Computing the Portfolio Conditional Value-at-Risk in the Alpha-Stable Case

Probability and Mathematical Statistics, Vol. 26, No. 1, pp. 1-22, 2006

25 Pages Posted: 21 Dec 2010

See all articles by Stoyan V. Stoyanov

Stoyan V. Stoyanov

Charles Schwab

Gennady Samorodnitsky

Cornell University

Svetlozar Rachev

Texas Tech University

Sergio Ortobelli Lozza

University of Bergamo - Mathematics, Statistics, Computer Science and Applications (MSIA)

Date Written: August 14, 2005

Abstract

The class of alpha-stable distributions is an attractive probabilistic model of asset returns distribution in the field of finance. When dealing with real issues, such as optimal portfolio selection, it is important that we can compute the Conditional Value-at-Risk (CVaR) accurately. CVaR is also known as expected tail loss (ETL) proposed in the literature as a coherent risk measure. In our paper, we propose an integral expression for the calculation of the CVaR of a stable law. We compare the current approach to some existing methods and we demonstrate how to relate the derived result to some common multivariate distributional assumptions.

Keywords: stable distributions, heavy tails, coherent risk measures, conditional value-at-risk, expected tail loss

JEL Classification: C16, G32

Suggested Citation

Stoyanov, Stoyan Veselinov and Samorodnitsky, Gennady and Rachev, Svetlozar and Ortobelli Lozza, Sergio, Computing the Portfolio Conditional Value-at-Risk in the Alpha-Stable Case (August 14, 2005). Probability and Mathematical Statistics, Vol. 26, No. 1, pp. 1-22, 2006, Available at SSRN: https://ssrn.com/abstract=1729002

Stoyan Veselinov Stoyanov (Contact Author)

Charles Schwab ( email )

101 Montgomery Street (120K-15)
San Francisco, CA 94104
United States

Gennady Samorodnitsky

Cornell University ( email )

School of Operations Research and Industrial Engineering; Department of Statistical Science
Ithaca, NY 14853
United States

Svetlozar Rachev

Texas Tech University ( email )

Dept of Mathematics and Statistics
Lubbock, TX 79409
United States
631-662-6516 (Phone)

Sergio Ortobelli Lozza

University of Bergamo - Mathematics, Statistics, Computer Science and Applications (MSIA) ( email )

Via Salvecchio, 19
Bergamo, 24129
Italy

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