Estimation of the Marginal Expected Shortfall: The Mean when a Related Variable is Extreme
AbstractAbstract: 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.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2012-080.
Date of creation: 2012
Date of revision:
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Web page: http://center.uvt.nl
Asymptotic normality; extreme values; tail dependence;
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-10-27 (All new papers)
- NEP-BAN-2012-10-27 (Banking)
- NEP-ECM-2012-10-27 (Econometrics)
- NEP-RMG-2012-10-27 (Risk Management)
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