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Management Science Vol. 46 No. 10 2000

Variance Reduction Techniques for Estimating Value-at-Risk

Paul Glasserman1; Philip Heidelberger2; Perwez Shahabuddin3

1 Columbia Business School, Columbia University, New York, New York 10027 · 2 IBM Research Division, T. J. Watson Research Center, Yorktown Heights, New York 10598 · 3 IEOR Department, Columbia University, New York, New York 10027;

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.

DOI
10.1287/mnsc.46.10.1349.12274
Volume
46
Issue
10
Pages
1349-1364
Language
en
Sources
openalex bibtex:phds-export.bib crossref

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