VaR bounds in models with partial dependence information on subgroups

Abstract

We derive improved estimates for the model risk of risk portfolios when additional to the marginals some partial dependence information is available.We consider models which are split into k subgroups and consider various classes of dependence information either within the subgroups or between the subgroups. As consequence we obtain improved VaR bounds for the joint portfolio compared to the case with only information on the marginals. Our paper adds to various recent approaches to obtain reliable and usable risk bounds resp. estimates of the model risk by including partial dependence information additional to the information on the marginals. In particular we extend an approach suggested in Bignozzi, Puccetti and Rüschendorf (2015) and in Puccetti, Rüschendorf, Small and Vanduffel (2017), which is based on positive dependence resp. on independence information available for some subgroups.

Keywords

• var bounds
• dependence orderings
• copula models
• risk factor models
• 91b30 (primary)
• 60e15 (secondary)