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Conditional Monte Carlo Estimation of Quantile Sensitivities

Michael C. Fu, L. Jeff Hong and Jian-Qiang Hu
Management Science
Vol. 55, No. 12 (Dec., 2009), pp. 2019-2027
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/40539262
Page Count: 9
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Conditional Monte Carlo Estimation of Quantile Sensitivities
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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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