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In Rememberance: World Trade Center (WTC)

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Exact Sampling of Jump-Diffusions

by Kay Giesecke of Stanford University, and
Dmitry Smelov of Stanford University

August 18, 2011

Abstract: Jump-diffusion processes are ubiquitous in finance and economics. They arise as models of security, energy and commodity prices, exchange and interest rates, and default timing. This paper develops a method for the exact simulation of a skeleton, a hitting time and other functionals of a one-dimensional jump-diffusion with state-dependent drift, volatility, jump intensity and jump size. The method requires the drift function to be C1, the volatility function to be C2, and the jump intensity function to be locally bounded. No further structure is imposed on these functions. The method leads to unbiased simulation estimators of security prices, transition densities, hitting probabilities, and other quantities. Numerical results illustrate its features.

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