On estimating the conditional expected shortfall

摘要

Unlike the value at risk, the expected shortfall is a coherent measure of risk. In this paper, we discuss estimation of the expected shortfall of a random variable Y{sub}t with special reference to the case when auxiliary information is available in the form of a set of predictors X{sub}t. We consider three classes of estimators of the conditional expected shortfall of Y{sub}t given X{sub}t: a class of fully non-parametric estimators and two classes of analog estimators based, respectively, on the empirical conditional quantile function and the empirical conditional distribution function. We study their sampling properties by means of a set of Monte Carlo experiments and analyze their performance in an empirical application to financial data.