Dependence uncertainty for aggregate risk: Examples and simple bounds

Abstract

Over the recent years, numerous results have been derived in order to assess the properties of regulatory risk measures (in particular VaR and ES) under dependence uncertainty. In this paper we complement this mainly methodological research by providing several numerical examples for both homogeneous as well as inhomogeneous portfolios. In particular, we investigate under which circumstances the so-called worst-case VaR can be well approximated by the worst-case (i.e. comonotonic) ES. We also study best-case values and simple lower bounds.