Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 18109, 22 pages
doi:10.1155/JAMSA/2006/18109

Option pricing in a regime-switching model using the fast Fourier transform

R. H. Liu,1 Q. Zhang,2 and G. Yin3

1Department of Mathematics, University of Dayton, 300 College Park, Dayton 45469-2316, OH, USA
2Department of Mathematics, The University of Georgia, Athens 30602-7403, GA, USA
3Department of Mathematics, Wayne State University, Detroit 48202, MI, USA

Received 6 December 2005; Revised 11 June 2006; Accepted 5 July 2006

Copyright © 2006 R. H. Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with fast Fourier transform (FFT) approach to option valuation, where the underlying asset price is governed by a regime-switching geometric Brownian motion. An FFT method for the regime-switching model is developed first. Aiming at reducing computational complexity, a near-optimal FFT scheme is proposed when the modulating Markov chain has a large state space. To test the FFT method, a novel semi-Monte Carlo simulation algorithm is developed. This method takes advantage of the observation that the option value for a given sample path of the underlying Markov chain can be calculated using the Black-Scholes formula. Finally, numerical results are reported.