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Article

Efficient Monte Carlo Barrier Option Pricing When the Underlying Security Price Follows a Jump-Diffusion Process

Sheldon M Ross and Samim Ghamami
The Journal of Derivatives Spring 2010, 17 (3) 45-52; DOI: https://doi.org/10.3905/jod.2010.17.3.045
Sheldon M Ross
is Epstein Chair Professor in the Epstein Department of Industrial and Systems Engineering at the University of Southern California in Los Angeles,CA.
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  • For correspondence: smross@usc.edu
Samim Ghamami
is a post-doctoral research associate in the Center for Risk and Economic Analysis of Terrorism Events (CREATE) at the University of Southern California in Los Angeles, CA.
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  • For correspondence: ghamami@usc.edu
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Abstract

We present efficient simulation procedures for pricing barrier options when the underlying security price follows a geometric Brownian motion with jumps. Metwally and Atiya [2002] developed a simulation approach for pricing knock-out options in the same setting, but no variance reduction was introduced. We improve upon Metwally and Atiya's method by innovative applications of well-known variance reduction techniques. We also show how to use simulation to price knock-in options. Numerical examples show that our proposed Monte Carlo procedures lead to substantial variance reduction as well as a reduction in computing time.

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The Journal of Derivatives: 17 (3)
The Journal of Derivatives
Vol. 17, Issue 3
Spring 2010
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Efficient Monte Carlo Barrier Option Pricing When the Underlying Security Price Follows a Jump-Diffusion Process
Sheldon M Ross, Samim Ghamami
The Journal of Derivatives Feb 2010, 17 (3) 45-52; DOI: 10.3905/jod.2010.17.3.045

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Efficient Monte Carlo Barrier Option Pricing When the Underlying Security Price Follows a Jump-Diffusion Process
Sheldon M Ross, Samim Ghamami
The Journal of Derivatives Feb 2010, 17 (3) 45-52; DOI: 10.3905/jod.2010.17.3.045
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  • Article
    • Abstract
    • Metwally and Atiya's Raw Simulation Estimator of an Up-and-Out Barrier Call Option
    • Variance Reduction in Estimating the Value of an Up-and-Out Barrier Option
    • Up-and-in Barrier Options
    • Numerical Examples
    • Appendix
    • References
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