The Heston Stochastic Volatility Model: an Approximate Approach

The aim of this thesis is to find an efficient simulation method of the Heston model of stochastic volatility to price path dependent derivatives. The volatility process in this model has an exact transition density defined as a scaled non central chi2 density. By implementing classic approaches of approximating the non central chi2 distribution, and modifying Andersen's Quadratic Exponential (QE) approximation of the bias free Exact Simulation Method (ESM), the computation time is reduced while the bias remains unchanged under some parameter sets. The proposed approach is to approximate the non central chi2 with chi2 distributions while the chi2 distributions in a second step are approximated by normal distributions. With this method the computation time in MATLAB is reduced by 35% on average. The bias remains virtually unchanged when the degrees of freedom of chi2 are larger than one but increases significantly when they are less than one. For less degrees of freedom one ought to keep the exact chi2 distribution which actually increases the computation time by 15% on average. These results are not significant since there are no guarantees that the reference algorithm was implemented in the most optimal way. Thus the original QE algorithm is considered a time efficient approximation of the ESM. Further research ought to be concentrated on reducing the bias. (Less)