Conditional Monte Carlo Estimation of Quantile Sensitivities
AbstractEstimating 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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Bibliographic InfoArticle provided by INFORMS in its journal Management Science.
Volume (Year): 55 (2009)
Issue (Month): 12 (December)
quantiles; value at risk; credit risk; Monte Carlo simulation; gradient estimation;
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- Kleijnen, Jack P.C. & Pierreval, H. & Zhang, J., 2011.
"Methodology for determining the acceptability of system designs in uncertain environments,"
Open Access publications from Tilburg University
urn:nbn:nl:ui:12-4274964, Tilburg University.
- 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.
- 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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