Variance Reduction Techniques for Simulating Value-at-Risk

Posted: 23 Nov 1999

See all articles by Paul Glasserman

Paul Glasserman

Columbia Business School

Philip Heidelberger

IBM Research Division

Perwez Shahabuddin

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: October 1999

Abstract

This paper describes, analyzes and evaluates an algorithm for estimating portfolio loss probabilities using Monte Carlo simulation. Obtaining accurate estimates of such loss probabilities is essential to calculating value-at-risk, which is a quantile of the loss distribution. The method employs a quadratic ("delta-gamma") approximation to the change in portfolio value to guide the selection of effective variance reduction techniques; specifically importance sampling and stratified sampling. If the approximation is exact, then the importance sampling is shown to be asymptotically optimal. Numerical results indicate that an appropriate combination of importance sampling and stratified sampling can result in large variance reductions when estimating the probability of large portfolio losses.

JEL Classification: G13, G28

Suggested Citation

Glasserman, Paul and Heidelberger, Philip and Shahabuddin, Perwez, Variance Reduction Techniques for Simulating Value-at-Risk (October 1999). Available at SSRN: https://ssrn.com/abstract=191568

Paul Glasserman (Contact Author)

Columbia Business School ( email )

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Philip Heidelberger

IBM Research Division ( email )

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Perwez Shahabuddin

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

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New York, NY 10027
United States

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