Using Brownian Bridge for Fast Simulation of Jump-Diffusion Processes and Barrier Options
by Steve A.K. Metwally of Lehman Brothers, and
Abstract: Barrier options are one of the most popular derivatives in the financial markets. The authors present a fast and unbiased Monte Carlo approach to pricing barrier options when the underlying security follows a simple jump-diffusion process with constant parameters and a continuously monitored barrier. Two algorithms are based on the Brownian bridge concept. The first one is based on a sampling approach to evaluate an integral that results from application of the Brownian bridge. The second approach approximates that integral using a Taylor series expansion.
Published in: Journal of Derivatives, Vol. 10, No. 1, (Fall 2002), pp. 43-54.