Univariate conditioning of vine copulas

Abstract

In this paper we deal with the tail behaviour of copulas. We compare the methods based on the univariate conditioning of a selected variable and on the tail dependence functions. We introduce a new subclass of vine copulas, consisting of regular vine copulas which are “rooted” at the first variable and study the limiting properties of such copulas. • We construct and study a new subclass of vine copulas which are characterized by a star like first level tree—C*-vines. • We study the interlink between tail dependence and univariate conditioning (truncation) of copulas. • The formulas for tail dependence functions and limit copulas of the univariate conditioning are provided for C*-vines. • The necessary and sufficient conditions for a C*-vine to be invariant with respect to univariate conditioning are presented. • The possible applications to risk management are discussed.