The Pricing Of Discrete Arithmetic Average Asian Options

Asian options are known as path dependent options.They have two merits:their path dependence characteristic can effectively protect the price of the underlying assets against manipulation; their risk smaller is much better for hedgers.Therefore, Asian options have great advantage on the risk management,the risk control and so on.It has been one of the most active Exotic options in financial markets.The pricing of Asian options has also been gradually becoming a hot issue on the research of the derivative assets pricing.The payoffs of Asian options relate to the average of underlying prices. According to the type of the average,Asian options can be divided into arithmetic average Asian options and geometric average Asian options. So far, geometric average Asian options usually have analytic formula,but there are some difficulties in the pricing of arithmetic average Asian options.Because the distribution of the arithmetic average of a series of logarithmic normal distribution random variables is not parsed, arithmetic average Asian options have no accurate analytic formula.The purpose of this paper is to study the pricing of discrete arithmetic average Asian options with a fixed strike price and discuss the European Asian options and American Asian options.Through the application of risk neutral pricing theorem and hedge risk method and in combination with Black-Scholes-Merton model and the Taylor expansion to the second order, this paper derives the approximate pricing formula for discrete arithmetic average European Asian options with a fixed strike price.To obtain a pricing method for discrete arithmetic average American Asian options with a fixed strike price, this paper combines the approximate pricing formula for discrete arithmetic average European Asian options with a fixed strike price, binomial tree model and the control variate method.