notebook/curve_v1_imbalance_fee.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c11576d4-bbac-4947-b122-ce228c1ec764",
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install matplotlib\n",
    "!pip install scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "105cd711-9d47-4423-a048-d127b38e643c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import fsolve\n",
    "import math\n",
    "\n",
    "def k(x0, x1, x2, A, D):\n",
    "    return A*x0*x1*x2/(D/3)**3\n",
    "\n",
    "def f(x0, x1, x2, A, D):\n",
    "    k0 = k(x0, x1, x2, A, D)\n",
    "    return x0*x1*x2 + k0*(x0+x1+x2)*(D**2) - (D/3)**3 - k0*D**3\n",
    "\n",
    "def calc_D(x0, x1, x2, A, D0):\n",
    "    def f_D(D, x0, x1, x2, A):\n",
    "        return f(x0, x1, x2, A, D)\n",
    "    return fsolve(f_D, D0, args=(x0, x1, x2, A))[0]\n",
    "\n",
    "# calc y for x0\n",
    "def calc_x0(x0, x1, x2, A, D):\n",
    "    return fsolve(f, x0, args=(x1, x2, A, D))[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c3219ad3-0bd2-4205-886f-f90395472fb5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-376.05791446736555, -84.61303075515724, -103.4159264785255]\n",
      "[3.7605791446736556, 0.8461303075515724, 1.034159264785255]\n",
      "299.8991189141142 581.8477119377197 576.3775010104971\n"
     ]
    }
   ],
   "source": [
    "# Add liquidity\n",
    "# balances\n",
    "b0 = [100, 90, 110]\n",
    "a = [300, 0, 0]\n",
    "b1 = [b0[0] + a[0], b0[1] + a[1], b0[2] + a[2]]\n",
    "\n",
    "A = 1\n",
    "fee = 0.01\n",
    "\n",
    "D0 = calc_D(b0[0], b0[1], b0[2], A, sum(b0) / 3)\n",
    "D1 = calc_D(b1[0], b1[1], b1[2], A, D0)\n",
    "\n",
    "# imbalance fees\n",
    "i_bals = [D1 / D0 * b for b in b1]\n",
    "diffs = [b - bi for (b, bi) in zip(b1, i_bals)]\n",
    "fees = [abs(d) * fee for d in diffs]\n",
    "b2 = [b - f for (b, f) in zip(b1, fees)]\n",
    "\n",
    "D2 = calc_D(b2[0], b2[1], b2[2], A, D1)\n",
    "\n",
    "print(diffs)\n",
    "print(fees)\n",
    "print(D0, D1, D2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a2ac3db5-2b03-4179-84d3-a6452bc1660a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Doesn't work on GitHub\n",
    "# plt.style.use('dark_background')\n",
    "\n",
    "x = [0, 1, 2]\n",
    "\n",
    "plt.bar(x, b1, color = \"tab:orange\", label = \"b1\")\n",
    "plt.bar(x, b_ideal, color = \"tab:green\", label = \"b ideal\")\n",
    "plt.bar(x, b0, color = \"tab:blue\", label = \"b0\")\n",
    "plt.axhline(D0 / 3, ls = \"--\", label = \"D0 / 3\", color = \"tab:blue\")\n",
    "plt.axhline(D1 / 3, ls = \"--\", label = \"D1 / 3\", color = \"tab:orange\")\n",
    "\n",
    "for i in x:\n",
    "    label = \"diff\" if i == 0 else None\n",
    "    plt.plot([i + 0.5, i + 0.5], [b_ideal[i], b_ideal[i] + diff[i]], color = 'blueviolet', linestyle = '-', linewidth = 2, label = label)\n",
    "\n",
    "plt.xticks([0, 1, 2], [\"DAI\", \"USDC\", \"USDT\"])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "182c085a-3851-4d4c-a0f3-b5aa31bd6cd2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-38.02847166646812, 18.0, 22.0]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Remove liquidity one coin\n",
    "# balances\n",
    "b0 = [100, 90, 110]\n",
    "\n",
    "A = 1\n",
    "# Initial guess to find D0\n",
    "D0 = sum(b0) / 3\n",
    "\n",
    "D0 = calc_D(b0[0], b0[1], b0[2], A, D0)\n",
    "D1 = 0.8 * D0\n",
    "\n",
    "b1 = [b for b in b0]\n",
    "b1[0] = calc_x0(b0[0], b0[1], b0[2], A, D1)\n",
    "\n",
    "b_ideal = [D1 / D0 * b for b in b0]\n",
    "diff = [b - bi for (b, bi) in zip(b1, b_ideal)]\n",
    "\n",
    "diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f2033727-96ff-4deb-b78c-255bc7d7616f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Doesn't work on GitHub\n",
    "# plt.style.use('dark_background')\n",
    "\n",
    "x = [0, 1, 2]\n",
    "\n",
    "plt.bar(x, b0, color = \"tab:blue\", label = \"b0\")\n",
    "plt.bar(x, b_ideal, color = \"tab:green\", label = \"b ideal\")\n",
    "# Only withdrawing x0 so b1[i] = b0[i] for i = 1, 2\n",
    "plt.bar([0], [b1[0]], color = \"tab:orange\", label = \"b1\")\n",
    "\n",
    "plt.axhline(D0 / 3, ls = \"--\", label = \"D0 / 3\", color = \"tab:blue\")\n",
    "plt.axhline(D1 / 3, ls = \"--\", label = \"D1 / 3\", color = \"tab:orange\")\n",
    "\n",
    "for i in x:\n",
    "    label = \"diff\" if i == 0 else None\n",
    "    plt.plot([i + 0.5, i + 0.5], [b_ideal[i], b_ideal[i] + diff[i]], color = 'blueviolet', linestyle = '-', linewidth = 2, label = label)\n",
    "\n",
    "plt.xticks([0, 1, 2], [\"DAI\", \"USDC\", \"USDT\"])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}