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Conditional Monte Carlo Estimation of Quantile Sensitivities

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Author Info

  • Michael C. Fu

    ()
    (Robert H. Smith School of Business and Institute for Systems Research, University of Maryland, College Park, Maryland 20742)

  • L. Jeff Hong

    ()
    (Department of Industrial Engineering and Logistics Management, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China)

  • Jian-Qiang Hu

    ()
    (Department of Management Science, School of Management, Fudan University, 200433 Shanghai, China)

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    Abstract

    Estimating quantile sensitivities is important in many optimization applications, from hedging in financial engineering to service-level constraints in inventory control to more general chance constraints in stochastic programming. Recently, Hong (Hong, L. J. 2009. Estimating quantile sensitivities. Oper. Res. 57 118-130) derived a batched infinitesimal perturbation analysis estimator for quantile sensitivities, and Liu and Hong (Liu, G., L. J. Hong. 2009. Kernel estimation of quantile sensitivities. Naval Res. Logist. 56 511-525) derived a kernel estimator. Both of these estimators are consistent with convergence rates bounded by n -1/3 and n -2/5 , respectively. In this paper, we use conditional Monte Carlo to derive a consistent quantile sensitivity estimator that improves upon these convergence rates and requires no batching or binning. We illustrate the new estimator using a simple but realistic portfolio credit risk example, for which the previous work is inapplicable.

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    File URL: http://dx.doi.org/10.1287/mnsc.1090.1090
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 55 (2009)
    Issue (Month): 12 (December)
    Pages: 2019-2027

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    Handle: RePEc:inm:ormnsc:v:55:y:2009:i:12:p:2019-2027

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    Related research

    Keywords: quantiles; value at risk; credit risk; Monte Carlo simulation; gradient estimation;

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    Cited by:
    1. Kleijnen, Jack P.C. & Pierreval, Henri & Zhang, Jin, 2011. "Methodology for determining the acceptability of system designs in uncertain environments," European Journal of Operational Research, Elsevier, vol. 209(2), pages 176-183, March.
    2. Bernd Heidergott & Warren Volk-Makarewicz, 2013. "A Measure-Valued Differentiation Approach to Sensitivity Analysis of Quantiles," Tinbergen Institute Discussion Papers 13-082/III, Tinbergen Institute.

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