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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
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:
Contact details of provider:
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)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Acharya, Viral V & Pedersen, Lasse H & Philippon, Thomas & Richardson, Matthew P, 2012.
"Measuring Systemic Risk,"
CEPR Discussion Papers
8824, C.E.P.R. Discussion Papers.
- repec:fip:fedhpr:y:2010:i:may:p:65-71 is not listed on IDEAS
- Einmahl, J.H.J., 1987. "Multivariate empirical processes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-142045, Tilburg University.
- Drees, Holger & Huang, Xin, 1998. "Best Attainable Rates of Convergence for Estimators of the Stable Tail Dependence Function," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 25-47, January.
- Vernic, Raluca, 2006. "Multivariate skew-normal distributions with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 413-426, April.
- repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
- Xiao Qin & Chen Zhou, 2013. "Systemic Risk Allocation for Systems with A Small Number of Banks," DNB Working Papers 378, Netherlands Central Bank, Research Department.
- Hua, Lei & Joe, Harry, 2014. "Strength of tail dependence based on conditional tail expectation," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 143-159.
- Areski Cousin & Elena Di Bernardinoy, 2013. "On Multivariate Extensions of Conditional-Tail-Expectation," Working Papers hal-00877386, HAL.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Richard Broekman).
If references are entirely missing, you can add them using this form.