Pricing exotic options in a regime switching economy: a Fourier transform method

This article considers the valuation of digital, barrier, and lookback options in a Markovian, regime-switching, Black-Scholes model. In Fourier space, integral representations for the option prices are derived via the theory on matrix Wiener-Hopf factorizations. Our main focus is on the 2-state case where the matrix Wiener-Hopf factorization is available analytically. A comparison to several numerical alternatives (analytical approximations, the Brownian bridge algorithm and a finite element scheme) demonstrates that the pricing formulas are easy to implement and lead to accurate price estimates.