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Conditional Monte Carlo Estimation of Quantile Sensitivities

Author

Listed:
  • 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)

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.

Suggested Citation

  • Michael C. Fu & L. Jeff Hong & Jian-Qiang Hu, 2009. "Conditional Monte Carlo Estimation of Quantile Sensitivities," Management Science, INFORMS, vol. 55(12), pages 2019-2027, December.
    • Handle: RePEc:inm:ormnsc:v:55:y:2009:i:12:p:2019-2027
    DOI: 10.1287/mnsc.1090.1090
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    References listed on IDEAS

    as
    1. L. Jeff Hong, 2009. "Estimating Quantile Sensitivities," Operations Research, INFORMS, vol. 57(1), pages 118-130, February.
    2. L. Jeff Hong & Guangwu Liu, 2009. "Simulating Sensitivities of Conditional Value at Risk," Management Science, INFORMS, vol. 55(2), pages 281-293, February.
    3. Achal Bassamboo & Sandeep Juneja & Assaf Zeevi, 2008. "Portfolio Credit Risk with Extremal Dependence: Asymptotic Analysis and Efficient Simulation," Operations Research, INFORMS, vol. 56(3), pages 593-606, June.
    Full references (including those not matched with items on IDEAS)

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