A Fast, Accurate, And Simple Method For Pricing European-Asian And Saving-Asian Options

With the rapid development of global economic integration and financial market, financial derivatives become more and more important, the financial derivatives is also called the financial derivative securities, their value depends on other more basic underlying variables. Under the current international financial markets, option is a kind of widely used financial instruments, many of the world’s exchange options trading is very active.Options can be divided into European and American options by using the strike time, American option holders can advance execution options, European option can only be exercised at the expiration date. An option gives the right, but not the obligation.In the study of financial derivatives, option pricing theory is one of the basis of modern finance, is also the most complicated problems in financial applications. Option pricing model and method is the most important, widely and the most difficult problems. The stock options price is based on the underlying stock price, it’s price is depended on the volatility of the stock price, the risk-free rate and other parameters. Current research on option pricing method of the main results are:(1) B-S formula option pricing method,(2) Binomial tree model method,(3) Monte Carlo method,(4) Finite difference method,(5) Arbitrage pricing method,(6) Interval pricing method, etc.This paper first introduces the AMO algorithm, and analyzes the error range and the time complexity of the algorithm, and also lists the other scholars such as Akcoglu and Dai improved the analysis results of the AMO algorithm. We propose an efficient and accurate randomized approximation algorithm for computing the price of European-Asian options, which can be seen as a modification of the AMO algorithm, the approximation algorithm improves the accuracy theoretically as well as practically, and gives the specific data and empirical analysis program. In this paper, the approximation algorithm can also be used for Saving-Asian option pricing, which combined with the advantages of European-Asian and American-Asian options, is a kind of new options.