Efficient Options Pricing Using the Fast Fourier Transform

Abstract

The Fourier transform methods provide the valuable and indispensable tools for option pricing under L´evy processes since the analytic representation of the haracteristic function of the underlying asset return is more readily available than that of the density function itself. When used together with the FFT algorithms, real time pricing of a wide range of option models under L'evy processes can be delivered using the Fourier transform approach with highaccuracy, efficiency and reliability. In particular, option prices across the whole spectrum of strikes can be obtained in one set of FFT calculations. In this paper, we demonstrate the effective use of the Fourier transformapproach as an effective tool in pricing options.

Keywords: option pricing, Fast Fourier transform, Levy processes, numerical algorithms

JEL Classification: G13