Estimation of the marginal expected shortfall: the mean when a related variable is extreme

• 成果类型: Article
• 署名作者: Cai, Juan-Juan; Einmahl, John H. J.; de Haan, Laurens; Zhou, Chen
• 署名单位: Delft University of Technology; Tilburg University; Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam; Universidade de Lisboa; European Central Bank; De Nederlandsche Bank NV; Tinbergen Institute
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12069
• 发表日期: 2015
• 页码: 417-442
• 关键词: weighted approximations; tail

摘要

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 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 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.