Kernel estimation of quantile sensitivities

Quantiles, also known as value-at-risks in the financial industry, are important measures of random performances. Quantile sensitivities provide information on how changes in input parameters affect output quantiles. They are very useful in risk management. In this article, we study the estimation of quantile sensitivities using stochastic simulation. We propose a kernel estimator and prove that it is consistent and asymptotically normally distributed for outputs from both terminating and steady-state simulations. The theoretical analysis and numerical experiments both show that the kernel estimator is more efficient than the batching estimator of Hong [9].