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On the Coherence of VaR Risk Measures for Levy Stable Distributions
Company: Australian Prudential Regulation Authority
Company Url: Click here to open
Year Of Publication: 2006
Month Of Publication: May
Pages: 15
Download Count: 12
View Count: 1903
Comment Num: 0
Language: English
Source: working paper
Who Can Read: Free
Date: 7-5-2010
Publisher: Administrator
Summary
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.
Author(s)
Sy, Wilson Sign in to follow this author
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