Bounds for Value at Risk for Asymptotically Dependent Assets - the Copula Approach

The theory of copulas provides a useful tool for modeling dependence in risk management. In insurance and finance, as well as in other applications, dependence of extreme events is particularly important, hence there is a need for the detailed study of the tail behaviour of the multivariate copulas. In this paper we investigate the class of copulas having homogeneous lower tails. We show that having only such information on the structure of dependence of returns from assets is enough to get estimates on Value at Risk of the multiasset portfolio in terms of Value at Risk of one-asset portfolios.