A Comparative Study Of Asian Option Pricing

Asian option,it is an innovative European option which is proposed by one Bankers Trust of the United States and appeared in the1990’s in the Tokyo of the Japan.Asian option is a strong path-dependent option which is the most actively traded in financial markets and is most widely used.In addition,because of its cheap,easy to control risk,hedging and other aspects advantages,Asian option is liked by the investors and managers.Risk management and control have become the focus of the world attention since the global crisis in2008,people are paying more attention to the Asian option,its pricing is becoming one of the hot research of the derivative asset pricing.This paper mainly studies the discrete fixed strike price of the European Asian option pricing problem.Firstly,I outline the preliminary knowledge of the option pricing,and then I price for the discrete geometric average Asian option and dis-crete arithmetic average Asian option respectively.For the discrete geometric average Asian option,if the underlying asset price follows a log-normal distribution,because the geometric mean of a series of log-normal distribution remains log-normal distri-bution, which can be quickly drawn the analytical solution of the geometric average Asian option pricing formula.For discrete arithmetic average Asian option,because the asset prices of the arithmetic mean are no longer log-normal distribution,so the pricing formula can not directly use the Black-Scholes formula,which can only be given the approximate pricing formula.In this paper, in order to explore the pricing formula of the arithmetic average Asian option,I adopt four methods,such as the relation between the mean are used to the approximate pricing,Taylor expansion to approximation pricing,the Monte Carlo analogue and the approximate different pricing methods.finally,I do an evaluation and comparison for each pricing methods by the Matlab software,and then I do a summary and analysis of the variety of pricing methods.