Pricing American Put Options: A Fast Fourier Transform Method

The pricing problem of the American option is currently studied as one of the important items 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 detailedly researches the characters of the American option and the principle of forming its value, and offers a new, very fast and accurate numerical pricing method of the American put option—"FFT" method. Firstly, the article studies the classic Black-Scholes Option Pricing Model and concludes the Black-Scholes Option Pricing Formula with the Risk-Neutral valuation method. Secondly, the article in detail researches the forming principle of American call and put values and their computing methods in the third chapter. At the beginning of fourth chapter, 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 to through Fourier transform again. At the last section of the fourth chapter, the article solves the initial value problem with the progressive Euler method and the finite element method. By valuing six American put options, the numerical experiment and analysis show that the Euler method with FFT is a fast and highly accurate numerical method.