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 (2009) derived a batched infinitesimal perturbation analysis estimator for quantile sensitivities, and Liu and Hong (2009) 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.