American Option Pricing Model Numerical Method

The pricing problem of the American option is currently regarded as one of the hot spot in Finance. Because the American option may early be exercised before the expiration date, its pricing is generally more difficult than that of the European option. The article researches the characters of the American option and the principle of forming its value, and emphasizes on how to compute the American option value and find the flee boundary by numerical methods.The main work of the article including:Firstly, gives a hybrid algorithm of solution American option pricing model, The article transforms the solving problem of partial differential equation for the American put price into a standard initial and boundary value problem of Parabolic type by making some transformations. Afterwards, the solving problem of Parabolic type is transformed into a initial value problem of ordinary differential equation with respect toτthrough Fourier transform again. At the last, the initial value problem is solved with the progressive Euler method.Secondly, the difference methods with variable meshes are proposed for the American option pricing problems in the free boundary value form. By means of an equation derived for the free boundary, the option values and optimal exercise boundary can be computed simultaneously by using the variable mesh technique. Both explicit and Crank-Nicolson difference schemes with variable meshes are discussed, and the stability and convergence are analyzed.Because the underlying stocks with paying the dividend of American options have no explicit closed-form formulas, and it is very close to actual transaction of financial markets. Researching more effective numerical methods to solve this problem has the important theoretical and practical significance.Finally, the numerical algorithm is combined with actual case and proved be efficient by calculation comparison...