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

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.