Extreme VaR Scenarios in Higher Dimensions

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Extreme VaR Scenarios in Higher Dimensions

by Paul Embrechts of ETH Zürich, and
Andrea Höing of ETH Zürich

February 10, 2006

Abstract: The dependence scenario yielding the worst possible Value-at-Risk at a given level α for X₁ + · · · + X_n is known for n = 2. In this paper we investigate this problem for higher dimensions. We provide a geometric interpretation highlighting the shape of the dependence structures which imply the worst possible scenario. For a portfolio (X₁, ... , X_n) with given uniform marginals, we give an analytical solution sustaining the main result of Rüschendorf (1982). In general, our approach allows for numerical computations.

JEL Classification: G10.

Subject Category: IM01, IM12, IM52.

Keywords: Value-at-Risk, dependent risks, copulas.

Published in: RISK, Vol. 19, No. 7, (July 2006), pp. 78-83.

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