English, Article, Journal or magazine article edition: On the Coherence of VAR Risk Measure for Levy Stable Distributions Wilson Sy

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Bookmark: http://trove.nla.gov.au/version/156
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • On the Coherence of VAR Risk Measure for Levy Stable Distributions
Author
  • Wilson Sy
Physical Description
  • preprint
Notes
  • 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.
  • RePEc:apr:aprewp:wp2006-02
Language
  • English
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