Methodology and Computing in Applied Probability

, Volume 13, Issue 3, pp 449–473

Exact Simulation of Jump-Diffusion Processes with Monte Carlo Applications

Authors

  • Bruno Casella
    • Department of StatisticsUniversity of Warwick
    • Department of StatisticsUniversity of Warwick
Article

DOI: 10.1007/s11009-009-9163-1

Cite this article as:
Casella, B. & Roberts, G.O. Methodol Comput Appl Probab (2011) 13: 449. doi:10.1007/s11009-009-9163-1

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 (Beskos et al., Bernoulli 12(6):1077–1098, 2006a). The simulation of the jump component instead employs a thinning algorithm with stochastic acceptance probabilities in the spirit of Glasserman and Merener (Proc R Soc Lond Ser A Math Phys Eng Sci 460(2041):111–127, 2004). 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.

Keywords

Jump diffusionSimulationExact AlgorithmsBarrier option pricing

AMS 2000 Subject Classifications

Primary 60K30; Secondary 65C05

Copyright information

© Springer Science+Business Media, LLC 2009