Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics

• 成果类型: Article
• 署名作者: Chun, So Yeon; Shapiro, Alexander; Uryasev, Stan
• 署名单位: Georgetown University; University System of Georgia; Georgia Institute of Technology; State University System of Florida; University of Florida
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1120.1072
• 发表日期: 2012
• 页码: 739-756
• 关键词: nonparametric-estimation; sensitivity-analysis; expected shortfall; portfolios; models

摘要

We discuss linear regression approaches to the estimation of law-invariant conditional risk measures. Two estimation procedures are considered and compared; one is based on residual analysis of the standard least-squares method, and the other is in the spirit of the M-estimation approach used in robust statistics. In particular, value-at-risk and average value-at-risk measures are discussed in detail. Large sample statistical inference of the estimators is derived. Furthermore, finite sample properties of the proposed estimators are investigated and compared with theoretical derivations in an extensive Monte Carlo study. Empirical results on the real data (different financial asset classes) are also provided to illustrate the performance of the estimators.