### Abstract

Original language | English |
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Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 28 |

Volume | 2012-080 |

Publication status | Published - 2012 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2012-080 |

### Fingerprint

### Keywords

- Asymptotic normality
- extreme values
- tail dependence

### Cite this

*Estimation of the Marginal Expected Shortfall: The Mean when a Related Variable is Extreme*. (CentER Discussion Paper; Vol. 2012-080). Tilburg: Econometrics.

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**Estimation of the Marginal Expected Shortfall : The Mean when a Related Variable is Extreme.** / Cai, J.; Einmahl, J.H.J.; de Haan, L.F.M.; Zhou, C.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Estimation of the Marginal Expected Shortfall

T2 - The Mean when a Related Variable is Extreme

AU - Cai, J.

AU - Einmahl, J.H.J.

AU - de Haan, L.F.M.

AU - Zhou, C.

N1 - Pagination: 28

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Asymptotic normality

KW - extreme values

KW - tail dependence

M3 - Discussion paper

VL - 2012-080

T3 - CentER Discussion Paper

BT - Estimation of the Marginal Expected Shortfall

PB - Econometrics

CY - Tilburg

ER -