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The Journal of Derivatives
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Primary Article

Using Brownian Bridge for Fast Simulation of Jump-Diffusion Processes and Barrier Options

Steve A.K. Metwally and Amir F. Atiya
The Journal of Derivatives Fall 2002, 10 (1) 43-54; DOI: https://doi.org/10.3905/jod.2002.319189
Steve A.K. Metwally
A vice president at Lehman Brothers in New York City.
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  • For correspondence: metwally@rcn.com
Amir F. Atiya
An associate professor of computer engineering at Cairo University in Egypt.
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  • For correspondence: amiratiya@link.net
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Abstract

Monte Carlo simulation has become a workhorse for practical derivatives valuation, because of its enormous flexibility. It can handle path-dependent payoffs and a wide range of stochastic processes, for example, but the drawback is the computational burden that can become enormous for realistic models of many real-world instruments. In this article, Metwally and Atiya present a clever technique for Monte Carlo simulation of a jump-diffusion process, and illustrate it in pricing path-dependent barrier options. The trick is to simulate the jumps first, then connect them with diffusion paths that follow Brownian Bridge processes. The result is unbiased, accurate, and highly efficient. A further simplification of the procedure that allows a small bias is found to perform even better in terms of accuracy per unit of computation time.

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The Journal of Derivatives
Vol. 10, Issue 1
Fall 2002
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Using Brownian Bridge for Fast Simulation of Jump-Diffusion Processes and Barrier Options
Steve A.K. Metwally, Amir F. Atiya
The Journal of Derivatives Aug 2002, 10 (1) 43-54; DOI: 10.3905/jod.2002.319189

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Using Brownian Bridge for Fast Simulation of Jump-Diffusion Processes and Barrier Options
Steve A.K. Metwally, Amir F. Atiya
The Journal of Derivatives Aug 2002, 10 (1) 43-54; DOI: 10.3905/jod.2002.319189
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