Using Order Statistics to Estimate Confidence Intervals for Quantile-Based Risk Measures

Abstract

This article shows how to apply the theory of order statistics to estimate confidence intervals for quantile-based risk measures, a class that includes the VaR, expected shortfall, and coherent, convex, and spectral risk measures. The proposed method can be applied to any parametric or nonparametric loss distribution, has a number of advantages relative to alternative methods of estimating confidence intervals for financial risk measures, and is straightforward to implement.