Numerical Computation and Monte Carlo Simulation of the Heston Stochastic Volatility Model

Specialeforsvar ved Yumo Zhang

Titel: Numerical Computation and Monte Carlo Simulation  of the Heston Stochastic Volatility Model

Abstract: In this thesis, we investigate the Heston stochastic volatility model and give an elaborate derivation for the semi-closed form solution of European call options. In light of the form of the formula, we revisit Gauss-Lobatto quadrature and Fast Fourier Transform and apply them to the Heston model. In addition to that, four distinct branches of Monte Carlo simulation methods are presented. Verifying the validity of all the proposed approaches in three typical scenarios, we find that Gauss-Lobatto quadrature and quadratic-exponential scheme have the best performance in terms of option pricing. We furthermore consider pricing sensitivity in the model and show that Gauss-Lobatto quadrature is available in calculating delta, vega and gamma whereas quadratic-exponential scheme is only valid with respect to delta and gamma by using finite difference estimation.

Vejleder:  Rolf Poulsen
Censor:    Elisa Nicolato, Aarhus Universitet