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 , 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 non-parametric class of bivariate distributions, we construct an estimator of the MES and establish the asymptotic normality of the estimator when p0, 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.
|Number of pages||25|
|Journal||Journal of the Royal Statistical Society, Series B|
|Early online date||15 May 2014|
|Publication status||Published - 1 Mar 2015|
- asymptotic normality
- conditional tail expectation
- extreme values