The Pricing Of Discrete Arithmetic Average Asian Options With Transaction Costs And Dividend

In nowadays financial derivatives market, trading options have standard options and a variety of types such as exotic options, Asian option is one of the most active species of exotic options. Asian option is also known as the path-dependent option,so it can effectively alleviate the speculation. In addition, Asian options has such merits as cheaper price and it can be used to hedge risk within a specified period of advantages, so research of Asian option pricing method is particularly important. This paper will discuss two explicit pricing formulas of discrete arithmetic average Asian option.This paper mainly studies the pricing problem of discrete arithmetic average Asian option with transaction costs and dividend. The thesis is divided into two parts. The first part puts forward two kinds of pricing method. The first kind of pricing method is asymptotic method which extend the asymptotic relationship between European option and arithmetic average Asian option. And then use the price of European option with transaction costs and dividend to obtain the approximate pricing formulas of discrete arithmetic average Asian option with transaction costs and dividend; The second kind of pricing method is binomial tree method, the method is based on binomial tree model of option pricing and it uses the exponential function model which estimate the mean price of the underlying asset that on the node to obtain the binomial tree pricing discrete arithmetic average Asian option with transaction costs and dividend. The second part get two pricing methods with the help of MATLAB programming, and compare the two pricing method with the Monte Carlo simulation method. The empirical results show that asymptotic method is effective. The option price which by asymptotic method is close to the price which by Monte Carlo simulation,and the relative error is no larger than 1%. The empirical results also show that binomial tree method is effective. The option price which by binomial tree method is close to the price which by Monte Carlo simulation,and the relative error is no larger than 5%.