Using Brownian Bridge for Fast Simulation of Jump-Diffusion Processes and Barrier Options

Abstract

Monte Carlo simulation has become a workhorse for practical derivatives valuation, because of its enormous flexibility. It can handle path-dependent payoffs and a wide range of stochastic processes, for example, but the drawback is the computational burden that can become enormous for realistic models of many real-world instruments. In this article, Metwally and Atiya present a clever technique for Monte Carlo simulation of a jump-diffusion process, and illustrate it in pricing path-dependent barrier options. The trick is to simulate the jumps first, then connect them with diffusion paths that follow Brownian Bridge processes. The result is unbiased, accurate, and highly efficient. A further simplification of the procedure that allows a small bias is found to perform even better in terms of accuracy per unit of computation time.