A Measure-Valued Differentiation Approach to Sensitivities of Quantiles

Quantiles play an important role in modelling quality of service in the service industry and in modelling risk in the financial industry. The recent discovery that efficient simulation-based estimators can be obtained for quantile sensitivities has led to an intensive search for sample-path differentiation-based estimators for quantile sensitivities. In this paper, we present a novel approach to quantile sensitivity estimation. Our approach elaborates on the concept of measure-valued differentiation. Thereby, we overcome the main obstacle of the sample-path approach, which is the requirement that the sample cost have to be Lipschitz continuous with respect to the parameter of interest. Specifically, we perform a sensitivity analysis of the value at risk in financial models. In addition, we discuss an application of our sensitivity estimator to queueing networks.