@techreport{e96e039fcb6b4cd5805b5611a64257f5,

title = "Estimation of the Marginal Expected Shortfall: The Mean when a Related Variable is Extreme",

abstract = "Abstract: 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 E(X | Y > QY (1−p)), 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 nonparametric class of bivariate distributions, we construct an estimator of the MES and establish the asymptotic normality of the estimator when p ↓ 0, 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 behavior. The finite sample performance of the estimator and the adequacy of the limit theorem are shown in a detailed simulation study. We also apply our method to estimate the MES of three large U.S. investment banks.",

keywords = "Asymptotic normality, extreme values, tail dependence",

author = "J. Cai and J.H.J. Einmahl and {de Haan}, L.F.M. and C. Zhou",

note = "Pagination: 28",

year = "2012",

language = "English",

volume = "2012-080",

series = "CentER Discussion Paper",

publisher = "Econometrics",

type = "WorkingPaper",

institution = "Econometrics",

}