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Estimation of the Marginal Expected Shortfall: The Mean when a Related Variable is Extreme

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Author Info

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

    (Tilburg University, Center for Economic Research)

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.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2012-080.

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Date of creation: 2012
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Handle: RePEc:dgr:kubcen:2012080

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Web page: http://center.uvt.nl

Related research

Keywords: Asymptotic normality; extreme values; tail dependence;

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References

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  1. Viral V. Acharya & Lasse H. Pedersen & Thomas Philippon & Matthew Richardson, 2010. "Measuring systemic risk," Working Paper 1002, Federal Reserve Bank of Cleveland.
  2. 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.
  3. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
  4. Einmahl, J.H.J., 1987. "Multivariate empirical processes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-142045, Tilburg University.
  5. repec:fip:fedhpr:y:2010:i:may:p:65-71 is not listed on IDEAS
  6. Vernic, Raluca, 2006. "Multivariate skew-normal distributions with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 413-426, April.
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Citations

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Cited by:
  1. 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.
  2. Areski Cousin & Elena Di Bernardinoy, 2013. "On Multivariate Extensions of Conditional-Tail-Expectation," Working Papers hal-00877386, HAL.
  3. 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.

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