Efficient Monte Carlo Barrier Option Pricing When the Underlying Security Price Follows a Jump-Diffusion Process

Abstract

We present efficient simulation procedures for pricing barrier options when the underlying security price follows a geometric Brownian motion with jumps. Metwally and Atiya [2002] developed a simulation approach for pricing knock-out options in the same setting, but no variance reduction was introduced. We improve upon Metwally and Atiya's method by innovative applications of well-known variance reduction techniques. We also show how to use simulation to price knock-in options. Numerical examples show that our proposed Monte Carlo procedures lead to substantial variance reduction as well as a reduction in computing time.