American Option Price And Sensitivities Estimation Via QMC

American options are one of the most active trading instruments in the market.However,due to their particularity of early exercise,theoretical pricing and sensitivity analysis are particularly difficult.Therefore,when analyzing specific issues,it is often necessary to use simulation methods.In this thesis,for two types of models: geometric Brownian motion and Variance-Gamma model,estimates of option price and Greeks are performed.The Monte Carlo(MC)method and Quasi-Monte Carlo(QMC)under different path-generating methods are compared.Under the geometric Brownian motion model,random walk,Brownian bridge and principal component path generation methods are utilized;under the Variance-Gamma model,time-transformed Brownian motion,Gamma bridge,principal component and series representations methods are utilized.Combining the above methods and applying them to American options,this thesis concludes:(1)Compared with MC,QMC can increase the accuracy of American option price and Greeks estimates;(2)Using the dimension reduction method to generate the path can significantly improve the results of QMC;(3)Under the Variance-Gamma model,model parameters affect the dimensionality reduction of the path generation method.