The Pricing Of Arithmetic Average Asian Options With Taxes And Transaction Costs

Asian option is one of the most active exotic options in the financial derivatives market. Its benefit is related to the average price of underlying asset in the valid period of the options. Asian option has such merits as the price is relatively cheap and low risk and so on. Investors love Asian options because it can effectively prevent the underlying asset price being manipulated. The pricing problem has also become a hot issue of research recently.According to the different average meanings, Asian options can be divided into geometric average Asian option and arithmetic average Asian option. The price of underlying asset obeys the lognormal distribution, so its geometric average also obeys the normal distribution. So far, geometric average Asian options have explicit pricing formula. However, arithmetic average Asian options haven’t, because the arithmetic average of underlying asset price doesn’t obey the lognormal distribution. This article will discuss the explicit pricing formula of arithmetic average Asian option.This paper mainly studies the pricing problem of arithmetic average Asian option with the taxes and transaction costs. In the first part,on the basis of previous studies, we build European option pricing model with the taxes and transaction costs by the method of△-hedge and calculate European option pricing formula with the taxes and transaction costs. Then we will prove to get an asymptotic relationship between arithmetic average Asian options and European options. We get approximate pricing formulas of arithmetic average Asian options with the taxes and transaction costs by this asymptotic relationship. The second part is numerical analysis, this paper takes the result of the monte carlo simulation method as the standard and calculates data with the help of MATLAB programming. We compare the pricing method of this paper with the monte carlo simulation method. Then we analyse the relative errors and illustrate that the proposed pricing method is feasible.