Munich Personal RePEc Archive

Exact Simulation of Jump-Diffusion Processes with Monte Carlo Applications

Casella, Bruno and Roberts, Gareth O. (2011): Exact Simulation of Jump-Diffusion Processes with Monte Carlo Applications. Published in: Methodology and Computing in Applied Probability , Vol. 13, No. 3 (9 January 2010): pp. 449-473.

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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.

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