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

Author

Listed:
  • Cai, J.

    (Tilburg University, School of Economics and Management)

  • Einmahl, J.H.J.

    (Tilburg University, School of Economics and Management)

  • de Haan, L.F.M.

    (Tilburg University, School of Economics and Management)

  • Zhou, C.

Abstract

type="main" xml:id="rssb12069-abs-0001"> 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 &7C Y > Q Y ( 1 − p ) } , where Q Y (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 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 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.
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Suggested Citation

  • Cai, J. & Einmahl, J.H.J. & de Haan, L.F.M. & Zhou, C., 2012. "Estimation of the Marginal Expected Shortfall : The Mean when a Related Variable is Extreme," Other publications TiSEM e96e039f-cb6b-4cd5-805b-5, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:e96e039f-cb6b-4cd5-805b-5611a64257f5
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    References listed on IDEAS

    as
    1. Viral V. Acharya & Lasse H. Pedersen & Thomas Philippon & Matthew Richardson, 2017. "Measuring Systemic Risk," The Review of Financial Studies, Society for Financial Studies, vol. 30(1), pages 2-47.
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    3. Einmahl, J.H.J. & de Haan, L.F.M. & Li, D., 2006. "Weighted approximations of tail copula processes with applications to testing the bivariate extreme value condition," Other publications TiSEM 18b65ac3-ba79-4bff-ad53-2, Tilburg University, School of Economics and Management.
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    6. Einmahl, J.H.J., 1987. "Multivariate empirical processes," Other publications TiSEM 4d74fa6b-5281-48ea-aa4d-5, Tilburg University, School of Economics and Management.
    7. 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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    More about this item

    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

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