B Casella and GO Roberts
Exact simulation of jump-diffusion processes with Monte Carlo applications
Abstract: We introduce a novel algorithm (JEA) to simulate exactly from a class of one-dimensional jump-diffusion processes with state-dependent intensity. The simulation of the continuous component builds on the recent Exact Algorithm ((1)). The simulation of the jump component instead employes a thinning algorithm with stochastic acceptance probabilities in the spirit of (14). In turn JEA allows unbiased Monte Carlo simulation of a wide class of functionals of the process’ trajectory, including discrete averages, max/min, crossing events, hitting times. Our numerical experiments show that the method outperforms Monte Carlo methods based on the Euler discretization.