On Multivariate Extensions of Value-at-Risk

Areski Cousin () and Elena Di Bernadino ()
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Areski Cousin: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Elena Di Bernadino: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon

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Abstract: In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk portfolio. The lower-orthant VaR is constructed from level sets of multivariate distribution functions whereas the upper-orthant VaR is constructed from level sets of multivariate survival functions. Several properties have been derived. In particular, we show that these risk measures both satisfy the positive homogeneity and the translation invariance property. Comparison between univariate risk measures and components of multivariate VaR are provided. We also analyze how these measures are impacted by a change in marginal distributions, by a change in dependence structure and by a change in risk level. Illustrations are given in the class of Archimedean copulas.

Keywords: Multivariate Risk Measures; Level sets of distribution functions; Kendall distributions; Copulas (search for similar items in EconPapers)
Date: 2013-04-04
New Economics Papers: this item is included in nep-ban and nep-rmg
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Citations: View citations in EconPapers (39)

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