# 13-082/III (2013-06-29)

Bernd Heidergott, VU University Amsterdam; Warren Volk-Makarewicz, VU University Amsterdam
quantile, sensitivity analysis, Monte-Carlo simulation, measure-valued differentiation, options, multi-asset option, Variance-Gamma process
JEL codes:
C44, C13, C63

This discussion paper led to a publication in 'Mathematics of Operations Research'.

Quantiles play an important role in modelling quality of service in the service industry and in modelling risk in the financial industry. Recently, Hong showed in his breakthrough papers that efficient simulation based estimators can be obtained for quantile sensitivities by means of sample path differentiation. This 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 (MVD). 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 quantile of the value of a multi-asset option and a portfolio. In addition, we discuss application of our sensitivity estimator to the Variance-Gamma process and to queueing networks.