Variance Reduction Techniques for Estimating Value-at-Risk

Paul Glasserman, Philip Heidelberger and Perwez Shahabuddin
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Paul Glasserman: Columbia Business School, Columbia University, New York, New York 10027
Philip Heidelberger: IBM Research Division, T.J. Watson Research Center, Yorktown Heights, New York, 10598
Perwez Shahabuddin: IEOR Department, Columbia University, New York, New York 10027

Management Science, 2000, vol. 46, issue 10, 1349-1364

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.

Keywords: value-at-risk; monte carlo; simulation; variance reduction technique; importance sampling; stratified sampling; rare event (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (44)

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