The Improvement Of The Least Squares Monte Carlo Method And The Application Research Of Option Pricing

F.Longstaff and E.S.Schwartz proposed the least squares Monte Carlo(LSM)simulation method by combining the least squares method and Monte Carlo method in 2001.Currently LSM method has become one of the main methods to price American option.Many people have effectively use the method to solve American option pricing problem.This article also uses LSM method for pricing American options.The operation efficiency is improved by new method on the basis of LSM method.First,in the third chapter,Principal Component Analysis(PCA)method and LSM method are combined in American Asian high-dimensional pricing problems.The results show that PCA method can indeed plays the role of reducing the size of high-dimensional problem to some extent,thus the computation time is reduced.Second,considering the dimensionality reduction will reduce the amount of information,resulting in the error between simulation results and the exact value.A basket of American options are taken as the object of this research in the fourth chapter.On the basis of LSM method,the method of Principal Component Analysis method and the Control Variables are combined.The size of the operation is reduced while the operation accuracy is not decreased.Thus the operational efficiency is improved.The validity of the proposed method is verified through numerical simulation.Finally,American option pricing problems in Heston stochastic volatility model is studied in the fifth chapter,the condition of Monte Carlo method is used to calculate the price of European option under stochastic volatility,and it is used as a control variable in order to make sample variance significantly reduced.