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