MONTE CARLO AND VARIANCE REDUCTION METHODS FOR OPTION PRICING

Abstract

In this project, we study the problem of pricing European call option. We shall give an overview of the problem and describe the related theory. To solve the problem, we propose two methods: the Monte Carlo method and the variance reduction method. We first apply the Monte Carlo method. In addition to the performance on the pricing problem, we also analyze the results via convergence rate and sensitivity analysis of variance. We notice the shortcomings of the Monte Carlo method and propose the variance reduction method as an improvement. The idea is to divide the maturity period into smaller time grids/sub-intervals. We shall run simulations to show its superiority over the Monte Carlo method. The performance is again analyzed via convergence rate and sensitivity analysis of variance.

In this thesis, all the simulations are conducted through R Programme.