Conditional Monte Carlo Estimation of Quantile Sensitivities

Authors:
Michael C. Fu;L. Jeff Hong;Jian-Qiang Hu
Affiliations:
Robert H. Smith School of Business and Institute for Systems Research, University of Maryland, College Park, Maryland 20742;Department of Industrial Engineering and Logistics Management, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China;Department of Management Science, School of Management, Fudan University, 200433 Shanghai, China
Venue:
Management Science
Year:
2009

Citing 4
Cited 4

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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.