Kernel quantile based estimation of expected shortfall

Keming Yu, Abdallah K. Ally, Shanchao Yang, David J. Hand

Abstract

ABSTRACT

Since its proposal as an alternative risk measure to value-at-risk (VaR), expected shortfall (ES) has attracted a great deal of attention in financial risk management, primarily owing to its coherent properties. Recently, there has been an upsurge of research on the estimation of ES from a nonparametric perspective. The focus of this paper is on a few kernel-based ES estimators, including jackknife-based bias-correction estimators that have theoretically been documented to reduce bias. Bias reduction is particularly effective in reducing the tail estimation bias as well as the consequential bias that arises in kernel smoothing and finite-sample fitting and, thus, serves as a natural approach to the estimation of extreme quantiles of asset price distributions. By taking advantage of ES as an integral of the quantile function, a new type of ES estimator is proposed. To compare the performance of the estimators, a series of comparative simulation studies are presented and the methods are applied to real data. An estimator that has an analytical form turned out to perform the best.