Counterdiagonal/nonpositive tail dependence in Vine copula constructions: application to portfolio management

Abstract
Accurately modelling the dependence structure between financial assets in a portfolio optimization framework has attracted growing attention in statistical and financial literature. Since in these assets several types of tail dependence might occur simultaneously, it is fundamental for parametric models to adequately replicate their whole tail dependence structure. This article investigates the effectiveness of Vine copulas in modelling counterdiagonal/nonpositive tail dependence, so far overlooked. We obtain expressions for their corresponding general tail dependence function which accounts for all dependences. This generalises the well-known approach of using the survival copula to study upper tail dependence, rather than using rotations on the data. We prove that, further to the already known flexibility to model asymmetric lower and upper tail dependence, Vine copulas can model all multivariate types of tail dependence simultaneously. In an empirical application, using a D-Vine copula with appropriate choices of bivariate linking copulas, we are able to capture the tail dependence structure of a portfolio of financial data in which different types of tail dependence coexist. Further to this, we test to what extent Vine copulas are able to model different types of tail dependence.