Finite Difference Method For Solving Ameircan Option With Perfectly Matched Layer

In this paper, we shall develop an efcient finite diference method based onperfectly matched layer (PML) for American option pricing, and apply it to Black-Scholes model and CEV model.It is well know that the American option has many applications. This type ofoption can be exercised anytime during its life, which generates an optimal exerciseboundary. In practise, it is very hard to obtain the option value since the optimal ex-ercise boundary is unknown. In fact, the American option pricing problem is definedon an semi-unbounded domain. The key to solve this problem is how to sovle the freeboundary and to truncate the semi-unbounded domain for computational purpose. Tosovle this problem, we will adopt Front-Fixing method for the irregular boundary andperfect match layer(PML) method for the semi-unbounded boundary, respectively.Finally, coupling Finite diference method with Newton iteration method, we proposean algorithm to solve the American option. By this algorithm, we can obtain the nu-merical approximation of the option value and the optimal exercise boundary simul-taneously. We shall give the positive property of this algorithm, and this algorithm isefective and has high order accuracy. The work here has theoretical significance andpractical value. Numerical experiments verify the efciency of this method.Times are changing, more and more kinds of option will be created. The re-search of the American option pricing problem will never ends. Although the con-tinuability of the numerical method we propose in this paper is still unknown, we willcontinue to work hard in this field.