Conditional Monte Carlo Estimation of Quantile Sensitivities

Michael C. Fu (), L. Jeff Hong () and Jian-Qiang Hu ()
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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

Management Science, 2009, vol. 55, issue 12, 2019-2027

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.

Keywords: quantiles; value at risk; credit risk; Monte Carlo simulation; gradient estimation (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (43)

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