Lower Tail Dependence for Archimedean Copulas: Characterizations and Pitfalls
CentER Discussion Paper Series No. 2006-29
11 Pages Posted: 9 May 2006
Date Written: April 2006
Tail dependence copulas provide a natural perspective from which one can study the dependence in the tail of a multivariate distribution. For Archimedean copulas with continuously differentiable generators, regular variation of the generator near the origin is known to be closely connected to convergence of the corresponding lower tail dependence copulas to the Clayton copula. In this paper, these characterizations are refined and extended to the case of generators which are not necessarily continuously differentiable. Moreover, a counterexample is constructed showing that even if the generator of a strict Archimedean copula is continuously differentiable and slowly varying at the origin, then the lower tail dependence copulas do not need to converge to the independent copula.
Keywords: Archimedean copula, regular variation, tail dependence, de Haan class
JEL Classification: C14, C16
Suggested Citation: Suggested Citation