On Path-Dependent Option Pricing for the Heston Model

Abstract

In this thesis, we are focusing on developing an efficient simulation algorithm to price the path-dependent options, which remains a challenging problem in derivatives finance. The Heston model, a widely used stochastic volatility model, will first be introduced. Then, we will discuss and evaluate several methods used in simulating the Heston model, including the Explicit and Weighted Heston simulation algorithm. The research will be extended to the path-dependent option pricing with the simulation results of the Heston model. The least squares Monte Carlo approach and its favorable alternative method, stochastic approximation, will be explained and compared. Finally, we will introduce the branching algorithm to improve the pricing scheme. Numerical results for pricing different kinds of path-dependent options will show the performance of the branching stochastic approximation algorithm is orders of magnitude better in pricing options than the traditional method.