The Asymptotic Expansion Approach To Pricing Asian Options And Compared With Other Method

Asian option (the average price of the option), is one of the most active trading exotic options in financial derivatives market, its maturity date income is closely related to the average price of the underlying asset during the contract period. It can prevent human speculation, insider trading which can lead to the price of the underlying asset up and down which make people unnecessary loss. In addition, the price of Asian option is cheaper than the standard options, thus it get people’s favor.In general, the average value of the underlying asset has two forms:the geometric mean and the arithmetic mean. We have had the explicit pricing formula of the geometric mean. It’s difficult to pricing the arithmetic average Asian option because the arithmetic average of the underlying asset prices generally does not follow a normal distribution. At present, there is some approximate explicit pricing formula for discrete arithmetic average Asian option, but for the continuous time model of arithmetic average Asian option, the approximate pricing formula is also rare.This paper will use the asymptotic expansion approach to price the continuous time model of arithmetic average Asian option and give its explicit approximate pricing formula. Under the assumption of risk-neutral, we use the characteristic function of the arithmetic average of the underlying asset prices to get the asymptotic expansions density function of the arithmetic average of the underlying asset prices, and by the asymptotic expansions density function to obtain the explicit approximate pricing formula of arithmetic average Asian call option. For arithmetic average Asian stock call option, through the numerical simulation method to compare the asymptotic expansion and the second moment approximation method with Monte Carlo simulation method. The results showed that the asymptotic expansion under different volatility and different maturities and different values of the state, the relative error rate is not more than 5% of the Monte Carlo pricing, and in most cases it is less than 1% of the Monte Carlo pricing. It is also similar to the use of a wide range of the second moment approximation pricing. So the asymptotic expansion method to price the continuous arithmetic average Asian option is feasible.