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Exact simulation of jump-diffusion processes with Monte Carlo applications

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Casella, Bruno and Roberts, Gareth O. (2011) Exact simulation of jump-diffusion processes with Monte Carlo applications. Methodology and Computing in Applied Probability, Vol.13 (No.3). pp. 449-473. doi:10.1007/s11009-009-9163-1 ISSN 1387-5841 .

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Official URL: http://dx.doi.org/10.1007/s11009-009-9163-1

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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.

Item Type:

Journal Article

Subjects:

Q Science > QA Mathematics

Divisions:

Faculty of Science, Engineering and Medicine > Science > Statistics

Library of Congress Subject Headings (LCSH):

Diffusion processes, Diffusion processes -- Computer simulation, Monte Carlo method

Journal or Publication Title:

Methodology and Computing in Applied Probability

Publisher:

Springer New York LLC

ISSN:

1387-5841

Official Date:

September 2011

Dates:

Date	Event
September 2011	Published

Volume:

Vol.13

Number:

No.3

Page Range:

pp. 449-473

DOI:

10.1007/s11009-009-9163-1

Institution:

University of Warwick

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Open Access (Creative Commons)

Funder:

Engineering and Physical Sciences Research Council (EPSRC)

Version or Related Resource:

Casella, B. and Roberts, G. (2008). Exact simulation of jump-diffusion processes with Monte Carlo applications. [Coventry] : University of Warwick. Centre for Research in Statistical Methodology. (Working papers, no.08-19).

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