Exact Sampling of Jump-Diffusions

Abstract

Jump-diffusion processes are ubiquitous in finance and economics. They arise as models of security, energy and commodity prices, exchange and interest rates, and default timing. This paper develops a method for the exact simulation of a skeleton, a hitting time and other functionals of a one-dimensional jump-diffusion with state-dependent drift, volatility, jump intensity and jump size. The method requires the drift function to be C¹, the volatility function to be C², and the jump intensity function to be locally bounded. No further structure is imposed on these functions. The method leads to unbiased simulation estimators of security prices, transition densities, hitting probabilities, and other quantities. Numerical results illustrate its features.