On the Coherence of VAR Risk Measures for Levy Stable Distributions

15 Pages Posted: 16 Oct 2015

See all articles by Wilson N. Sy

Wilson N. Sy

Investment Analytics Research

Date Written: May 16, 2006


The Value-at-Risk (VaR) risk measure has been widely used in finance and insurance for capital and risk management. However, in recent years it has fallen somewhat out of favour due to a seminal paper by Artzner et al. (1999) who showed that VaR does not in general have all the four coherence properties which are desirable for a risk measure. In particular, the violation of the sub-additive property discourages diversification and is counter-intuitive to risk finance. In this paper, it is proved (Theorem 3.1) that VaR for independent Levy-stable random variates is a coherent risk measure being translational invariant, monotonic, positively homogeneous and sub-additive. That is, Levy-stable distributions are VaR coherent. As Levy-stable distributions are a rich class of probability distributions, the VaR risk measure may still have widespread applications. A brief comparative discussion is also given for L-stable variates for the expected shortfall risk measure.

Keywords: Coherencce, VaR, Risk Measure, Levy-stable

JEL Classification: G18, G28, G38

Suggested Citation

Sy, Wilson N., On the Coherence of VAR Risk Measures for Levy Stable Distributions (May 16, 2006). Available at SSRN: https://ssrn.com/abstract=2674989 or http://dx.doi.org/10.2139/ssrn.2674989

Wilson N. Sy (Contact Author)

Investment Analytics Research ( email )

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Balmain East, NSW 2041
0424669802 (Phone)

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