Estimation of the marginal expected shortfall: the mean when a related variable is extreme

Denote the loss return on the equity of a financial institution as X and that of the entire market as Y. For a given very small value of p>0, the marginal expected shortfall (MES) is defined as , where QY(1?p) is the (1?p)th quantile of the distribution of Y. The MES is an important factor when measuring the systemic risk of financial institutions. For a wide non-parametric class of bivariate distributions, we construct an estimator of the MES and establish the asymptotic normality of the estimator when p0, as the sample size n?. Since we are in particular interested in the case p=O(1/n), we use extreme value techniques for deriving the estimator and its asymptotic behaviour. The finite sample performance of the estimator and the relevance of the limit theorem are shown in a detailed simulation study. We also apply our method to estimate the MES of three large US investment banks.