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

J. Cai, J.H.J. Einmahl, L.F.M. de Haan, C. Zhou

Research output: Contribution to journalArticleScientificpeer-review

61 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)417-442
Number of pages25
JournalJournal of the Royal Statistical Society, Series B
Issue number2
Early online date15 May 2014
Publication statusPublished - 1 Mar 2015


  • asymptotic normality
  • conditional tail expectation
  • extreme values


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