Extreme VaR Scenarios in Higher Dimensions
by Paul Embrechts of ETH Zürich, and
February 10, 2006
Abstract: The dependence scenario yielding the worst possible Value-at-Risk at a given level α for X 1 + · · · + 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 (X 1 , ... , 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.
Subject Category: IM01, IM12, IM52.
Keywords: Value-at-Risk, dependent risks, copulas.
Published in: Extremes, Vol, 9, No. 3-4, (December 2006), pp. 177-192.