Study Of American Option Pricing

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 free boundary by numerical methods.Chapter one summarizes the option pricing theory, the significance, necessity and objectives of the research of the subject, as well as, the basic route and logic structure of writing. Chapter two studies the forming principle of American option values, and establishes American option's differential equation and the free boundary. Chapter three studies the numerical methods of American put option. The paper transforms the solving problem of partial differential equation for the American put price into an initial and boundary value problem of Parabolic Type by making some transformations. Afterwards, it derives a new integral equation representation for the free boundary and the price of the option using Melllin transform techniques. Then, the paper solves the problem with numerical methods and compares the results with results of Binomial tree method, finite-difference method and SOR method using computers. By valuing six American put options, the numerical experiment and analysis show that the Mellin transform method is a fast and highly accurate numerical method.