Double Barrier Options in Regime-Switching Hyper-Exponential Jump-Diffusion Models

Abstract

We present a fast and accurate algorithm for calculating prices of finite lived double barrier options with arbitrary terminal payoff functions under regime-switching hyper-exponential jump-diffusion models, which generalize Kou's model. Extensive numerical tests demonstrate excellent agreement of our results with those obtained using other methods. The first step of our approach is Carr's randomization, which we prove for barrier options under strong Markov processes of a wide class. The resulting sequence of perpetual option pricing problems is solved using an efficient iteration algorithm and the Wiener-Hopf factorization.

Keywords: Option pricing, double barrier options, double-no-touch options, Levy processes, Kou's model, hyper-exponential jump-diffusions, regime switching, stochastic volatility, stochastic interest rates, Carr's randomization, Canadization, analytic method of lines, Wiener-Hopf factorization

JEL Classification: C63, G13