Markov functional model

[MarcusRainbow]

The problem with the BlackDiffusion model is that it only reprices one European option correctly -- the at the money forward option that has the same strike that the BlackDiffusion model uses.

We can wrap this model in one that applies a QQ-map (see Quantile-Quantile plot in Wikipedia) to correct the values of European options at other strikes. It can do this by calibrating a QQ-map to the values of European options, then adjusting the weights of the paths accordingly.

This model need not only be used as a decorator to the BlackDiffusion model. It can be used to correct any model that does not exactly reprice Europeans -- for example Heston.