Moment-Based CVaR Estimation: Quasi-Closed Formulas

16 Pages Posted: 4 Jun 2011

See all articles by Patrizia Stucchi

Patrizia Stucchi

Università degli Studi di Udine

Date Written: May 31, 2011


The evaluation of quantiles (or VaR, Value at Risk) and that of CVaR, Conditional Value at Risk in risk management (or mean excess in actuarial sciences) is a very crucial point in the decision processes. Indeed, there are often great difficulties (or impossibilities) in finding the kind of distribution followed by the key random variable (r.v.). Several approaches suggest suitable transformations of the standard normal variable which may represent a good proxy of the key r.v. The transformations considered here are based on the first three (Normal-Power) or four (Johnson's systems) moments. In this paper, for any kind of r.v., closed or quasi-closed formulas for CVaR are given (starting from their first four moments) using the Normal-Power and Johnson's systems. Here there is also the analysis of the efficiency of the Johnson's method with reference to financial applications.

Keywords: Risk Measures, Conditional Value at Risk, Skewness, Kurtosis

JEL Classification: G11, C63

Suggested Citation

Stucchi, Patrizia, Moment-Based CVaR Estimation: Quasi-Closed Formulas (May 31, 2011). Available at SSRN: or

Patrizia Stucchi (Contact Author)

Università degli Studi di Udine ( email )

Via Tarcisio Petracco, Palazzo antonini, 8
Udine, 33100

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