A PDE Method For Pricing Asian Option

In today's complex and volatile financial markets, financial derivative products are enjoyed by most of the investors because of its powerful leverage and hedge function. The development of financial derivatives is a new melody in the international financial fields now. As the core of financial derivatives, option becomes focus of studying in theory and practice. Above all, it must be solved that how to price option and get its numerical results. In 1970's, Black and Scholes derived the Partial Differential Equation with no dividend through studying stock price changes and hedge thinking, which successfully solved the problem of pricing the Euro Option. This way we now call B-S model give us a very good idea to price options. On the foundation of standard contract, more different characteristics exotic finance derivatives were designed in order to satisfy the finance market and the different investor especial needs and keep away the risk which many investors might face. One of them is the Asian option, it is a path dependent option whose payoff depends on the average of underlying asset price attained over a certain period of time. It is more complicated to price the Asian option because of the path dependence. Moreover, it is difficult to obtain analytical solutions of arithmetic average Asian option, so people research geometric average Asian option more.Options on a trade account are a kind of option, Asian option is a special case of it. Because options on a traded account meet with the same form equation, the price of the Asian option is characterized by a simple one-dimensional partial differential equation. only need to change the trading strategy. We priced fixed strike arithmetic average Asian option in use of finite difference method. Moreover, we studied its truncation error. Finally, we obtained the numerical solution of the equation in MATLAB, and compared the data with which is got in use of other methods, achieved satisfactory results...