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

Chun, So Yeon and Shapiro, Alexander and Uryasev, Stan (2011): Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics. Forthcoming in:

Abstract

We discuss linear regression approaches to conditional Value-at-Risk and Average Value-at-Risk (Conditional Value-at-Risk, Expected Shortfall) risk measures. Two estimation procedures are considered for each conditional risk measure, one is direct and the other is based on residual analysis of the standard least squares method. Large sample statistical inference of the estimators obtained 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Value-at-Risk, Average Value-at-Risk, Conditional Value-at-Risk, Expected Shortfall, linear regression, least squares residual, quantile regression, conditional risk measures, statistical inference
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty; G - Financial Economics > G3 - Corporate Finance and Governance > G32 - Financing Policy ; Financial Risk and Risk Management ; Capital and Ownership Structure ; Value of Firms ; Goodwill; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General

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