Exact Simulation of Jump-Diffusion Processes with Monte Carlo Applications

Bruno Casella and Gareth O. Roberts ()
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Bruno Casella: University of Warwick
Gareth O. Roberts: University of Warwick

Methodology and Computing in Applied Probability, 2011, vol. 13, issue 3, 449-473

Abstract: 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; Primary 60K30; Secondary 65C05 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s11009-009-9163-1

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