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Variance Reduction Techniques for Estimating Value-at-Risk

Author

Listed:
  • 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)

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.

Suggested Citation

  • Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2000. "Variance Reduction Techniques for Estimating Value-at-Risk," Management Science, INFORMS, vol. 46(10), pages 1349-1364, October.
    • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:10:p:1349-1364
    DOI: 10.1287/mnsc.46.10.1349.12274
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    References listed on IDEAS

    as
    1. Perwez Shahabuddin, 1994. "Importance Sampling for the Simulation of Highly Reliable Markovian Systems," Management Science, INFORMS, vol. 40(3), pages 333-352, March.
    2. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 1999. "Asymptotically Optimal Importance Sampling and Stratification for Pricing Path‐Dependent Options," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 117-152, April.
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