Efficient Estimation of First Passage Time Density Function for Jump-Diffusion Processes

The first passage time problem has attracted considerable research interest in the field of stochastic processes. It concerns the estimation of the probability density of the time for a random process to cross a specified boundary level. Even though there are many theoretical advances in solving this problem, for many classes of random processes no analytical solution exists. The jumpdiffusion process is one such class. Recent research in finance theory has renewed the interest in jump diffusion processes, and the first passage time problem for such processes is applicable to several finance problems. In this paper we develop fast Monte Carlo-type numerical methods for computing the first passage density function for jump-diffusion processes. Compared with the standard Monte Carlo approach, our approaches are about 10-30 times faster. keywords: Monte Carlo Simulation, Brownian Motion, Brownian Bridge, Jump Diffusion, First Passage Time, Poisson process, inverse