Conditional Monte Carlo Estimation of Quantile Sensitivities

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.