On Conditional Value at Risk (CoVaR) for tail-dependent copulas

Abstract

The paper deals with Conditional Value at Risk (CoVaR) for copulas with nontrivial tail dependence. We show that both in the standard and the modified settings, the tail dependence function determines the limiting properties of CoVaR as the conditioning event becomes more extreme. The results are illustrated with examples using the extreme value, conic and truncation invariant families of bivariate tail-dependent copulas.