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

So Yeon Chun (), Alexander Shapiro () and Stan Uryasev ()
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Alexander Shapiro: School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
Stan Uryasev: Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611

Operations Research, 2012, vol. 60, issue 4, 739-756

Abstract: 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.

Keywords: value-at-risk; average value-at-risk; linear regression; least-squares residuals; M-estimators; quantile regression; conditional risk measures; law-invariant risk measures; statistical inference (search for similar items in EconPapers)
Date: 2012
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Handle: RePEc:inm:oropre:v:60:y:2012:i:4:p:739-756