, Volume 13, Issue 3, pp 449-473
Date: 09 Jan 2010

Exact Simulation of Jump-Diffusion Processes with Monte Carlo Applications

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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.

Research supported by EPSRC.
Both authors are indebted to Alex Beskos, Omiros Papaspiliopoulos and Stefano Peluchetti for many stimulating discussions.