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.
|Place of Publication||Tilburg|
|Number of pages||28|
|Publication status||Published - 2012|
|Name||CentER Discussion Paper|
- Asymptotic normality
- extreme values
- tail dependence
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. (CentER Discussion Paper; Vol. 2012-080). Econometrics.