User's Guide to Pricing Double Barrier Options. Part I: Kou's Model and Generalizations

Abstract

We present a very accurate algorithm for calculating prices of double barrier options, together with a simple set of detailed step-by-step instructions for implementing it in practice. Our algorithm works 5-10 times faster than any other known algorithm. At the same time, it involves no complicated technical tools, and can therefore be easily implemented in any programming language that supports elementary operations on real numbers.

Our method applies to pricing double barrier options with arbitrary terminal payoff functions under Kou's model (a.k.a. the double-exponential jump-diffusion model), as well as generalizations of Kou's model that are referred to as hyper-exponential jump-diffusion (HEJD) models. Extensive numerical tests demonstrate excellent agreement of our results with those obtained using other approaches.

Keywords: Option pricing, double barrier options, double-no-touch options, Levy processes, Kou's model, hyper-exponential jump-diffusions, Carr's randomization, Canadization, Wiener-Hopf factorization

JEL Classification: C63, G13