Sema Coskun

• In this thesis, we focus on the application of the Heath-Platen (HP) estimator in option pricing. In particular, we extend the approach of the HP estimator for pricing path dependent options under the Heston model. The theoretical background of the estimator was first introduced by Heath and Platen [32]. The HP estimator was originally interpreted as a control variate technique and an application for European vanilla options was presented in [32]. For European vanilla options, the HP estimator provided a considerable amount of variance reduction. Thus, applying the technique for path dependent options under the Heston model is the main contribution of this thesis. The first part of the thesis deals with the implementation of the HP estimator for pricing one-sided knockout barrier options. The main difficulty for the implementation of the HP estimator is located in the determination of the first hitting time of the barrier. To test the efficiency of the HP estimator we conduct numerical tests with regard to various aspects. We provide a comparison among the crude Monte Carlo estimation, the crude control variate technique and the HP estimator for all types of barrier options. Furthermore, we present the numerical results for at the money, in the money and out of the money barrier options. As numerical results imply, the HP estimator performs superior among others for pricing one-sided knockout barrier options under the Heston model. Another contribution of this thesis is the application of the HP estimator in pricing bond options under the Cox-Ingersoll-Ross (CIR) model and the Fong-Vasicek (FV) model. As suggested in the original paper of Heath and Platen [32], the HP estimator has a wide range of applicability for derivative pricing. Therefore, transferring the structure of the HP estimator for pricing bond options is a promising contribution. As the approximating Vasicek process does not seem to be as good as the deterministic volatility process in the Heston setting, the performance of the HP estimator in the CIR model is only relatively good. However, for the FV model the variance reduction provided by the HP estimator is again considerable. Finally, the numerical result concerning the weak convergence rate of the HP estimator for pricing European vanilla options in the Heston model is presented. As supported by numerical analysis, the HP estimator has weak convergence of order almost 1.