Fast Monte Carlo valuation of barrier options for jump diffusion processes

We 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. We develop an algorithm that is based on the Brownian bridge concept and on a sampling approach to successively evaluate an integral that results from the application of the Brownian bridge. This method achieves zero bias. In addition, it is about 100 times faster than the conventional Monte Carlo method for which the discretization interval is chosen so as to achieve acceptable bias.