Quasi-Monte Carlo Method In Option Pricing

This thesis considers a special Monte Carlo?MC?method–Quasi Monte Carlo?QMC?method on the pricing of American option.In the past decades,the Monte Carlo method is widely used in American option pricing.However,the convergence rate of MC is very slow.To overcome this drawback,the QMC method is proposed to improve the convergence rate from O(1/N^1/2)to O?1/N?,where N is the number of simulation paths.Here we combine QMC method and duality method on the pricing of American option.Duality method is based on the equivalence of American option pricing problem and the optimal stopping time problem.Since this method can overcome the limit of American option pricing dimension compared with previous algorithms,it can solve high-dimensional American option pricing problem quickly.In addition,we will introduce several construction modes of martingale process,then give the detailed procedure of duality method solving American option pricing.Numerical results tests show that the combination of QMC method and duality method is accurate and take less time.It can improve the computing efficiency of MC simulation sharply,the method is very effective in practical application.