUlKRXXnlFL774ol599VUtWrRId999t5YvX642bdrk+L5atWpp+vTpatCggc6fP6833nhDLVq00M6dOxUVFZXje1JTU5Wamup4nZiYKEmy2+2y2+2uv7lrkHldT13flQxD2r1bWrLER0uW2LRqlU2XLmU9Cufra6hFC0MxMYZiYjLUsKHkc8VoJFemoDDl1ZuQV+uQW2uQV2uQV+uQW2uQ17xxRZ5shnHlfEGeY7PZNG/ePEevxtGjR1WxYkX17t1bc+bMcRzXvXt3FS9eXJ9//vk1nddut6tOnTrq3bu3JkyYkOMxY8eO1bhx47JtnzNnjoKDg/N+M1BKip+2bQvX5s2R2rSprE6edM5jeHiKmjQ5oSZNTqh+/ZMqXvyyhyIFAADAtUhJSVGfPn10/vx5hYaG5uscXtvzER4eLj8/P9WtW9dpe506dfTTTz9d83n8/f3VuHFj7d27N9djRo8erZEjRzpeJyYmKjo6WjExMflO7PWy2+2Ki4tTx44d5e/v/YvhGYa0bVtW78aaNTZdvpzVu1GsmKHWrbN6N+rU8ZfNVlFSRbfGWdDyWlCQV+uQW2uQV2uQV+uQW2uQ17zJfDroenht8VGsWDE1a9bMadYqSdqzZ48q52Ee1fT0dG3fvl1dunTJ9ZiAgAAFBARk2+7v7+/xD6I3xJCbM2ekuLisRf4SEpz316iRNXajTRubihfPLEY8P2Lcm/NakJFX65Bba5BXa5BX65Bba5DXa+OKHHm0+EhKSnLqkThw4IC2bNmisLAwVapUSaNGjVKvXr3UunVrtWvXTosWLdL//d//acWKFY739O3bVxUrVtTEiRMlSePHj9ett96qG264QefOndPrr7+uP//8U4MGDXL37RU66enmwn6LFkkLF0q//CJlZGTtDw6Wbr89q+C4honJAAAAUIR4tPjYuHGj2rVr53id+ehTv379NHPmTN111116//33NXHiRA0fPly1atXSN998o9tuu83xnvj4ePlcMTr57NmzGjx4sI4dO6bSpUuradOmWrt2bbbHt3Btjh83ezUWLZKWLDEX8rvSjTdmFRu33Sbl0IEEAAAASPJw8dG2bVv93Xj3AQMGaMCAAbnuv7IXRJImT56syZMnuyK8Islul9avz+rd2LzZeX9oqDn9befOUqdOUnS0Z+IEAABAweO1Yz7gPocOZa25sXSp9NexRE2bZvVu3HKLxCORAAAAyA+KjyIoNVVavTqrd+O335z3lylj9mp07izFxJiL/gEAAADXi+KjiNi7N6t3Y/lyc5XxTD4+0q23ZvVuNGki+Xp+QioAAAAUMhQfhVRysrRiRVbvxr59zvvLlzcLjdhYqUMHqXRpj4QJAACAIoTio5AwDPPxqczejVWrpLS0rP3+/uZsVJm9G/XrSzZb7ucDAAAAXI3iowA7f15atszs2Vi0SDp82Hl/lSpZvRvt2kkhIR4JEwAAAJBE8VGgZGRIW7Zk9W6sXWsu/JcpMFBq2zard6NmTXo3AAAA4D0oPrzcqVPm2I2FC83F/k6ccN5fq5bZs9G5s9S6tRQU5JEwAQAAgL9F8eGFtmyRvv7aR19+2Vp79/rpynUYS5SQ2rfPWuSvalWPhQkAAADkCcWHF5o1S5o82VeSOQVVgwZZvRstWkjFink2PgAAACA/KD680J13SocOZah8+a168skbVbkyS4oDAACg4KP48EJt2kgtWqRrwYJ4Vahwo6fDAQAAAFzCx9MBAAAAACgaKD4AAAAAuAXFBwAAAAC3oPgAAAAA4BYUHwAAAADcguIDAAAAgFtQfAAAAABwC9b5yIFhGJKkxMREj8Vgt9uVkpKixMRE+fuzyKCrkFdrkFfrkFtrkFdrkFfrkFtrkNe8yfxunPldOT8oPnJw4cIFSVJ0dLSHIwEAAAC8y4ULF1SyZMl8vddmXE/pUkhlZGTo6NGjCgkJkc1m80gMiYmJio6O1qFDhxQaGuqRGAoj8moN8modcmsN8moN8modcmsN8po3hmHowoULqlChgnx88jd6g56PHPj4+CgqKsrTYUiSQkND+cNgAfJqDfJqHXJrDfJqDfJqHXJrDfJ67fLb45GJAecAAAAA3ILiAwAAAIBbUHx4qYCAAI0ZM0YBAQGeDqVQIa/WIK/WIbfWIK/WIK/WIbfWIK/ux4BzAAAAAG5BzwcAAAAAt6D4AAAAAOAWFB8AAAAA3ILiAwAAAIBbUHy4ycSJE9WsWTOFhIQoMjJSPXr00O7du52Oefjhh1W9enUFBQUpIiJCd955p37//XenY+Lj49W1a1cFBwcrMjJSo0aN0uXLl915K17HVbkdPny4mjZtqoCAADVq1MiNd+CdXJHXrVu3qnfv3oqOjlZQUJDq1KmjKVOmuPtWvI4rcnv69Gl17txZFSpUUEBAgKKjozVs2DAlJia6+3a8hqt+F2Q6ffq0oqKiZLPZdO7cOTfcgXdyVV5tNlu2n7lz57rzVryOKz+zM2fOVIMGDRQYGKjIyEgNHTrUXbfhdVyR15kzZ+b4mbXZbDpx4oS7b6lQofhwk5UrV2ro0KFav3694uLiZLfbFRMTo+TkZMcxTZs21YwZM7Rr1y4tXrxYhmEoJiZG6enpkqT09HR17dpVaWlpWrt2rT799FPNnDlTL7zwgqduyyu4IreZBgwYoF69ern7FrySK/L666+/KjIyUv/5z3+0c+dOPfvssxo9erSmTp3qqdvyCq7IrY+Pj+6880798MMP2rNnj2bOnKmlS5fqkUce8dRteZwrfxdI0sCBA9WgQQN33oJXcmVeZ8yYoYSEBMdPjx493Hw33sVVuX3zzTf17LPP6plnntHOnTu1dOlSderUyRO35BVckddevXo5fVYTEhLUqVMntWnTRpGRkZ66tcLBgEecOHHCkGSsXLky12O2bt1qSDL27t1rGIZhLFiwwPDx8TGOHTvmOGbatGlGaGiokZqaannMBUV+cnulMWPGGA0bNrQwwoLpevOa6bHHHjPatWtnRYgFlqtyO2XKFCMqKsqKEAuk68nre++9Z7Rp08ZYtmyZIck4e/asxdEWHPnNqyRj3rx5boiw4MpPbs+cOWMEBQUZS5cudVeYBY4rfseeOHHC8Pf3N2bNmmVVmEUGPR8ecv78eUlSWFhYjvuTk5M1Y8YMVa1aVdHR0ZKkdevWqX79+ipbtqzjuE6dOikxMVE7d+60PugCIj+5xd9zVV7Pnz+f6zmKKlfk9ujRo/r222/Vpk0by+IsaPKb199++03jx4/XrFmz5OPDX5N/dT2f16FDhyo8PFw333yzpk+fLoOlxpzkJ7dxcXHKyMjQkSNHVKdOHUVFRalnz546dOiQ2+L2dq74HTtr1iwFBwfr3nvvtSzOIsPT1U9RlJ6ebnTt2tVo2bJltn3vvvuuUbx4cUOSUatWLacKfPDgwUZMTIzT8cnJyYYkY8GCBZbHXRDkN7dXoucjO1fk1TAMY82aNYafn5+xePFiK8MtUK43t/fff78RFBRkSDK6detmXLx40R1he7385vXSpUtGgwYNjM8++8wwDMNYvnw5PR9XuJ7P6/jx442ffvrJ2LRpk/HKK68YAQEBxpQpU9wVutfLb24nTpxo+Pv7G7Vq1TIWLVpkrFu3zmjfvr1Rq1YtnoowXPf3V506dYxHH33UylCLDIoPD3jkkUeMypUrG4cOHcq279y5c8aePXuMlStXGt26dTOaNGni+DJB8fH38pvbK1F8ZOeKvG7fvt0IDw83JkyY4I6QC4zrzW1CQoKxa9cu4/vvvzfq1q3LX47/k9+8/vOf/zR69erlOJbiw5krfhdkev7553lM8Ar5ze1LL71kSHL6R50TJ04YPj4+xqJFi9wWv7dyxWd27dq1hiRj48aN7gi50KP4cLOhQ4caUVFRxv79+//22NTUVCM4ONiYM2eOYRjmL+q/finev3+/IcnYtGmTFeEWKNeT2ytRfDhzRV537txpREZGGv/+97+tCrNActVnNtPq1asNScbRo0ddGWaBcz15bdiwoeHj42P4+voavr6+ho+PjyHJ8PX1NV544QWrQ/dqrv68/ve//zUkGZcuXXJlmAXS9eR2+vTphqRsX64jIyONDz/80JJ4CwpXfWYHDBhgNGrUyIoQiyQ/9z7kVXQZhqHHH39c8+bN04oVK1S1atVreo9hGEpNTZUkNW/eXC+99JJOnDjhmGkhLi5OoaGhqlu3rqXxezNX5BbZuSqvO3fu1O23365+/frppZdesjLkAsOqz2xGRoYkFdnPtSvy+s033+jixYuO/Rs2bNCAAQO0evVqVa9e3bLYvZlVn9ctW7aodOnSCggIcGW4BYorctuyZUtJ0u7duxUVFSVJOnPmjE6dOqXKlStbF7wXc+VnNikpSV9++aUmTpxoVbhFj/vqnKLt0UcfNUqWLGmsWLHCSEhIcPykpKQYhmEY+/btM15++WVj48aNxp9//mmsWbPG6NatmxEWFmYcP37cMAzDuHz5snHjjTcaMTExxpYtW4xFixYZERERxujRoz15ax7nitwahmH88ccfxubNm42HH37YqFmzprF582Zj8+bNRfaZWVfkdfv27UZERITxj3/8w+kcJ06c8OSteZwrcjt//nxj+vTpxvbt240DBw4Y//3vf406derk+FxzUeGq3wVX4rEr1+T1hx9+MD766CNj+/btxh9//GG89957RnBwcJHvTXLVZ/bOO+806tWrZ6xZs8bYvn27cccddxh169Y10tLSPHVrHuXK3wUff/yxERgYWKR/B7gaxYebSMrxZ8aMGYZhGMaRI0eM2NhYIzIy0vD39zeioqKMPn36GL///rvTeQ4ePGjExsYaQUFBRnh4uPHkk08adrvdA3fkPVyV2zZt2uR4ngMHDrj/pryAK/I6ZsyYHM9RuXJlz9yUl3BFbn/88UejefPmRsmSJY3AwECjRo0axtNPP12k/4J01e+CK1F8uCavCxcuNBo1amSUKFHCKF68uNGwYUPj/fffN9LT0z10V97BVZ/Z8+fPGwMGDDBKlSplhIWFGXfddZcRHx/vgTvyDq78XdC8eXOjT58+br6Dws1mGMxzBwAAAMB6TGAOAAAAwC0oPgAAAAC4BcUHAAAAALeg+AAAAADgFhQfAAAAANyC4gMAAACAW1B8AAAAAHALig8AAAAAbkHxAQAAAMAtKD4AAAAAuAXFBwAAAAC3oPgAAAAA4BYUHwAAAADcguIDAAAAgFtQfAAAAABwC4oPAAAAAG5B8QEAAADALSg+AAAAALhFoSw+Jk6cqGbNmikkJESRkZHq0aOHdu/e7emwAAAAgCKtUBYfK1eu1NChQ7V+/XrFxcXJbrcrJiZGycnJng4NAAAAKLJshmEYng7CaidPnlRkZKRWrlyp1q1bezocAAAAoEjy83QA7nD+/HlJUlhY2DUdn5GRoaNHjyokJEQ2m83K0AAAAIACwTAMXbhwQRUqVJCPT/4eoCr0PR8ZGRnq3r27zp07p59++inHY1JTU5Wamup4feTIEdWtW9ddIQIAAAAFxqFDhxQVFZWv9xb6no+hQ4dqx44duRYekjlAfdy4cdm2f/zxxwoODrYyPAAAAKBASElJ0aBBgxQSEpLvcxTqno9hw4bp+++/16pVq1S1atVcj/trz0diYqKio6N16tQphYaGuiPUQs1utysuLk4dO3aUv7+/p8PBX9A+3o328V60jXejfbwb7eO9rtY2iYmJCg8P1/nz5/P9HblQ9nwYhqHHH39c8+bN04oVK65aeEhSQECAAgICsm339/fnD4QLkU/vRvt4N9rHe9E23o328W60j/fKqW1c0VaFsvgYOnSo5syZo++//14hISE6duyYJKlkyZIKCgrycHQAAABA0VQo1/mYNm2azp8/r7Zt26p8+fKOny+++MLToQEAAABFVqHs+SjEw1gAAACAAqtQ9nwAAAAA8D4UHwAAAADcguIDAAAAgFtQfAAAAABwi0I54LywqPLMfE+H4BIBvoZeu1m6cexipabbPB0O/oL28W6Z7QMAQGFAzwcAAAAAt6D4AAAAAOAWFB8AAAAA3ILiAwAAAIBbUHwAAAAAcAuKDwAAAABuQfEBAAAAwC0oPgAAAAC4BcUHAAAAALeg+AAAAADgFhQfAAAAANyC4gMAAACAW1B8AAAAAHALig8AAAAAbkHxAQAAAMAtKD4AAAAAuAXFBwAAAAC3oPgAAAAA4BYUHwAAAADcguIDAAAAgFtQfAAAAABwC4oPAAAAAG5B8QEAAADALSg+AAAAALgFxQcAAAAAt6D4AAAAAOAWFB8AAAAA3ILiAwAAAIBbUHwAAAAAcAuKDwAAAABuQfEBAAAAwC0oPgAAAAC4BcUHAAAAALeg+AAAAADgFhQfAAAAANyC4gMAAACAW1B8AAAAAHALig8AAAAAbkHxAQAAAMAtKD4AAAAAuAXFBwAAAAC3KJTFx6pVq9StWzdVqFBBNptN3333nadDAgAAAIq8Qll8JCcnq2HDhnr33Xc9HQoAAACA//HzdABWiI2NVWxsrKfDAAAAAHCFQll85FVqaqpSU1MdrxMTEyVJdrtddrvdU2EpwNfw2LVdKcDHcPovvAvt490y28WTv4uQs8w2oW28E+3j3Wgf73W1tnFFe9kMwyjU3zhsNpvmzZunHj165HrM2LFjNW7cuGzb58yZo+DgYAujAwAAAAqGlJQU9enTR+fPn1doaGi+zkHxoZx7PqKjo3Xq1Kl8J9YVbhy72GPXdqUAH0MTbsrQ8xt9lJph83Q4+Avax7tltk/Hjh3l7+/v6XBwBbvdrri4ONrGS9E+3o328V5Xa5vExESFh4dfV/HBY1eSAgICFBAQkG27v7+/R/9ApKYXri+CqRm2QndPhQnt4908/fsIuaNtvBvt491oH++VU9u4oq0K5WxXAAAAALxPoez5SEpK0t69ex2vDxw4oC1btigsLEyVKlXyYGQAAABA0VUoi4+NGzeqXbt2jtcjR46UJPXr108zZ870UFQAAABA0VYoi4+2bduqkI+jBwAAAAocxnwAAAAAcAuKDwAAAABuQfEBAAAAwC0oPgAAAAC4BcUHAAAAALeg+AAAAADgFhQfAAAAANyC4gMAAACAW1B8AAAAAHALig8AAAAAbkHxAQAAAMAtKD4AAAAAuAXFBwAAAAC38PN0AACAv3fj2MVKTbd5OgxcIcDX0Gs3u6dtDr7S1dLzA4C70PMBAAAAwC0oPgAAAAC4BcUHAAAAALeg+AAAAADgFhQfAAAAANyC4gMAAACAW1B8AAAAAHALig8AAAAAbkHxAQAAAMAtLC8+Ll++rKVLl+qDDz7QhQsXJElHjx5VUlKS1ZcGAAAA4EX8rDz5n3/+qc6dOys+Pl6pqanq2LGjQkJC9Oqrryo1NVXvv/++lZcHAAAA4EUs7fl44okndNNNN+ns2bMKCgpybL/rrru0bNkyKy8NAAAAwMtY2vOxevVqrV27VsWKFXPaXqVKFR05csTKSwMAAADwMpb2fGRkZCg9PT3b9sOHDyskJMTKSwMAAADwMpYWHzExMXrrrbccr202m5KSkjRmzBh16dLFyksDAAAA8DKWPnY1adIkderUSXXr1tWlS5fUp08f/fHHHwoPD9fnn39u5aUBAAAAeBlLi4+oqCht3bpVX3zxhbZu3aqkpCQNHDhQDzzwgNMAdAAAAACFn6XFhyT5+fnpgQce0AMPPGD1pQAAAAB4MUvHfEycOFHTp0/Ptn369Ol69dVXrbw0AAAAAC9jafHxwQcfqHbt2tm216tXjwUGAQAAgCLG0uLj2LFjKl++fLbtERERSkhIsPLSAAAAALyMpcVHdHS01qxZk237mjVrVKFCBSsvDQAAAMDLWDrgfPDgwRoxYoTsdrtuv/12SdKyZcv0r3/9S08++aSVlwYAAADgZSwtPkaNGqXTp0/rscceU1pamiQpMDBQTz/9tEaPHm3lpQEAAAB4GUuLD5vNpldffVXPP/+8du3apaCgINWoUUMBAQFWXhYAAACAF7J8nQ9JKlGihJo1a+aOSwEAAADwUpYWH8nJyXrllVe0bNkynThxQhkZGU779+/fb+XlAQAAAHgRS4uPQYMGaeXKlXrwwQdVvnx52Ww2Ky8HAAAAwItZWnwsXLhQ8+fPV8uWLa28DAAAAIACwNJ1PkqXLq2wsDArLwEAAACggLC0+JgwYYJeeOEFpaSkWHkZAAAAAAWApcXHpEmTtHjxYpUtW1b169dXkyZNnH6s9u6776pKlSoKDAzULbfcol9++cXyawIAAADImaVjPnr06GHl6a/qiy++0MiRI/X+++/rlltu0VtvvaVOnTpp9+7dioyM9FhcAAAAQFFlafExZswYK09/VW+++aYGDx6s/v37S5Lef/99zZ8/X9OnT9czzzzjsbgAAACAosryRQbPnTunr7/+Wvv27dOoUaMUFhamTZs2qWzZsqpYsaIl10xLS9Ovv/6q0aNHO7b5+PioQ4cOWrduXbbjU1NTlZqa6nidmJgoSbLb7bLb7ZbEeC0CfA2PXduVAnwMp//Cu9A+3o328V7ubBtP/l1UUGXmjNx5J9rHe12tbVzRXjbDMCz7rblt2zZ16NBBJUuW1MGDB7V7925Vq1ZNzz33nOLj4zVr1ixLrnv06FFVrFhRa9euVfPmzR3b//Wvf2nlypX6+eefnY4fO3asxo0bl+08c+bMUXBwsCUxAgAAAAVJSkqK+vTpo/Pnzys0NDRf57C052PkyJF66KGH9NprrykkJMSxvUuXLurTp4+Vl86T0aNHa+TIkY7XiYmJio6OVkxMTL4Tiyx2u11xcXHq2LGj/P39PR0O/oL28W6Z7fP8Rh+lZrBQqzcJ8DE04aYM2sZL0T7ejfbJnx1jO1l+jat9L8h8Ouh6WFp8bNiwQR988EG27RUrVtSxY8csu254eLh8fX11/Phxp+3Hjx9XuXLlsh0fEBCggICAbNv9/f35MuZC5NO70T7eLTXDptR0/oL2RrSNd6N9vBvtkzfu/Hs6p+8Frri+pVPtBgQE5Fgh7dmzRxEREZZdt1ixYmratKmWLVvm2JaRkaFly5Y5PYYFAAAAwH0sLT66d++u8ePHOwan2Gw2xcfH6+mnn9Y999xj5aU1cuRIffTRR/r000+1a9cuPfroo0pOTnbMfgUAAADAvSx97GrSpEm69957FRkZqYsXL6pNmzY6duyYmjdvrpdeesnKS6tXr146efKkXnjhBR07dkyNGjXSokWLVLZsWUuvCwAAACBnlhYfJUuWVFxcnNasWaOtW7cqKSlJTZo0UYcOHay8rMOwYcM0bNgwt1wLAAAAwNVZVnzY7XYFBQVpy5YtatmypVq2bGnVpQAAAAAUAJaN+fD391elSpWUnp5u1SUAAAAAFCCWDjh/9tln9e9//1tnzpyx8jIAAAAACgBLx3xMnTpVe/fuVYUKFVS5cmUVL17caf+mTZusvDwAAAAAL2Jp8dGjRw8rTw8AAACgALG0+BgzZoyVpwcAAABQgFg65kOSzp07p48//lijR492jP3YtGmTjhw5YvWlAQAAAHgRS3s+tm3bpg4dOqhkyZI6ePCgBg8erLCwMH377beKj4/XrFmzrLw8AAAAAC9iac/HyJEj9dBDD+mPP/5QYGCgY3uXLl20atUqKy8NAAAAwMtYWnxs2LBBDz/8cLbtFStW1LFjx6y8NAAAAAAvY2nxERAQoMTExGzb9+zZo4iICCsvDQAAAMDLWFp8dO/eXePHj5fdbpck2Ww2xcfH6+mnn9Y999xj5aUBAAAAeBlLi49JkyYpKSlJkZGRunjxotq0aaMbbrhBISEheumll6y8NAAAAAAvY+lsVyVLllRcXJzWrFmjrVu3KikpSU2aNFGHDh2svCwAAAAAL+Ty4iMsLEx79uxReHi4BgwYoClTpqhly5Zq2bKlqy8FAAAAoABx+WNXaWlpjkHmn376qS5duuTqSwAAAAAogFze89G8eXP16NFDTZs2lWEYGj58uIKCgnI8dvr06a6+PAAAAAAv5fLi4z//+Y8mT56sffv2SZLOnz9P7wcAAAAA1xcfZcuW1SuvvCJJqlq1qj777DOVKVPG1ZcBAAAAUMC4fMxHWFiYTp06JUlq166dihUr5upLAAAAACiAGHAOAAAAwC0YcA4AAADALSwdcG6z2RhwDgAAAEASA84BAAAAuInLi48rHThwwMrTAwAAAChAXF58vP322xoyZIgCAwP19ttvX/XY4cOHu/ryAAAAALyUy4uPyZMn64EHHlBgYKAmT56c63E2m43iAwAAAChCXF58XPmoFY9dAQAAAMjk8uJj5MiR13SczWbTpEmTXH15AAAAAF7K5cXH5s2bnV5v2rRJly9fVq1atSRJe/bska+vr5o2berqSwMAAADwYi4vPpYvX+74/zfffFMhISH69NNPVbp0aUnS2bNn1b9/f7Vq1crVlwYAAADgxXysPPmkSZM0ceJER+EhSaVLl9aLL77II1cAAABAEWNp8ZGYmKiTJ09m237y5ElduHDByksDAAAA8DKWFh933XWX+vfvr2+//VaHDx/W4cOH9c0332jgwIG6++67rbw0AAAAAC9j6Qrn77//vp566in16dNHdrvdvKCfnwYOHKjXX3/dyksDAAAA8DKWFh/BwcF677339Prrr2vfvn2SpOrVq6t48eJWXhYAAACAF7K0+MhUvHhxNWjQwB2XAgAAAOClLB3zAQAAAACZKD4AAAAAuAXFBwAAAAC3oPgAAAAA4BYUHwAAAADcguIDAAAAgFtQfAAAAABwC4oPAAAAAG5R6IqPl156SS1atFBwcLBKlSrl6XAAAAAA/E+hKz7S0tJ033336dFHH/V0KAAAAACu4OfpAFxt3LhxkqSZM2d6NhAAAAAATgpdzwcAAAAA71Toej7yIzU1VampqY7XiYmJkiS73S673e6psAqNzBySS+9E+3i3zHYJ8DE8HAn+KrNNaBvvRPt4N9onf9zxd/XVvhe44vo2wzC8vtWfeeYZvfrqq1c9ZteuXapdu7bj9cyZMzVixAidO3fub88/duxYx+NaV5ozZ46Cg4PzHC8AAABQ2KSkpKhPnz46f/68QkND83WOAlF8nDx5UqdPn77qMdWqVVOxYsUcr/NSfOTU8xEdHa1Tp07lO7HIYrfbFRcXp44dO8rf39/T4eAvaB/vRvt4L3e2zY1jF1t6/sIowMfQhJsy9PxGH6Vm2DwdDv6C9smfHWM7WX6Nq/1uS0xMVHh4+HUVHwXisauIiAhFRERYdv6AgAAFBARk2+7v789f9i5EPr0b7ePdaB/v5Y62SU3ny1l+pWbYyJ8Xo33yxp1/D+T0u80V1y8QxUdexMfH68yZM4qPj1d6erq2bNkiSbrhhhtUokQJzwYHAAAAFGGFrvh44YUX9OmnnzpeN27cWJK0fPlytW3b1kNRAQAAACh0U+3OnDlThmFk+6HwAAAAADyr0BUfAAAAALwTxQcAAAAAt6D4AAAAAOAWFB8AAAAA3ILiAwAAAIBbUHwAAAAAcAuKDwAAAABuQfEBAAAAwC0oPgAAAAC4BcUHAAAAALeg+AAAAADgFhQfAAAAANyC4gMAAACAW1B8AAAAAHALig8AAAAAbkHxAQAAAMAtKD4AAAAAuAXFBwAAAAC3oPgAAAAA4BYUHwAAAADcguIDAAAAgFtQfAAAAABwC4oPAAAAAG5B8QEAAADALSg+AAAAALgFxQcAAAAAt6D4AAAAAOAWFB8AAAAA3ILiAwAAAIBbUHwAAAAAcAuKDwAAAABuQfEBAAAAwC0oPgAAAAC4BcUHAAAAALeg+AAAAADgFhQfAAAAANyC4gMAAACAW1B8AAAAAHALig8AAAAAbkHxAQAAAMAtKD4AAAAAuAXFBwAAAAC3oPgAAAAA4BYUHwAAAADcguIDAAAAgFtQfAAAAABwi0JXfBw8eFADBw5U1apVFRQUpOrVq2vMmDFKS0vzdGgAAABAkebn6QBc7ffff1dGRoY++OAD3XDDDdqxY4cGDx6s5ORkvfHGG54ODwAAACiyCl3x0blzZ3Xu3Nnxulq1atq9e7emTZtG8QEAAAB4UKErPnJy/vx5hYWF5bo/NTVVqampjteJiYmSJLvdLrvdbnl8hV1mDsmld6J9vBvt473c2TYBvobl1yhsAnwMp//Cu9A++eOO3zdX+93miuvbDMMo1K2+d+9eNW3aVG+88YYGDx6c4zFjx47VuHHjsm2fM2eOgoODrQ4RAAAA8HopKSnq06ePzp8/r9DQ0Hydo8AUH88884xeffXVqx6za9cu1a5d2/H6yJEjatOmjdq2bauPP/441/fl1PMRHR2tU6dO5TuxyGK32xUXF6eOHTvK39/f0+HgL2gf70b7eC93ts2NYxdbev7CKMDH0ISbMvT8Rh+lZtg8HQ7+gvbJnx1jO1l+jav9bktMTFR4ePh1FR8F5rGrJ598Ug899NBVj6lWrZrj/48ePap27dqpRYsW+vDDD6/6voCAAAUEBGTb7u/vz1/2LkQ+vRvt491oH+/ljrZJTefLWX6lZtjInxejffLGnX8P5PS7zRXXLzDFR0REhCIiIq7p2CNHjqhdu3Zq2rSpZsyYIR+fQjejMACgCDn4SldPh1Dg2O12LViwQDvGdqJw90K0T9FVYIqPa3XkyBG1bdtWlStX1htvvKGTJ0869pUrV86DkQEAAABFW6ErPuLi4rR3717t3btXUVFRTvsKyPAWAAAAoFAqdM8jPfTQQzIMI8cfAAAAAJ5T6IoPAAAAAN6J4gMAAACAW1B8AAAAAHALig8AAAAAbkHxAQAAAMAtKD4AAAAAuEWhW+fDFTKn5U1MTPRwJIWD3W5XSkqKEhMTWcXUC9E+3o328V60jXejfbwb7eO9rtY2md+Nr2cJC4qPHFy4cEGSFB0d7eFIAAAAAO9y4cIFlSxZMl/vtRmsvpdNRkaGjh49qpCQENlsNk+HU+AlJiYqOjpahw4dUmhoqKfDwV/QPt6N9vFetI13o328G+3jva7WNoZh6MKFC6pQoYJ8fPI3eoOejxz4+PgoKirK02EUOqGhofyC8WK0j3ejfbwXbePdaB/vRvt4r9zaJr89HpkYcA4AAADALSg+AAAAALgFxQcsFxAQoDFjxiggIMDToSAHtI93o328F23j3Wgf70b7eC+r24YB5wAAAADcgp4PAAAAAG5B8QEAAADALSg+AAAAALgFxQcAAAAAt6D4QL5MnDhRzZo1U0hIiCIjI9WjRw/t3r3bsf/MmTN6/PHHVatWLQUFBalSpUoaPny4zp8/n+1cM2fOVIMGDRQYGKjIyEgNHTrUnbdSKLmqfTZs2KD27durVKlSKl26tDp16qStW7e6+3YKnb9rH0l6+OGHVb16dQUFBSkiIkJ33nmnfv/9d6dj4uPj1bVrVwUHBysyMlKjRo3S5cuX3XkrhY4r2mbr1q3q3bu3oqOjFRQUpDp16mjKlCnuvpVCyVV/djKdPn1aUVFRstlsOnfunBvuoPByZdvwvcD1XNU+rvheQPGBfFm5cqWGDh2q9evXKy4uTna7XTExMUpOTpYkHT16VEePHtUbb7yhHTt2aObMmVq0aJEGDhzodJ4333xTzz77rJ555hnt3LlTS5cuVadOnTxxS4WKK9onKSlJnTt3VqVKlfTzzz/rp59+UkhIiDp16iS73e6pWysU/q59JKlp06aaMWOGdu3apcWLF8swDMXExCg9PV2SlJ6erq5duyotLU1r167Vp59+qpkzZ+qFF17w1G0VCq5om19//VWRkZH6z3/+o507d+rZZ5/V6NGjNXXqVE/dVqHhiva50sCBA9WgQQN33kKh5aq24XuBNVzRPi77XmAALnDixAlDkrFy5cpcj/nyyy+NYsWKGXa73TAMwzhz5owRFBRkLF261F1hFln5aZ8NGzYYkoz4+HjHMdu2bTMkGX/88YflMRcl19I+W7duNSQZe/fuNQzDMBYsWGD4+PgYx44dcxwzbdo0IzQ01EhNTbU85qIiP22Tk8cee8xo166dFSEWadfTPu+9957Rpk0bY9myZYYk4+zZsxZHW7Tkp234XuA++WkfV30voOcDLpH5uE5YWNhVjwkNDZWfn58kKS4uThkZGTpy5Ijq1KmjqKgo9ezZU4cOHXJLzEVJftqnVq1aKlOmjD755BOlpaXp4sWL+uSTT1SnTh1VqVLFHWEXGX/XPsnJyZoxY4aqVq2q6OhoSdK6detUv359lS1b1nFcp06dlJiYqJ07d1ofdBGRn7bJ7TxX+/OH/Mlv+/z2228aP368Zs2aJR8fvgpZIT9tw/cC98lP+7jse0H+aybAlJ6ebnTt2tVo2bJlrsecPHnSqFSpkvHvf//bsW3ixImGv7+/UatWLWPRokXGunXrjPbt2xu1atXiX25dKL/tYxiGsX37dqN69eqGj4+P4ePjY9SqVcs4ePCg1SEXKVdrn3fffdcoXry4IcmoVauW07/cDh482IiJiXE6Pjk52ZBkLFiwwPK4i4L8ts1frVmzxvDz8zMWL15sZbhFTn7b59KlS0aDBg2Mzz77zDAMw1i+fDk9Hy6W37bhe4F7XM/vNld8L6D4wHV75JFHjMqVKxuHDh3Kcf/58+eNm2++2ejcubORlpbm2P7SSy8Zkpz+Qj5x4oTh4+NjLFq0yPK4i4r8tk9KSopx8803G3379jV++eUXY926dcY999xj1KtXz0hJSXFX+IXe1drn3Llzxp49e4yVK1ca3bp1M5o0aWJcvHjRMAyKD3fIb9tcafv27UZ4eLgxYcIEd4RcpOS3ff75z38avXr1chxL8eF6+W0bvhe4R37bx1XfCyg+cF2GDh1qREVFGfv3789xf2JiotG8eXOjffv22f5inj59uiEp24c/MjLS+PDDDy2LuSi5nvb5+OOPjcjISCM9Pd2xLTU11QgODjY+//xzS+MuKv6ufa6Umfs5c+YYhmEYzz//vNGwYUOnY/bv329IMjZt2mRFuEXK9bRNpp07dxqRkZHZehRx/a6nfRo2bGj4+PgYvr6+hq+vr+Hj42NIMnz/v527Z2ksiMI4ftSVaOPVYFIFgthFrUXSpVACithKQEiXwsrKRqv4NfwEIliJVUCChRZCfAVFLVQMNrFQhOCzhWvW7Aq+zb1hs/8f3CK5N8MMDwnnkGHa2rSwsOD31Jved7KhLvDfd/JxVRf8+PQmMcDMJNns7Kytrq5aoVCwvr6+v565u7uzsbExC4VCtra2Zh0dHXX3k8mkmZkdHx9bLBYzs+cjYG9vby0ej/u/iCbmIp/7+3trbW21lpaW2nsvr5+ennxfQzP7SD5vfUaSPT4+mpnZyMiI5fN5K5fLFo1Gzex5v3RXV5clEglf59/MXGRjZra/v2+pVMpmZmYsn8/7OeX/iot8VlZW7OHhoXZ/e3vbstmsbW5uWn9/v29zb3YusqEu8I+LfJzVBR9uU4BXcrmcPM9ToVDQ9fV17Xr5261SqWh4eFhDQ0M6OTmpe6ZardbGmZyc1MDAgIrFokqlksbHx5VIJOq2/+DzXORzeHioUCikXC6ng4MD7e3tKZPJyPM8XV1dNXJ5/7z38jk9PdXS0pJ2dnZ0cXGhYrGoiYkJhcNh3dzcSJKq1aoGBwc1Ojqq3d1dra+vKxKJaH5+vpFL++e5yKZUKikSiSiTydSNUS6XG7m0puAinz+x7coNV9lQF/jDRT6u6gKaD3yJmb15LS8vS/r9Y/7WdXZ2VhunUqkom82qu7tb4XBYU1NTdUe44Wtc5bOxsaFkMinP89TT06NUKqWtra3GLKqJvJfP5eWl0um0otGo2tvbFYvFND09raOjo7pxzs/PlU6n1dnZqd7eXs3NzdWOSsbXuMhmcXHxzTHi8XhjFtVEXH13XqP5cMNVNtQF/nCVj4u6oOXXhAAAAADAVxxuDQAAACAQNB8AAAAAAkHzAQAAACAQNB8AAAAAAkHzAQAAACAQNB8AAAAAAkHzAQAAACAQNB8AAAAAAkHzAQAAACAQNB8AAAAAAkHzAQAAACAQNB8AAAAAAvETmw1l9ibqcuwAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Team Member A - Discussion About Graph - Step 2\n",
        "\n",
        "In the graph comparing model prices with market prices for call options in Step 2, we can observe that the model prices generally follow the trend of the market prices, especially for options with shorter maturities. However, discrepancies become more pronounced for higher strikes in the 60 and 120-day call options.\n",
        "\n",
        "On the other hand, the graph for put options in Step 2 displays even more significant variations across all strikes and maturities. The divergences between model and market prices for put options are notably larger compared to call options, underscoring the challenges in accurately capturing the pricing dynamics for these options using the Bates model.\n",
        "\n",
        "It's important again to note that calibration is an iterative process, and achieving a perfect fit between the model and market prices is often challenging. The objective is to find parameter values that provide a reasonable approximation to market data while adhering to the model's assumptions, but some level of variance is expected, especially in the presence of complex market dynamics and option features."
      ],
      "metadata": {
        "id": "JN9FcCf9scJO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "TEAM MEMBER B Step 1\n",
        "\n",
        "Carr-Madan Model for Heston (1993)\n",
        "In order to double-check the different model parameters resulting from a calibration, Team member B will repeat the same process as Team member A, but using the Carr-Madan (1999) pricing approach to calibrate the Heston (1993) model. Make sure that you repeat all the tasks in (a), including a discussion on why (or why not) you obtain similar values for the different parameters as via Lewis (2001). You can use put-call parity as well to calibrate to put option prices."
      ],
      "metadata": {
        "id": "tN1x1n6_TjAt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Loading libraries\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import warnings\n",
        "from scipy.integrate import quad\n",
        "from numpy.fft import fft\n",
        "import sys\n",
        "\n",
        "from scipy.optimize import brute, fmin"
      ],
      "metadata": {
        "id": "GyTVcp1TgiAa"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Read the Option Data\n",
        "option_data = pd.read_excel(\"GWP.xlsx\")\n",
        "option_data"
      ],
      "metadata": {
        "id": "QsaIEN_Hgl5S",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 990
        },
        "outputId": "99950e51-9df7-4953-eeed-6f200dea8ad3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    Days to maturity  Strike      Price Type\n",
              "0                 15   227.5  10.520000    C\n",
              "1                 15   230.0  10.050000    C\n",
              "2                 15   232.5   7.750000    C\n",
              "3                 15   235.0   6.010000    C\n",
              "4                 15   237.5   4.750000    C\n",
              "5                 60   227.5  16.780000    C\n",
              "6                 60   230.0  17.650000    C\n",
              "7                 60   232.5  16.860000    C\n",
              "8                 60   235.0  16.050000    C\n",
              "9                 60   237.5  15.100000    C\n",
              "10               120   227.5  27.920000    C\n",
              "11               120   230.0  24.120000    C\n",
              "12               120   232.5  22.970000    C\n",
              "13               120   235.0  21.750000    C\n",
              "14               120   237.5  18.060000    C\n",
              "15                15   227.5   4.320000    P\n",
              "16                15   230.0   5.200000    P\n",
              "17                15   232.5   6.450000    P\n",
              "18                15   235.0   7.560000    P\n",
              "19                15   237.5   8.780000    P\n",
              "20                60   227.5  11.030000    P\n",
              "21                60   230.0  12.150000    P\n",
              "22                60   232.5  13.370000    P\n",
              "23                60   235.0  14.750000    P\n",
              "24                60   237.5  15.620000    P\n",
              "25               120   227.5  14.530629    P\n",
              "26               120   230.0  16.250000    P\n",
              "27               120   232.5  17.220000    P\n",
              "28               120   235.0  18.740000    P\n",
              "29               120   237.5  19.730000    P"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-3a919ee5-c707-4227-9823-f069e68bf85a\" class=\"colab-df-container\">\n",
              "    <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Days to maturity</th>\n",
              "      <th>Strike</th>\n",
              "      <th>Price</th>\n",
              "      <th>Type</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>15</td>\n",
              "      <td>227.5</td>\n",
              "      <td>10.520000</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>15</td>\n",
              "      <td>230.0</td>\n",
              "      <td>10.050000</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>15</td>\n",
              "      <td>232.5</td>\n",
              "      <td>7.750000</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>15</td>\n",
              "      <td>235.0</td>\n",
              "      <td>6.010000</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>15</td>\n",
              "      <td>237.5</td>\n",
              "      <td>4.750000</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>60</td>\n",
              "      <td>227.5</td>\n",
              "      <td>16.780000</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>60</td>\n",
              "      <td>230.0</td>\n",
              "      <td>17.650000</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>60</td>\n",
              "      <td>232.5</td>\n",
              "      <td>16.860000</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>60</td>\n",
              "      <td>235.0</td>\n",
              "      <td>16.050000</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>60</td>\n",
              "      <td>237.5</td>\n",
              "      <td>15.100000</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>120</td>\n",
              "      <td>227.5</td>\n",
              "      <td>27.920000</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>120</td>\n",
              "      <td>230.0</td>\n",
              "      <td>24.120000</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>120</td>\n",
              "      <td>232.5</td>\n",
              "      <td>22.970000</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>120</td>\n",
              "      <td>235.0</td>\n",
              "      <td>21.750000</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>120</td>\n",
              "      <td>237.5</td>\n",
              "      <td>18.060000</td>\n",
              "      <td>C</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>15</td>\n",
              "      <td>227.5</td>\n",
              "      <td>4.320000</td>\n",
              "      <td>P</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>15</td>\n",
              "      <td>230.0</td>\n",
              "      <td>5.200000</td>\n",
              "      <td>P</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>15</td>\n",
              "      <td>232.5</td>\n",
              "      <td>6.450000</td>\n",
              "      <td>P</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>15</td>\n",
              "      <td>235.0</td>\n",
              "      <td>7.560000</td>\n",
              "      <td>P</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>15</td>\n",
              "      <td>237.5</td>\n",
              "      <td>8.780000</td>\n",
              "      <td>P</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>60</td>\n",
              "      <td>227.5</td>\n",
              "      <td>11.030000</td>\n",
              "      <td>P</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>60</td>\n",
              "      <td>230.0</td>\n",
              "      <td>12.150000</td>\n",
              "      <td>P</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>60</td>\n",
              "      <td>232.5</td>\n",
              "      <td>13.370000</td>\n",
              "      <td>P</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>60</td>\n",
              "      <td>235.0</td>\n",
              "      <td>14.750000</td>\n",
              "      <td>P</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>60</td>\n",
              "      <td>237.5</td>\n",
              "      <td>15.620000</td>\n",
              "      <td>P</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>120</td>\n",
              "      <td>227.5</td>\n",
              "      <td>14.530629</td>\n",
              "      <td>P</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>120</td>\n",
              "      <td>230.0</td>\n",
              "      <td>16.250000</td>\n",
              "      <td>P</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>120</td>\n",
              "      <td>232.5</td>\n",
              "      <td>17.220000</td>\n",
              "      <td>P</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>120</td>\n",
              "      <td>235.0</td>\n",
              "      <td>18.740000</td>\n",
              "      <td>P</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>120</td>\n",
              "      <td>237.5</td>\n",
              "      <td>19.730000</td>\n",
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              "    </div>\n",
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            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data = option_data.copy() # Copy the data for a version and keeping old version for the later stages\n",
        "S0=232.90 # The SM stock is currently traded at $232.90"
      ],
      "metadata": {
        "id": "jwbWlFzChbrf"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Select the Call Option data and Put Option data in seperated objects\n",
        "call_options = data[data.Type == \"C\"].drop(columns=[\"Type\"])\n",
        "call_options.columns = [\"Days to Maturity\", \"Strike\", \"market_call\"]\n",
        "put_options = data[data.Type == \"P\"].drop(columns=[\"Type\"])\n",
        "put_options.columns = [\"Days to Maturity\", \"Strike\", \"market_put\"]\n",
        "options = pd.merge(call_options, put_options, on=[\"Days to Maturity\", \"Strike\"], how=\"outer\")\n",
        "options.loc[:,\"T\"] = options.loc[:, \"Days to Maturity\"] / 250 #Generating T value based on 250 trading date\n",
        "options[\"r\"] = 0.015  #  annual risk free rate of 1.5%\n",
        "options = options[options[\"Days to Maturity\"] == 15] #maturity for the derivative (around 15 days)\n",
        "options"
      ],
      "metadata": {
        "id": "lbxSY4Ahhekq",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "outputId": "934c4e19-5189-4edd-87ba-80d749c8b823"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   Days to Maturity  Strike  market_call  market_put     T      r\n",
              "0                15   227.5        10.52        4.32  0.06  0.015\n",
              "1                15   230.0        10.05        5.20  0.06  0.015\n",
              "2                15   232.5         7.75        6.45  0.06  0.015\n",
              "3                15   235.0         6.01        7.56  0.06  0.015\n",
              "4                15   237.5         4.75        8.78  0.06  0.015"
            ],
            "text/html": [
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              "                                                    [key], {});\n",
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              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
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              "        const charts = await google.colab.kernel.invokeFunction(\n",
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              "        console.error('Error during call to suggestCharts:', error);\n",
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              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
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          },
          "metadata": {},
          "execution_count": 4
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      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Heston (1993) characteristic function:\n",
        "def H93_char_func(u, T, r, kappa_v, theta_v, sigma_v, rho, v0):\n",
        "    c1 = kappa_v * theta_v\n",
        "    c2 = -np.sqrt(\n",
        "        (rho * sigma_v * u * 1j - kappa_v) ** 2 - sigma_v**2 * (-u * 1j - u**2)\n",
        "    )\n",
        "    c3 = (kappa_v - rho * sigma_v * u * 1j + c2) / (\n",
        "        kappa_v - rho * sigma_v * u * 1j - c2\n",
        "    )\n",
        "    H1 = r * u * 1j * T + (c1 / sigma_v**2) * (\n",
        "        (kappa_v - rho * sigma_v * u * 1j + c2) * T\n",
        "        - 2 * np.log((1 - c3 * np.exp(c2 * T)) / (1 - c3))\n",
        "    )\n",
        "    H2 = (\n",
        "        (kappa_v - rho * sigma_v * u * 1j + c2)\n",
        "        / sigma_v**2\n",
        "        * ((1 - np.exp(c2 * T)) / (1 - c3 * np.exp(c2 * T)))\n",
        "    )\n",
        "    char_func_value = np.exp(H1 + H2 * v0)\n",
        "    return char_func_value\n",
        "\n",
        "def H93_call_FFT(S0, K, T, r,  kappa_v, theta_v, sigma_v, rho, v0):\n",
        "    \"\"\"European Call option price in Haston93 under FFT\"\"\"\n",
        "\n",
        "    k = np.log(K / S0)\n",
        "    x0 = np.log(S0 / S0)\n",
        "    g = 1  # Factor to increase accuracy\n",
        "    N = g * 4096\n",
        "    eps = (g * 150) ** -1\n",
        "    eta = 2 * np.pi / (N * eps)\n",
        "    b = 0.5 * N * eps - k\n",
        "    u = np.arange(1, N + 1, 1)\n",
        "    vo = eta * (u - 1)\n",
        "\n",
        "    # Modifications to ensure integrability\n",
        "    if S0 >= 0.95 * K:  # ITM Case\n",
        "        alpha = 1.5\n",
        "        v = vo - (alpha + 1) * 1j\n",
        "        modcharFunc = np.exp(-r * T) * (\n",
        "            H93_char_func(u, T, r, kappa_v, theta_v, sigma_v, rho, v0)\n",
        "            / (alpha**2 + alpha - vo**2 + 1j * (2 * alpha + 1) * vo)\n",
        "        )\n",
        "\n",
        "    else:\n",
        "        alpha = 1.1\n",
        "        v = (vo - 1j * alpha) - 1j\n",
        "        modcharFunc1 = np.exp(-r * T) * (\n",
        "            1 / (1 + 1j * (vo - 1j * alpha))\n",
        "            - np.exp(r * T) / (1j * (vo - 1j * alpha))\n",
        "            - H93_char_func(u, T, r, kappa_v, theta_v, sigma_v, rho, v0)\n",
        "            / ((vo - 1j * alpha) ** 2 - 1j * (vo - 1j * alpha))\n",
        "        )\n",
        "\n",
        "        v = (vo + 1j * alpha) - 1j\n",
        "\n",
        "        modcharFunc2 = np.exp(-r * T) * (\n",
        "            1 / (1 + 1j * (vo + 1j * alpha))\n",
        "            - np.exp(r * T) / (1j * (vo + 1j * alpha))\n",
        "            - H93_char_func(u, T, r, kappa_v, theta_v, sigma_v, rho, v0)\n",
        "            / ((vo + 1j * alpha) ** 2 - 1j * (vo + 1j * alpha))\n",
        "        )\n",
        "\n",
        "    # Numerical FFT Routine\n",
        "    delt = np.zeros(N)\n",
        "    delt[0] = 1\n",
        "    j = np.arange(1, N + 1, 1)\n",
        "    SimpsonW = (3 + (-1) ** j - delt) / 3\n",
        "    if S0 >= 0.95 * K:\n",
        "        FFTFunc = np.exp(1j * b * vo) * modcharFunc * eta * SimpsonW\n",
        "        payoff = (fft(FFTFunc)).real\n",
        "        CallValueM = np.exp(-alpha * k) / np.pi * payoff\n",
        "    else:\n",
        "        FFTFunc = (\n",
        "            np.exp(1j * b * vo) * (modcharFunc1 - modcharFunc2) * 0.5 * eta * SimpsonW\n",
        "        )\n",
        "        payoff = (fft(FFTFunc)).real\n",
        "        CallValueM = payoff / (np.sinh(alpha * k) * np.pi)\n",
        "\n",
        "    pos = int((k + b) / eps)\n",
        "    CallValue = CallValueM[pos] * S0\n",
        "\n",
        "    return CallValue\n",
        "\n",
        "def H93_error_function_carr_ma_call(p0):\n",
        "    \"\"\"Error function for parameter calibration via\n",
        "    Lewis (2001) Fourier approach for Heston (1993).\n",
        "    Parameters\n",
        "    ==========\n",
        "    kappa_v: float\n",
        "        mean-reversion factor\n",
        "    theta_v: float\n",
        "        long-run mean of variance\n",
        "    sigma_v: float\n",
        "        volatility of variance\n",
        "    rho: float\n",
        "        correlation between variance and stock/index level\n",
        "    v0: float\n",
        "        initial, instantaneous variance\n",
        "    Returns\n",
        "    =======\n",
        "    MSE: float\n",
        "        mean squared error\n",
        "    \"\"\"\n",
        "    global i, min_MSE\n",
        "    kappa_v, theta_v, sigma_v, rho, v0 = p0\n",
        "    if kappa_v < 0.0 or theta_v < 0.005 or sigma_v < 0.0 or rho < -1.0 or rho > 1.0:\n",
        "        return min_MSE\n",
        "    if 2 * kappa_v * theta_v < sigma_v**2:\n",
        "        return min_MSE\n",
        "    se = []\n",
        "    for row, option in options.iterrows():\n",
        "        model_value = H93_call_FFT(\n",
        "            S0,\n",
        "            option[\"Strike\"],\n",
        "            option[\"T\"],\n",
        "            option[\"r\"],\n",
        "            kappa_v,\n",
        "            theta_v,\n",
        "            sigma_v,\n",
        "            rho,\n",
        "            v0,\n",
        "        )\n",
        "        se.append((model_value - option[\"market_call\"]) ** 2)\n",
        "    MSE = sum(se) / len(se)\n",
        "    min_MSE = min(min_MSE, MSE)\n",
        "    if i % 100 == 0:\n",
        "        print(\"%4d |\" % i, np.array(p0), \"| %7.3f | %7.3f\" % (MSE, min_MSE))\n",
        "    i += 1\n",
        "    return MSE\n",
        "\n",
        "\n",
        "def H93_error_function_carr_ma_put(p0):\n",
        "    \"\"\"Error function for parameter calibration via\n",
        "    Lewis (2001) Fourier approach for Heston (1993).\n",
        "    Parameters\n",
        "    ==========\n",
        "    kappa_v: float\n",
        "        mean-reversion factor\n",
        "    theta_v: float\n",
        "        long-run mean of variance\n",
        "    sigma_v: float\n",
        "        volatility of variance\n",
        "    rho: float\n",
        "        correlation between variance and stock/index level\n",
        "    v0: float\n",
        "        initial, instantaneous variance\n",
        "    Returns\n",
        "    =======\n",
        "    MSE: float\n",
        "        mean squared error\n",
        "    \"\"\"\n",
        "    global i, min_MSE\n",
        "    kappa_v, theta_v, sigma_v, rho, v0 = p0\n",
        "    if kappa_v < 0.0 or theta_v < 0.005 or sigma_v < 0.0 or rho < -1.0 or rho > 1.0:\n",
        "        return min_MSE\n",
        "    if 2 * kappa_v * theta_v < sigma_v**2:\n",
        "        return min_MSE\n",
        "    se = []\n",
        "    for row, option in options.iterrows():\n",
        "        K=option[\"Strike\"]\n",
        "        T=option[\"T\"]\n",
        "        r=option[\"r\"]\n",
        "\n",
        "        model_value = H93_call_FFT(\n",
        "            S0,\n",
        "            K,\n",
        "            T,\n",
        "            r,\n",
        "            kappa_v,\n",
        "            theta_v,\n",
        "            sigma_v,\n",
        "            rho,\n",
        "            v0,\n",
        "        )\n",
        "        put_val = model_value +K*np.exp(-r*T)-S0\n",
        "        se.append((put_val - option[\"market_put\"]) ** 2)\n",
        "    MSE = sum(se) / len(se)\n",
        "    min_MSE = min(min_MSE, MSE)\n",
        "    if i % 100 == 0:\n",
        "        print(\"%4d |\" % i, np.array(p0), \"| %7.3f | %7.3f\" % (MSE, min_MSE))\n",
        "    i += 1\n",
        "    return MSE\n",
        "\n",
        "\n",
        "def H93_calibration_full_carr_ma_call():\n",
        "    \"\"\"Calibrates Heston (1993) stochastic volatility model to market quotes.\"\"\"\n",
        "    # First run with brute force\n",
        "    # (scan sensible regions, for faster convergence)\n",
        "    p0 = brute(\n",
        "        H93_error_function_carr_ma_call,\n",
        "        (\n",
        "            (2.5, 10.6, 5.0),  # kappa_v\n",
        "            (0.01, 0.041, 0.01),  # theta_v\n",
        "            (0.05, 0.251, 0.1),  # sigma_v\n",
        "            (-0.75, 0.01, 0.25),  # rho\n",
        "            (0.01, 0.031, 0.01),\n",
        "        ),  # v0\n",
        "        finish=None,\n",
        "    )\n",
        "\n",
        "    # Second run with local, convex minimization\n",
        "    # (we dig deeper where promising results)\n",
        "    opt = fmin(\n",
        "        H93_error_function_carr_ma_call, p0, xtol=0.000001, ftol=0.000001, maxiter=1000, maxfun=2000\n",
        "    )\n",
        "    return opt\n",
        "\n",
        "def H93_calibration_full_carr_ma_put():\n",
        "    \"\"\"Calibrates Heston (1993) stochastic volatility model to market quotes.\"\"\"\n",
        "    # First run with brute force\n",
        "    # (scan sensible regions, for faster convergence)\n",
        "    p0 = brute(\n",
        "        H93_error_function_carr_ma_put,\n",
        "        (\n",
        "            (2.5, 10.6, 5.0),  # kappa_v\n",
        "            (0.01, 0.041, 0.01),  # theta_v\n",
        "            (0.05, 0.251, 0.1),  # sigma_v\n",
        "            (-0.75, 0.01, 0.25),  # rho\n",
        "            (0.01, 0.031, 0.01),\n",
        "        ),  # v0\n",
        "        finish=None,\n",
        "    )\n",
        "\n",
        "    # Second run with local, convex minimization\n",
        "    # (we dig deeper where promising results)\n",
        "    opt = fmin(\n",
        "        H93_error_function_carr_ma_put, p0, xtol=0.000001, ftol=0.000001, maxiter=1000, maxfun=2000\n",
        "    )\n",
        "    return opt\n",
        "\n",
        "def plot_full_calibration_results_heston_memberB(call_params, put_params):\n",
        "\n",
        "    options[\"model_call\"] = 0\n",
        "    options[\"model_put\"] = 0\n",
        "    for idx in range(options.shape[0]):\n",
        "#         print(options.iloc[idx, :])\n",
        "        kappa_v, theta_v, sigma_v, rho, v0 = call_params\n",
        "\n",
        "        options.loc[idx, \"model_call\"] = H93_call_FFT(\n",
        "            S0, options.loc[idx, \"Strike\"], options.loc[idx, \"T\"], options.loc[idx, \"r\"],\n",
        "            kappa_v, theta_v, sigma_v, rho, v0)\n",
        "\n",
        "        kappa_v, theta_v, sigma_v, rho, v0 = put_params\n",
        "        options.loc[idx, \"model_put\"] = H93_call_FFT(\n",
        "            S0, options.loc[idx, \"Strike\"], options.loc[idx, \"T\"], options.loc[idx, \"r\"],\n",
        "            kappa_v, theta_v, sigma_v, rho, v0)\n",
        "        options.loc[idx, \"model_put\"] = (\n",
        "            options.loc[idx, \"model_put\"] + options.loc[idx, \"Strike\"] * np.exp(-options.loc[idx, \"r\"] * options.loc[idx, \"T\"]) - S0\n",
        "        )\n",
        "    plt.figure(figsize=(10, 5))\n",
        "    # ------- comparison --------\n",
        "    plt.subplot(221)\n",
        "    plt.grid()\n",
        "    plt.title(\"Call Option Calibration\")\n",
        "    plt.ylabel(\"option values\")\n",
        "    color = [\"blue\", \"red\", \"deepskyblue\", \"orange\", \"green\", \"mediumvioletred\"]\n",
        "    color_idx = 0\n",
        "    for mat in options[\"Days to Maturity\"].unique():\n",
        "        opt_data = options[options[\"Days to Maturity\"] == mat]\n",
        "        plt.plot(opt_data[\"Strike\"], opt_data[\"market_call\"], color[color_idx], label=f\"market: (Maturity={mat})\")\n",
        "        plt.plot(opt_data[\"Strike\"], opt_data[\"model_call\"], color[color_idx+1], marker = \"o\", linestyle='None', label=f\"model: (Maturity={mat})\")\n",
        "        color_idx += 2\n",
        "    plt.legend(loc=0)\n",
        "    plt.axis(\n",
        "            [\n",
        "                min(options.Strike) - 1,\n",
        "                max(options.Strike) + 1,\n",
        "                min(options.market_call) - 10,\n",
        "                max(options.market_call) + 10,\n",
        "    ] )\n",
        "\n",
        "    plt.subplot(222)\n",
        "    plt.grid()\n",
        "    plt.title(\"Put Option Calibration\")\n",
        "    plt.ylabel(\"option values\")\n",
        "    color = [\"blue\", \"red\", \"deepskyblue\", \"orange\", \"green\", \"mediumvioletred\"]\n",
        "    color_idx = 0\n",
        "    for mat in options[\"Days to Maturity\"].unique():\n",
        "        opt_data = options[options[\"Days to Maturity\"] == mat]\n",
        "        plt.plot(opt_data[\"Strike\"], opt_data[\"market_put\"], color[color_idx], label=f\"market: (Maturity={mat})\")\n",
        "        plt.plot(opt_data[\"Strike\"], opt_data[\"model_put\"], color[color_idx+1], marker = \"o\", linestyle='None', label=f\"model: (Maturity={mat})\")\n",
        "        color_idx += 2\n",
        "    plt.legend(loc=0)\n",
        "    plt.axis(\n",
        "            [\n",
        "                min(options.Strike) - 1,\n",
        "                max(options.Strike) + 1,\n",
        "                min(options.market_put) - 10,\n",
        "                max(options.market_put) + 10,\n",
        "    ] )\n",
        "\n",
        "\n",
        "    # ----- difference --------\n",
        "    plt.subplot(223)\n",
        "    plt.grid()\n",
        "    wi = 2\n",
        "\n",
        "    for mat in options[\"Days to Maturity\"].unique():\n",
        "        opt_data = options[options[\"Days to Maturity\"] == mat]\n",
        "        diffs = opt_data[\"model_call\"].values - opt_data[\"market_call\"].values\n",
        "        plt.bar(opt_data[\"Strike\"].values, diffs, width=wi, alpha=0.5, label = f\"Diff. (Maturity={mat})\")\n",
        "\n",
        "        color_idx += 2\n",
        "\n",
        "    plt.ylabel(\"difference\")\n",
        "    plt.axis( [\n",
        "        min(options.Strike) - 1,\n",
        "        max(options.Strike) + 1,\n",
        "        -3,\n",
        "        3,\n",
        "    ] )\n",
        "    plt.legend(loc=0)\n",
        "    plt.tight_layout()\n",
        "\n",
        "    plt.subplot(224)\n",
        "    plt.grid()\n",
        "    wi = 2\n",
        "    for mat in options[\"Days to Maturity\"].unique():\n",
        "        opt_data = options[options[\"Days to Maturity\"] == mat]\n",
        "        diffs = opt_data[\"model_put\"].values - opt_data[\"market_put\"].values\n",
        "        plt.bar(opt_data[\"Strike\"].values, diffs, width=wi, alpha=0.5, label = f\"Diff. (Maturity={mat})\")\n",
        "\n",
        "    plt.ylabel(\"difference\")\n",
        "    plt.axis( [\n",
        "        min(options.Strike) - 1,\n",
        "        max(options.Strike) + 1,\n",
        "        -3,\n",
        "        3,\n",
        "    ] )\n",
        "    plt.legend(loc=0)\n",
        "    plt.tight_layout()"
      ],
      "metadata": {
        "id": "DJuv0l3fnAeq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "## The code is modified from Module 1 and 2 Jupyter Notebooks:\n",
        "# Develop the charactersitic function of the Heston (1993):\n",
        "def H93_char_func(u, T, r, kappa_v, theta_v, sigma_v, rho, v0):\n",
        "    c1 = kappa_v * theta_v\n",
        "    c2 = -np.sqrt(\n",
        "        (rho * sigma_v * u * 1j - kappa_v) ** 2 - sigma_v**2 * (-u * 1j - u**2)\n",
        "    )\n",
        "    c3 = (kappa_v - rho * sigma_v * u * 1j + c2) / (\n",
        "        kappa_v - rho * sigma_v * u * 1j - c2\n",
        "    )\n",
        "    H1 = r * u * 1j * T + (c1 / sigma_v**2) * (\n",
        "        (kappa_v - rho * sigma_v * u * 1j + c2) * T\n",
        "        - 2 * np.log((1 - c3 * np.exp(c2 * T)) / (1 - c3))\n",
        "    )\n",
        "    H2 = (\n",
        "        (kappa_v - rho * sigma_v * u * 1j + c2)\n",
        "        / sigma_v**2\n",
        "        * ((1 - np.exp(c2 * T)) / (1 - c3 * np.exp(c2 * T)))\n",
        "    )\n",
        "    char_func_value = np.exp(H1 + H2 * v0)\n",
        "    return char_func_value\n",
        "# Develop the integration function of the Heston (1993):\n",
        "def H93_int_func(u, S0, K, T, r, kappa_v, theta_v, sigma_v, rho, v0):\n",
        "    char_func_value = H93_char_func(\n",
        "        u - 1j * 0.5, T, r, kappa_v, theta_v, sigma_v, rho, v0\n",
        "    )\n",
        "    int_func_value = (\n",
        "        1 / (u**2 + 0.25) * (np.exp(1j * u * np.log(S0 / K)) * char_func_value).real\n",
        "    )\n",
        "    return int_func_value\n",
        "# Develop the derivative pricing function in Heston via Lewis (2001):\n",
        "def H93_call_value(S0, K, T, r, kappa_v, theta_v, sigma_v, rho, v0):\n",
        "    \"\"\"Valuation of European call option in H93 model via Lewis (2001)\n",
        "\n",
        "    Parameter definition:\n",
        "    ==========\n",
        "    S0: float\n",
        "        initial stock/index level\n",
        "    K: float\n",
        "        strike price\n",
        "    T: float\n",
        "        time-to-maturity (for t=0)\n",
        "    r: float\n",
        "        constant risk-free short rate\n",
        "    kappa_v: float\n",
        "        mean-reversion factor\n",
        "    theta_v: float\n",
        "        long-run mean of variance\n",
        "    sigma_v: float\n",
        "        volatility of variance\n",
        "    rho: float\n",
        "        correlation between variance and stock/index level\n",
        "    v0: float\n",
        "        initial level of variance\n",
        "    Returns\n",
        "    =======\n",
        "    call_value: float\n",
        "        present value of European call option\n",
        "    \"\"\"\n",
        "    int_value = quad(\n",
        "        lambda u: H93_int_func(u, S0, K, T, r, kappa_v, theta_v, sigma_v, rho, v0),\n",
        "        0,\n",
        "        np.inf,\n",
        "        limit=250,\n",
        "    )[0]\n",
        "    call_value = max(0, S0 - np.exp(-r * T) * np.sqrt(S0 * K) / np.pi * int_value)\n",
        "    return call_value\n",
        "\n",
        "\n",
        "def H93_error_function(p0):\n",
        "    \"\"\"Error function for parameter calibration via\n",
        "    Lewis (2001) Fourier approach for Heston (1993).\n",
        "    Parameters\n",
        "    ==========\n",
        "    kappa_v: float\n",
        "        mean-reversion factor\n",
        "    theta_v: float\n",
        "        long-run mean of variance\n",
        "    sigma_v: float\n",
        "        volatility of variance\n",
        "    rho: float\n",
        "        correlation between variance and stock/index level\n",
        "    v0: float\n",
        "        initial, instantaneous variance\n",
        "    Returns\n",
        "    =======\n",
        "    MSE: float\n",
        "        mean squared error\n",
        "    \"\"\"\n",
        "    global i, min_MSE\n",
        "    kappa_v, theta_v, sigma_v, rho, v0 = p0\n",
        "    if kappa_v < 0.0 or theta_v < 0.005 or sigma_v < 0.0 or rho < -1.0 or rho > 1.0:\n",
        "        return 500.0\n",
        "    if 2 * kappa_v * theta_v < sigma_v**2:\n",
        "        return 500.0\n",
        "    se = []\n",
        "    for row, option in options.iterrows():\n",
        "        model_value = H93_call_value(\n",
        "            S0,\n",
        "            option[\"Strike\"],\n",
        "            option[\"T\"],\n",
        "            option[\"r\"],\n",
        "            kappa_v,\n",
        "            theta_v,\n",
        "            sigma_v,\n",
        "            rho,\n",
        "            v0,\n",
        "        )\n",
        "        se.append((model_value - option[\"Call\"]) ** 2)\n",
        "    MSE = sum(se) / len(se)\n",
        "    min_MSE = min(min_MSE, MSE)\n",
        "    if i % 250 == 0:\n",
        "        print(\"%4d |\" % i, np.array(p0), \"| %7.3f | %7.3f\" % (MSE, min_MSE))\n",
        "    i += 1\n",
        "    return MSE\n",
        "\n",
        "def H93_calibration_full():\n",
        "    \"\"\"Calibrates Heston (1993) stochastic volatility model to market quotes.\"\"\"\n",
        "    # First run with brute force\n",
        "    # (scan sensible regions, for faster convergence)\n",
        "    p0 = brute(\n",
        "        H93_error_function,\n",
        "        (\n",
        "            (2.5, 10.6, 5.0),  # kappa_v\n",
        "            (0.01, 0.041, 0.01),  # theta_v\n",
        "            (0.05, 0.251, 0.1),  # sigma_v\n",
        "            (-0.75, 0.01, 0.25),  # rho\n",
        "            (0.01, 0.031, 0.01),\n",
        "        ),  # v0\n",
        "        finish=None,\n",
        "    )\n",
        "\n",
        "    # Second run with local, convex minimization\n",
        "    # (we dig deeper where promising results)\n",
        "    opt = fmin(\n",
        "        H93_error_function, p0, xtol=0.000001, ftol=0.000001, maxiter=1000, maxfun=2000\n",
        "    )\n",
        "    return opt\n",
        "\n",
        "def plot_full_calibration_results_heston_memberA(call_params, put_params):\n",
        "\n",
        "    options[\"model_call\"] = 0\n",
        "    options[\"model_put\"] = 0\n",
        "    for idx in range(options.shape[0]):\n",
        "#         print(options.iloc[idx, :])\n",
        "        kappa_v, theta_v, sigma_v, rho, v0 = call_params\n",
        "\n",
        "\n",
        "        options.loc[idx, \"model_call\"] = H93_call_value(\n",
        "            S0, options.loc[idx, \"Strike\"], options.loc[idx, \"T\"], options.loc[idx, \"r\"],\n",
        "            kappa_v, theta_v, sigma_v, rho, v0)\n",
        "\n",
        "        kappa_v, theta_v, sigma_v, rho, v0 = put_params\n",
        "        options.loc[idx, \"model_put\"] = H93_call_value(\n",
        "            S0, options.loc[idx, \"Strike\"], options.loc[idx, \"T\"], options.loc[idx, \"r\"],\n",
        "            kappa_v, theta_v, sigma_v, rho, v0)\n",
        "        options.loc[idx, \"model_put\"] = (\n",
        "            options.loc[idx, \"model_put\"] + options.loc[idx, \"Strike\"] * np.exp(-options.loc[idx, \"r\"] * options.loc[idx, \"T\"]) - S0\n",
        "        )\n",
        "    plt.figure(figsize=(10, 5))\n",
        "    # ------- comparison --------\n",
        "    plt.subplot(221)\n",
        "    plt.grid()\n",
        "    plt.title(\"Call Option Calibration\")\n",
        "    plt.ylabel(\"option values\")\n",
        "    color = [\"blue\", \"red\", \"deepskyblue\", \"orange\", \"green\", \"mediumvioletred\"]\n",
        "    color_idx = 0\n",
        "    for mat in options[\"Days to Maturity\"].unique():\n",
        "        opt_data = options[options[\"Days to Maturity\"] == mat]\n",
        "        plt.plot(opt_data[\"Strike\"], opt_data[\"market_call\"], color[color_idx], label=f\"market: (Maturity={mat})\")\n",
        "        plt.plot(opt_data[\"Strike\"], opt_data[\"model_call\"], color[color_idx+1], marker = \"o\", linestyle='None', label=f\"model: (Maturity={mat})\")\n",
        "        color_idx += 2\n",
        "    plt.legend(loc=0)\n",
        "    plt.axis(\n",
        "            [\n",
        "                min(options.Strike) - 1,\n",
        "                max(options.Strike) + 1,\n",
        "                min(options.market_call) - 10,\n",
        "                max(options.market_call) + 10,\n",
        "    ] )\n",
        "\n",
        "    plt.subplot(222)\n",
        "    plt.grid()\n",
        "    plt.title(\"Put Option Calibration\")\n",
        "    plt.ylabel(\"option values\")\n",
        "    color = [\"blue\", \"red\", \"deepskyblue\", \"orange\", \"green\", \"mediumvioletred\"]\n",
        "    color_idx = 0\n",
        "    for mat in options[\"Days to Maturity\"].unique():\n",
        "        opt_data = options[options[\"Days to Maturity\"] == mat]\n",
        "        plt.plot(opt_data[\"Strike\"], opt_data[\"market_put\"], color[color_idx], label=f\"market: (Maturity={mat})\")\n",
        "        plt.plot(opt_data[\"Strike\"], opt_data[\"model_put\"], color[color_idx+1], marker = \"o\", linestyle='None', label=f\"model: (Maturity={mat})\")\n",
        "        color_idx += 2\n",
        "    plt.legend(loc=0)\n",
        "    plt.axis(\n",
        "            [\n",
        "                min(options.Strike) - 1,\n",
        "                max(options.Strike) + 1,\n",
        "                min(options.market_put) - 10,\n",
        "                max(options.market_put) + 10,\n",
        "    ] )\n",
        "\n",
        "\n",
        "    # ----- difference --------\n",
        "    plt.subplot(223)\n",
        "    plt.grid()\n",
        "    wi = 2\n",
        "\n",
        "    for mat in options[\"Days to Maturity\"].unique():\n",
        "        opt_data = options[options[\"Days to Maturity\"] == mat]\n",
        "        diffs = opt_data[\"model_call\"].values - opt_data[\"market_call\"].values\n",
        "        plt.bar(opt_data[\"Strike\"].values, diffs, width=wi, alpha=0.5, label = f\"Diff. (Maturity={mat})\")\n",
        "\n",
        "        color_idx += 2\n",
        "\n",
        "    plt.ylabel(\"difference\")\n",
        "    plt.axis( [\n",
        "        min(options.Strike) - 1,\n",
        "        max(options.Strike) + 1,\n",
        "        -3,\n",
        "        3,\n",
        "    ] )\n",
        "    plt.legend(loc=0)\n",
        "    plt.tight_layout()\n",
        "\n",
        "    plt.subplot(224)\n",
        "    plt.grid()\n",
        "    wi = 2\n",
        "    for mat in options[\"Days to Maturity\"].unique():\n",
        "        opt_data = options[options[\"Days to Maturity\"] == mat]\n",
        "        diffs = opt_data[\"model_put\"].values - opt_data[\"market_put\"].values\n",
        "        plt.bar(opt_data[\"Strike\"].values, diffs, width=wi, alpha=0.5, label = f\"Diff. (Maturity={mat})\")\n",
        "\n",
        "    plt.ylabel(\"difference\")\n",
        "    plt.axis( [\n",
        "        min(options.Strike) - 1,\n",
        "        max(options.Strike) + 1,\n",
        "        -3,\n",
        "        3,\n",
        "    ] )\n",
        "    plt.legend(loc=0)\n",
        "    plt.tight_layout()"
      ],
      "metadata": {
        "id": "QZVKeRONhEkU"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Call Option Parameter Calibration\n",
        "np.random.seed(42)\n",
        "i = 0\n",
        "min_MSE = 5000\n",
        "step1_memB_calibrated_params_call = H93_calibration_full_carr_ma_call()\n",
        "\n",
        "print(step1_memB_calibrated_params_call)"
      ],
      "metadata": {
        "id": "EJiGaIxuMnPT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0705fa51-e244-4bad-c618-ea6cc1ef98d6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "   0 | [ 2.5   0.01  0.05 -0.75  0.01] |   0.940 |   0.940\n",
            " 100 | [ 2.5   0.04  0.05 -0.5   0.02] |   8.302 |   0.863\n",
            " 200 | [ 7.5   0.02  0.25 -0.25  0.03] |  13.673 |   0.815\n",
            " 300 | [7.56755922e+00 9.96640060e-03 2.82117744e-01 2.05539418e-04\n",
            " 7.96585042e-03] |   0.646 |   0.638\n",
            "Optimization terminated successfully.\n",
            "         Current function value: 0.636310\n",
            "         Iterations: 117\n",
            "         Function evaluations: 262\n",
            "[ 7.91532543e+00  9.41904524e-03  3.86147140e-01 -2.10843147e-03\n",
            "  8.86924109e-03]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Put Option Parameter Calibration\n",
        "np.random.seed(42)\n",
        "i = 0\n",
        "min_MSE = 5000\n",
        "step1_memB_calibrated_params_put = H93_calibration_full_carr_ma_put()\n",
        "\n",
        "print(step1_memB_calibrated_params_put)"
      ],
      "metadata": {
        "id": "TM1Lu7BOhvlz",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6fd134bf-3471-4136-b994-316233409baf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "   0 | [ 2.5   0.01  0.05 -0.75  0.01] |   1.850 |   1.850\n",
            " 100 | [ 2.5   0.04  0.05 -0.5   0.02] |  12.373 |   1.584\n",
            " 200 | [ 7.5   0.02  0.25 -0.25  0.03] |  18.978 |   1.459\n",
            " 300 | [8.13616431e+00 1.00300409e-02 2.81559167e-01 4.80743413e-04\n",
            " 6.34587523e-03] |   0.187 |   0.147\n",
            " 400 | [8.31921341e+00 1.01221826e-02 2.95547759e-01 3.86484764e-04\n",
            " 5.57637819e-03] |   0.137 |   0.137\n",
            " 500 | [ 7.62548877e+00  8.76299959e-03  3.64729005e-01 -3.38733320e-04\n",
            "  6.28448766e-03] |   0.136 |   0.136\n",
            "Optimization terminated successfully.\n",
            "         Current function value: 0.136403\n",
            "         Iterations: 210\n",
            "         Function evaluations: 417\n",
            "[ 7.61957375e+00  8.75429689e-03  3.65250620e-01 -3.41571955e-04\n",
            "  6.28517863e-03]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Visualization:\n",
        "plot_full_calibration_results_heston_memberB(step1_memB_calibrated_params_call, step1_memB_calibrated_params_put)"
      ],
      "metadata": {
        "id": "NCBu7HO-h0Ui",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 507
        },
        "outputId": "c7e8dfef-8fb7-43c4-86ad-9beb0f176d4d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 4 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Step 2 - Team member B\n",
        "70 days maturity and moneyness of 95%"
      ],
      "metadata": {
        "id": "KbhOlWYlJ6b4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Set seed\n",
        "np.random.seed(42)\n",
        "\n",
        "# Input Parameters.\n",
        "S0  = 232\n",
        "K= S0 * 0.95 # Moneyness of 95% Strike\n",
        "r = 0.015\n",
        "sigma = 0.35\n",
        "\n",
        "M = 70  # Maturity changed to 70 days\n",
        "T = M / 365\n",
        "Ite = 500000  # Number of simulations\n",
        "dt = 1 / 365\n",
        "\n",
        "# Heston model\n",
        "def SDE_vol(v0, kappa, theta, sigma, T, M, Ite, rand, row, cho_matrix):\n",
        "    dt = T / M  # T = maturity, M = number of time steps\n",
        "    v = np.zeros((M + 1, Ite), dtype=np.float)\n",
        "    v[0] = v0\n",
        "    sdt = np.sqrt(dt)  # Sqrt of dt\n",
        "    for t in range(1, M + 1):\n",
        "        ran = np.dot(cho_matrix, rand[:, t])\n",
        "        v[t] = np.maximum(\n",
        "            0,\n",
        "            v[t - 1]\n",
        "            + kappa * (theta - v[t - 1]) * dt\n",
        "            + np.sqrt(v[t - 1]) * sigma * ran[row] * sdt,\n",
        "        )\n",
        "    return v\n",
        "\n",
        "def Heston_paths(S0, r, v, row, cho_matrix, rand):\n",
        "    S = np.zeros((M + 1, Ite), dtype=float)\n",
        "    S[0] = S0\n",
        "    sdt = np.sqrt(dt)\n",
        "    for t in range(1, M + 1, 1):\n",
        "        ran = np.dot(cho_matrix, rand[:, t])\n",
        "        S[t] = S[t - 1] * np.exp((r - 0.5 * v[t]) * dt + np.sqrt(v[t]) * ran[row] * sdt)\n",
        "\n",
        "    return S\n",
        "\n",
        "def heston_simulation(v0, kappa, theta, sigma, rho,\n",
        "                      S0, r, T, M, Ite):\n",
        "  # generate random numbers\n",
        "  rand = np.random.standard_normal((2, M + 1, Ite))\n",
        "\n",
        "  # Covariance Matrix\n",
        "  covariance_matrix = np.zeros((2, 2), dtype=np.float)\n",
        "  covariance_matrix[0] = [1.0, rho]\n",
        "  covariance_matrix[1] = [rho, 1.0]\n",
        "  cho_matrix = np.linalg.cholesky(covariance_matrix)\n",
        "\n",
        "  # Volatility process paths\n",
        "  V = SDE_vol(v0, kappa, theta, sigma, T, M, Ite, rand, 1, cho_matrix)\n",
        "\n",
        "  # Underlying price process paths\n",
        "  S = Heston_paths(S0, r, V, 0, cho_matrix, rand)\n",
        "\n",
        "  return S\n",
        "\n",
        "# Monte_Carlo method for Asian Option via Heston (1993) model:\n",
        "def heston_asian_option_mc(S, K, r, T, t, optype):\n",
        "\n",
        "    if optype in ['c', 'call']:\n",
        "      payoff = np.maximum(0, np.mean(S, 0) - K)\n",
        "    elif optype in ['p', 'put']:\n",
        "      payoff = np.maximum(0, K - np.mean(S, 0))\n",
        "    else:\n",
        "      raise ValueError()\n",
        "\n",
        "    average = np.mean(payoff)\n",
        "\n",
        "    return np.exp(-r * (T - t)) * average\n",
        "\n",
        "S_heston = heston_simulation(0.01005242,\n",
        "                             5.07543848,\n",
        "                             0.03325956,\n",
        "                             0.56321925,\n",
        "                             -0.63875854,\n",
        "                             S0, r, T, M, Ite)\n",
        "heston_call_price = heston_asian_option_mc(S_heston, K, r, T, dt, optype='c')\n",
        "heston_put_price = heston_asian_option_mc(S_heston, K, r, T, dt, optype='p')\n",
        "\n",
        "paid_call_price = heston_call_price * 1.04\n",
        "paid_put_price = heston_put_price * 1.04\n",
        "\n",
        "pd.DataFrame(\n",
        "    {\n",
        "      \"Call\": [heston_call_price, paid_call_price],\n",
        "      \"Put\": [heston_put_price, paid_put_price],\n",
        "   },\n",
        "   index=[\"Price\", 'Paid price']\n",
        ").round(2)"
      ],
      "metadata": {
        "id": "-inJqlwdKCoP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 236
        },
        "outputId": "dab0bda1-5629-4080-e588-280e0ce8cbe2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-13-603691870e94>:47: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
            "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
            "  covariance_matrix = np.zeros((2, 2), dtype=np.float)\n",
            "<ipython-input-13-603691870e94>:18: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
            "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
            "  v = np.zeros((M + 1, Ite), dtype=np.float)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "            Call   Put\n",
              "Price       8.54  0.63\n",
              "Paid price  8.88  0.66"
            ],
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              "      <th>Price</th>\n",
              "      <td>8.54</td>\n",
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          },
          "metadata": {},
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        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Step 1: Team member C"
      ],
      "metadata": {
        "id": "lxGSof7QdGlu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def asian_option_mc(S_ini, K, T, r, sigma, N, M):\n",
        "    dt = T / N  # Define time step\n",
        "    u = np.exp(sigma * np.sqrt(dt))  # Define u\n",
        "    d = np.exp(-sigma * np.sqrt(dt))  # Define d\n",
        "    p = (np.exp(r * dt) - d) / (u - d)  # risk neutral probs\n",
        "    Asian = np.zeros([M])  # Asian prices\n",
        "    S = np.zeros([M, N + 1])  # underlying price\n",
        "    S[:, 0] = S_ini\n",
        "\n",
        "    for j in range(0, M):\n",
        "        random = np.random.binomial(1, p, N + 1)\n",
        "        Total = S_ini\n",
        "        for i in range(1, N + 1):\n",
        "            if random[i] == 1:\n",
        "                S[j, i] = S[j, i - 1] * u\n",
        "                Total = Total + S[j, i]\n",
        "            else:\n",
        "                S[j, i] = S[j, i - 1] * d\n",
        "                Total = Total + S[j, i]\n",
        "\n",
        "        Asian[j] = np.exp(-r * T) * max(Total / (N + 1) - K, 0)\n",
        "\n",
        "    return S, Asian"
      ],
      "metadata": {
        "id": "ses0kuFNc_Ih"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "S, Asian = asian_option_mc(232.90, 232.90, 20/250, 0.015, 0.01005242, 20, 10000)"
      ],
      "metadata": {
        "id": "_rSwzv4ndCxS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(np.mean(Asian)*1.04)"
      ],
      "metadata": {
        "id": "n6JcXcU3dOKj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We used the variance that calibrated from the bates model to compute the asian options, and we also get the risk-neutral probabilities in our calculations. At the final pricing of the options we include the 4% charge as well."
      ],
      "metadata": {
        "id": "S_3hMFVJdRyI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Step 2 : Team member C"
      ],
      "metadata": {
        "id": "jUsmwUcMKwdQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Import Options File\n",
        "google_drive_link = \"https://docs.google.com/spreadsheets/d/1aWg1hoNmdXHnvRFn0LvhbHqNEBWmwmiN/edit?usp=sharing&ouid=111861681755998244691&rtpof=true&sd=true\"\n",
        "local_file_path = \"/content/drive/MyDrive/WQU Stochastic Modelling/options_data.xlsx\"\n",
        "options_df = load_excel_from_google_drive(google_drive_link, local_file_path)\n",
        "\n",
        "# Pivot the DataFrame to have separate columns for call and put prices\n",
        "pivot_df = options_df.pivot_table(index=[\"Days to maturity\", \"Strike\"], columns=\"Type\", values=\"Price\").reset_index()\n",
        "\n",
        "# Rename columns for clarity\n",
        "pivot_df.rename(columns={\"C\": \"Call\", \"P\": \"Put\"}, inplace=True)\n",
        "\n",
        "# Fill any missing values with 0 if necessary\n",
        "pivot_df.fillna(0, inplace=True)\n",
        "pivot_df.head()\n",
        "\n",
        "S0 = 232.90\n",
        "\n",
        "# Option Selection\n",
        "tol = 0.02  # Tolerance level to select ATM options (percent around ITM/OTM options)\n",
        "options = pivot_df[(np.abs(pivot_df[\"Strike\"] - S0) / S0) < tol]\n",
        "\n",
        "for row, option in options.iterrows():\n",
        "    T = (option[\"Days to maturity\"]) / 250 # Convert Days to Maturity to years\n",
        "    options.loc[row, \"T\"] = T\n",
        "    options.loc[row, \"r\"] = 0.015  # Constant short-rate"
      ],
      "metadata": {
        "id": "CCdLmrEVM5Y-"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Option Parameters\n",
        "S0 = 232.90\n",
        "K = 232.90\n",
        "T = 60/250\n",
        "r = 0.015\n",
        "\n",
        "# Heston(1993) Parameters for Asian Options\n",
        "kappa_v = 1.5     # Mean-reversion factor for variance\n",
        "theta_v = 0.02    # Long-run mean of variance\n",
        "sigma_v = 0.1     # Volatility of variance\n",
        "rho = 0.25        # Correlation between variance and stock/index level\n",
        "v0 = 0.01         # Initial level of variance\n",
        "\n",
        "N = 10\n",
        "M = 100\n",
        "seed_value = 42\n",
        "\n",
        "\n",
        "i = 0\n",
        "min_MSE = 500\n"
      ],
      "metadata": {
        "id": "2PfOBgvpM7m5"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# General Parameters\n",
        "S0 = 100\n",
        "K = 100\n",
        "T = 1\n",
        "r = 0.05\n",
        "\n",
        "# Heston'93 Parameters\n",
        "kappa_v = 1.5\n",
        "theta_v = 0.02\n",
        "sigma_v = 0.15\n",
        "rho = 0.1\n",
        "v0 = 0.01\n",
        "\n",
        "# Merton'76 Parameters\n",
        "lamb = 0.25\n",
        "mu = -0.2\n",
        "delta = 0.1\n",
        "sigma = np.sqrt(v0)"
      ],
      "metadata": {
        "id": "F--3AJN1LACv"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "params = B96_calibration_short()"
      ],
      "metadata": {
        "id": "uzcTLzGJRSpw"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def B96_jump_calculate_model_values(p0):\n",
        "    \"\"\"Calculates all model values given parameter vector p0.\"\"\"\n",
        "    lamb, mu, delta = p0\n",
        "    values = []\n",
        "    for row, option in options.iterrows():\n",
        "        T = (option[\"Maturity\"] - option[\"Date\"]).days / 365.0\n",
        "        r = 0.02\n",
        "        model_value = B96_call_value(\n",
        "            S0,\n",
        "            option[\"Strike\"],\n",
        "            T,\n",
        "            r,\n",
        "            kappa_v,\n",
        "            theta_v,\n",
        "            sigma_v,\n",
        "            rho,\n",
        "            v0,\n",
        "            lamb,\n",
        "            mu,\n",
        "            delta,\n",
        "        )\n",
        "        values.append(model_value)\n",
        "    return np.array(values)"
      ],
      "metadata": {
        "id": "UT9Efu_eV0Wi"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "p0 = [kappa_v, theta_v, sigma_v, rho, v0, lamb, mu, delta]"
      ],
      "metadata": {
        "id": "0zpupyzHWRUk"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "i = 0\n",
        "min_MSE = 5000.0\n",
        "\n",
        "\n",
        "def B96_full_error_function(p0):\n",
        "    global i, min_MSE\n",
        "    kappa_v, theta_v, sigma_v, rho, v0, lamb, mu, delta = p0\n",
        "\n",
        "    if (\n",
        "        kappa_v < 0.0\n",
        "        or theta_v < 0.005\n",
        "        or sigma_v < 0.0\n",
        "        or rho < -1.0\n",
        "        or rho > 1.0\n",
        "        or v0 < 0.0\n",
        "        or lamb < 0.0\n",
        "        or mu < -0.6\n",
        "        or mu > 0.0\n",
        "        or delta < 0.0\n",
        "    ):\n",
        "        return 5000.0\n",
        "\n",
        "    if 2 * kappa_v * theta_v < sigma_v**2:\n",
        "        return 5000.0\n",
        "\n",
        "    se = []\n",
        "    for row, option in options.iterrows():\n",
        "        model_value = B96_call_value(\n",
        "            S0,\n",
        "            option[\"Strike\"],\n",
        "            option[\"T\"],\n",
        "            option[\"r\"],\n",
        "            kappa_v,\n",
        "            theta_v,\n",
        "            sigma_v,\n",
        "            rho,\n",
        "            v0,\n",
        "            lamb,\n",
        "            mu,\n",
        "            delta,\n",
        "        )\n",
        "        se.append((model_value - option[\"Call\"]) ** 2)\n",
        "\n",
        "    MSE = sum(se) / len(se)\n",
        "    min_MSE = min(min_MSE, MSE)\n",
        "    if i % 25 == 0:\n",
        "        print(\"%4d |\" % i, np.array(p0), \"| %7.3f | %7.3f\" % (MSE, min_MSE))\n",
        "    i += 1\n",
        "    return MSE"
      ],
      "metadata": {
        "id": "VRMZPFIsWSMS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def B96_calibration_full():\n",
        "    opt = fmin(\n",
        "        B96_full_error_function, p0, xtol=0.001, ftol=0.001, maxiter=1250, maxfun=650\n",
        "    )\n",
        "    return opt"
      ],
      "metadata": {
        "id": "MsaicbxmWWFi"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def B96_calculate_model_values(p0):\n",
        "    kappa_v, theta_v, sigma_v, rho, v0, lamb, mu, delta = p0\n",
        "    values = []\n",
        "    for row, option in options.iterrows():\n",
        "        model_value = B96_call_value(\n",
        "            S0,\n",
        "            option[\"Strike\"],\n",
        "            option[\"T\"],\n",
        "            option[\"r\"],\n",
        "            kappa_v,\n",
        "            theta_v,\n",
        "            sigma_v,\n",
        "            rho,\n",
        "            v0,\n",
        "            lamb,\n",
        "            mu,\n",
        "            delta,\n",
        "        )\n",
        "\n",
        "        values.append(model_value)\n",
        "\n",
        "    return np.array(values)"
      ],
      "metadata": {
        "id": "80XsZ-uHWYWm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "full_params = B96_calibration_full()"
      ],
      "metadata": {
        "id": "uBxUQLHPWdKz"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_full_calibration_results(p0):\n",
        "    options[\"Model\"] = B96_calculate_model_values(p0)\n",
        "    plt.figure(figsize=(8, 6))\n",
        "    plt.subplot(211)\n",
        "    plt.grid()\n",
        "    plt.title(\"Maturity %s\" % str(options[\"Maturity\"].iloc[0])[:10])\n",
        "    plt.ylabel(\"option values\")\n",
        "    plt.plot(options.Strike, options.Call, \"b\", label=\"market\")\n",
        "    plt.plot(options.Strike, options.Model, \"ro\", label=\"model\")\n",
        "    plt.legend(loc=0)\n",
        "    plt.axis(\n",
        "        [\n",
        "            min(options.Strike) - 10,\n",
        "            max(options.Strike) + 10,\n",
        "            min(options.Call) - 10,\n",
        "            max(options.Call) + 10,\n",
        "        ]\n",
        "    )\n",
        "    plt.subplot(212)\n",
        "    plt.grid()\n",
        "    wi = 5.0\n",
        "    diffs = options.Model.values - options.Call.values\n",
        "    plt.bar(options.Strike.values - wi / 2, diffs, width=wi)\n",
        "    plt.ylabel(\"difference\")\n",
        "    plt.axis(\n",
        "        [\n",
        "            min(options.Strike) - 10,\n",
        "            max(options.Strike) + 10,\n",
        "            min(diffs) * 1.1,\n",
        "            max(diffs) * 1.1,\n",
        "        ]\n",
        "    )\n",
        "    plt.tight_layout()"
      ],
      "metadata": {
        "id": "X6c4mAtBWltg"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plot_full_calibration_results(full_params)"
      ],
      "metadata": {
        "id": "Et9tA_b2Wq-7"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "kappa_v, theta_v, sigma_v, rho, v0, lamda, mu, delta = full_params"
      ],
      "metadata": {
        "id": "knOyHC_qYUtQ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "H93_asian_call_value(S0, K, T, r, kappa_v, theta_v, sigma_v, rho, v0, N, M, seed_value)"
      ],
      "metadata": {
        "id": "iC-Cfy-fLEp6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "H93_asian_put_value(S0, K, T, r, kappa_v, theta_v, sigma_v, rho, v0, N, M, seed_value)"
      ],
      "metadata": {
        "id": "F3T_Cy35Ymtk"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Step 3: Part A"
      ],
      "metadata": {
        "id": "pjaoHLjHdZyr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mat_list = np.array((7, 30, 90, 180, 360)) / 360\n",
        "rate_list = (\n",
        "    np.array((0.648, 0.679, 1.173, 1.809, 2.556)) / 100\n",
        ")"
      ],
      "metadata": {
        "id": "AVLfsU5RdVKp"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "r0 = rate_list[0]\n",
        "factors = 1 + mat_list * rate_list\n",
        "zero_rates = 1 / mat_list * np.log(factors)"
      ],
      "metadata": {
        "id": "tCp79vtZdgc2"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.interpolate import splev, splrep\n",
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "muqp5188djZN"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "bspline = splrep(mat_list, zero_rates, k=3)  # Cubic spline\n",
        "mat_list_n = np.linspace(\n",
        "    0.0, 1.0, 24\n",
        ")  # Create 24 equally spaced maturities between 0 and 1\n",
        "inter_rates = splev(mat_list_n, bspline, der=0)  # Interpolated rates\n",
        "\n",
        "first_der = splev(mat_list_n, bspline, der=1)  # First derivative of spline\n",
        "f = (\n",
        "    inter_rates + first_der * mat_list_n\n",
        ")  # Forward rate given interpolated ones and first derivative"
      ],
      "metadata": {
        "id": "nlhKtZVndl1c"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(12, 6))\n",
        "plt.plot(mat_list, zero_rates, \"r.\", markersize=\"15\", label=\"Market quotes\")\n",
        "plt.plot(mat_list_n, inter_rates, \"--\", markersize=\"10\", label=\"Interpolation\")\n",
        "plt.plot(mat_list_n, first_der, \"g--\", markersize=\"10\", label=\"1st derivative\")\n",
        "plt.xlabel(\"Time Horizon\")\n",
        "plt.ylabel(\"Zero forward rate\")\n",
        "plt.title(\"Term Structure Euribor\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "5oU_MCTldqXw"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def CIR_forward_rate(alpha):\n",
        "    \"\"\"\n",
        "    Forward rates in CIR (1985) model\n",
        "    The set of parameters is called alpha and include Kappa_r, Theta_r and Sigma_r\n",
        "    \"\"\"\n",
        "\n",
        "    kappa_r, theta_r, sigma_r = alpha\n",
        "\n",
        "    t = mat_list_n\n",
        "    g = np.sqrt(kappa_r**2 + 2 * sigma_r**2)\n",
        "\n",
        "    s1 = (kappa_r * theta_r * (np.exp(g * t) - 1)) / (\n",
        "        2 * g + (kappa_r + g) * (np.exp(g * t) - 1)\n",
        "    )\n",
        "\n",
        "    s2 = r0 * (\n",
        "        (4 * g**2 * np.exp(g * t)) / (2 * g + (kappa_r + g) * (np.exp(g * t)) ** 2)\n",
        "    )\n",
        "\n",
        "    return s1 + s2"
      ],
      "metadata": {
        "id": "neBZZmQkdtGI"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def CIR_error_function(alpha):\n",
        "    \"\"\"\n",
        "    Error function to calibrate CIR (1985) model\n",
        "    \"\"\"\n",
        "\n",
        "    kappa_r, theta_r, sigma_r = alpha\n",
        "\n",
        "    # Few remarks to avoid problems for certain values of parameters:\n",
        "    if 2 * kappa_r * theta_r < sigma_r**2:\n",
        "        return 100\n",
        "    if kappa_r < 0 or theta_r < 0 or sigma_r < 0.001:\n",
        "        return 100\n",
        "\n",
        "    forward_rates = CIR_forward_rate(alpha)\n",
        "    MSE = np.sum((f - forward_rates) ** 2) / len(f)\n",
        "\n",
        "    return MSE"
      ],
      "metadata": {
        "id": "sCag-XogdxuO"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.optimize import fmin"
      ],
      "metadata": {
        "id": "XD8Wyd8td4Tq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def CIR_calibration():\n",
        "    opt = fmin(\n",
        "        CIR_error_function,\n",
        "        [1.0, 0.02, 0.1],\n",
        "        xtol=0.00001,\n",
        "        ftol=0.00001,\n",
        "        maxiter=300,\n",
        "        maxfun=500,\n",
        "    )\n",
        "\n",
        "    return opt"
      ],
      "metadata": {
        "id": "DJlJsHHGeA7L"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "params = CIR_calibration()\n",
        "k = params[0]\n",
        "theta = params[1]\n",
        "sigma = params[2]"
      ],
      "metadata": {
        "id": "FtqU8XsMeLEu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_calibrated_frc(opt):\n",
        "    \"\"\"Plots market and calibrated forward rate curves.\"\"\"\n",
        "    forward_rates = CIR_forward_rate(opt)\n",
        "    plt.figure(figsize=(12, 8))\n",
        "    plt.subplot(211)\n",
        "    plt.title(\"CIR model calibration\")\n",
        "    plt.ylabel(\"Forward rate $f(0,T)$\")\n",
        "    plt.plot(mat_list_n, f, \"ro\", label=\"market\")\n",
        "    plt.plot(mat_list_n, forward_rates, \"b--\", label=\"model\")\n",
        "    plt.legend(loc=0)\n",
        "    plt.axis(\n",
        "        [min(mat_list_n) - 0.05, max(mat_list_n) + 0.05, min(f) - 0.005, max(f) * 1.1]\n",
        "    )\n",
        "    plt.subplot(212)\n",
        "    wi = 0.02\n",
        "    plt.bar(mat_list_n - wi / 2, forward_rates - f, width=wi)\n",
        "    plt.xlabel(\"Time horizon\")\n",
        "    plt.ylabel(\"Difference\")\n",
        "    plt.axis(\n",
        "        [\n",
        "            min(mat_list_n) - 0.05,\n",
        "            max(mat_list_n) + 0.05,\n",
        "            min(forward_rates - f) * 1.1,\n",
        "            max(forward_rates - f) * 1.1,\n",
        "        ]\n",
        "    )\n",
        "    plt.tight_layout()"
      ],
      "metadata": {
        "id": "BXGib3_0eTPR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plot_calibrated_frc(params)"
      ],
      "metadata": {
        "id": "rAkopvE2eV-o"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "H93_asian_call_value(S0, K, T, r, kappa_v, theta_v, sigma_v, rho, v0, N, M, seed_value)"
      ],
      "metadata": {
        "id": "dEMr_x7mXbPI"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Stpe 3: Part B"
      ],
      "metadata": {
        "id": "ktURou06edPV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def cir(r0, k, theta, sigma, T, N, M):\n",
        "    dt = T / N\n",
        "    rates = np.zeros((N, M))\n",
        "    rates[0, :] = r0\n",
        "    for j in range(M):\n",
        "        for i in range(1, N):\n",
        "            dr = (\n",
        "                k * (theta - rates[i - 1, j]) * dt\n",
        "                + sigma\n",
        "                * np.sqrt(dt)\n",
        "                * np.sqrt(np.maximum(rates[i - 1, j], 0))\n",
        "                * np.random.normal()\n",
        "            )\n",
        "            rates[i, j] = rates[i - 1, j] + dr\n",
        "    return rates"
      ],
      "metadata": {
        "id": "S_j86Ok-ebEc"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "M = 100000  # Number of paths for MC\n",
        "N = 250  # Number of steps, trading days in a year\n",
        "T = 1.0  # Maturity\n",
        "t = np.linspace(0, T, N)\n",
        "\n",
        "rates_cir = cir(r0, k, theta, sigma, T, N, M)"
      ],
      "metadata": {
        "id": "eAMvHdgrehk8"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "max_euri = np.average(rates_cir[-1,:]) + 1.96 * sigma/(np.sqrt(M))\n",
        "min_euri = np.average(rates_cir[-1,:]) - 1.96 * sigma/(np.sqrt(M))"
      ],
      "metadata": {
        "id": "hix80omiekVV"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(f'The maximum 12-month Euribor is {max_euri}')\n",
        "print(f'The minimum 12-month Euribor is {min_euri}')"
      ],
      "metadata": {
        "id": "Fr0__Gs5enpW"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "for j in range(M):\n",
        "    plt.plot(t, rates_cir[:, j])\n",
        "\n",
        "plt.xlabel(\"Time $t$\", fontsize=14)\n",
        "plt.ylabel(\"$r(t)$\", fontsize=14)\n",
        "plt.title(\"CIR Paths\", fontsize=14)\n",
        "axes = plt.gca()\n",
        "axes.set_xlim([0, T])\n",
        "plt.xticks(fontsize=14)\n",
        "plt.yticks(fontsize=14)\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "d4hogtmNesxr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(f'The expected value of 12-month Euribor in 1 year is {np.average(rates_cir)}')"
      ],
      "metadata": {
        "id": "WyzAUmM4ev5Z"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def asian_put_option_mc(S_ini, K, T, r, sigma, N, M):\n",
        "    dt = T / N  # Define time step\n",
        "    u = np.exp(sigma * np.sqrt(dt))  # Define u\n",
        "    d = np.exp(-sigma * np.sqrt(dt))  # Define d\n",
        "    p = (np.exp(r * dt) - d) / (u - d)  # risk neutral probs\n",
        "    Asian = np.zeros([M])  # Asian prices\n",
        "    S = np.zeros([M, N + 1])  # underlying price\n",
        "    S[:, 0] = S_ini\n",
        "\n",
        "    for j in range(0, M):\n",
        "        random = np.random.binomial(1, p, N + 1)\n",
        "        Total = S_ini\n",
        "        for i in range(1, N + 1):\n",
        "            if random[i] == 1:\n",
        "                S[j, i] = S[j, i - 1] * u\n",
        "                Total = Total + S[j, i]\n",
        "            else:\n",
        "                S[j, i] = S[j, i - 1] * d\n",
        "                Total = Total + S[j, i]\n",
        "\n",
        "        Asian[j] = np.exp(-r * T) * max(K - Total / (N + 1), 0)\n",
        "\n",
        "    return S, Asian"
      ],
      "metadata": {
        "id": "A2z5uQVKgkJR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "S1, Asian1 = asian_option_mc(232.90, 232.90, 20/250, 0.043688484598803326, 0.01005242, 20, 10000)\n",
        "S2, Asian2 = asian_put_option_mc(232.90, 232.90, 20/250, 0.043688484598803326, 0.01005242, 20, 10000)\n",
        "asian_call_f = np.mean(Asian1)\n",
        "asian_put_f = np.mean(Asian2)\n",
        "print(f'The asian call option will be {asian_call_f}')\n",
        "print(f'The asian put option will be {asian_put_f}')"
      ],
      "metadata": {
        "id": "AKvhmBe_ezC6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "S3, Asian3 = asian_option_mc(232.90, 232.90, 20/250, 2.556/100, 0.01005242, 20, 10000)\n",
        "S4, Asian4 = asian_put_option_mc(232.90, 232.90, 20/250, 2.556/100, 0.01005242, 20, 10000)\n",
        "asian_call_f1 = np.mean(Asian3)\n",
        "asian_put_f1 = np.mean(Asian4)\n",
        "print(f\"The difference between the new 12-month Euribor and the current 12-month Euribor for the asian call options pricing are {asian_call_f-asian_call_f1}\")\n",
        "print(f\"The difference between the new 12-month Euribor and the current 12-month Euribor for the asian put options pricing are {asian_put_f-asian_put_f1}\")"
      ],
      "metadata": {
        "id": "KCvhN2cWdeE3"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}