Fast calibration in the Heston model

Abstract

The Heston model is one of the most popular stochastic volatility models for derivatives pricing. The model proposed by Heston (1993) takes into account non-lognormal distribution of the assets returns, leverage effect and the important mean-reverting property of volatility. In addition, it has a semi-closed form solution for European options. It therefore extends the Black and Scholes model and includes it as a special case.<br />The prices produced by the model are quite parameter sensitive, hence the calibration of the parameters is as crucial as the model itself. The calibration must be robust and stable and should not be too computer intensive, which rules out global optimisation algorithms. The general approach of applying a least-square type procedure is very sensitive to the choice of the initial point. Therefore, literature on closed-form asymptotic approximations has grown rapidly in the past few years. An overview of these approximations will be presented in this thesis and some will be proved for their accuracy in delivering a starting point for the calibration.