Exact Simulation of Jump-Diffusion Processes with Monte Carlo Applications

Bruno Casella and Gareth O. Roberts

MPRA Paper from University Library of Munich, Germany

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 diffusion; Simulation; Exact Algorithms; Barrier option pricing (search for similar items in EconPapers)
JEL-codes: C15 C18 C63 (search for similar items in EconPapers)
Date: 2011-09-01
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Citations: View citations in EconPapers (10)

Published in Methodology and Computing in Applied Probability 3.13(2010): pp. 449-473

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