The Fast Fourier Transform Method for the Valuation of European Style Options in-the-Money (ITM), at-the-Money (ATM) and out-of-the-Money (OTM)

摘要

This paper presents the fast Fourier transform method for the valuation of European style options in-the-money, at-the-money and out-of-the-money. The fast Fourier transform method utilizes the characteristic function of the underlying instrument’s price process. A fast and accurate numerical solution by means of the Fourier transform method was developed. The fast Fourier transform method is useful for empirical analysis of the underlying asset price. This method can also be used for pricing contingent claims when the characteristic function of the return is known analytically.