Copulas and Tail Dependence in Finance

Abstract

This chapter discusses the copula methods for application in finance. It provides an overview of the concept of copula, and the underlying statistical theories as well as theorems involved. The focus is on two copula families, namely, the elliptical and Archimedean copulas. The Gaussian and Student’s t copulas in the family of elliptical copulas which have symmetrical tails in their distributions are explained. The Clayton and Gumbel copulas in the family of Archimedean copulas whose distributions are asymmetrical are also described. Elaborations are given on tail dependence and the associated measures for these copulas. The estimation process is illustrated using an application of the methods on the returns of two exchange series.