Heston Model 

This is a very interesting  project. Heston uses a Stochastic Differential Equation to model the behaviour of stock prices, then solves it using a Fourier Transform There is also the Millstein discretization for Monte Carlo. Naturally the Monte Carlo is a bit slower than the Heston solution.

There are problems with the usual assumption of a log normal distribution of stock prices, the most important discrepancy is to be found in the tails and in time dependent volatility. To get a more accurate model of the distribution of stock prices one suggestion is to use a stochastic volatility (SV) model. This project concentrates on Heston's stochastic volatility model. This provides a very useful way to price exotic options based on the prices for plain vanillas. Heston's model is particularly useful as it is possible to find explicit formulas for the distribution of prices for Heston's SV model. Further improvements are mentioned namely adding jumps to the stochastic volatility model, (SVJ) and the SABR model.

Here is a draft version of the project


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