Modeling Dependence Between Financial Returns Using Pair-Copula Constructions

In this chapter, we compare three constructions for modeling higher-dimensional dependence: the Student copula, the partially nested Archimedean construction (PNAC) and the pair-copula construction. For the latter two, a multivariate data set is modeled using a cascade of lower-dimensional copulae. They differ, however, in their construction of the dependence structure. The PNAC is more restrictive than the PCC in two respects. There are strong limitations on the degree of dependence in each level of the PNAC, and all the bivariate copulae in this construction has to be Archimedean. The PCC, on the other hand, can be built using copulae from any class and there are no constraints on the parameters. We show through two applications that the PCC provides a better fit to financial data than the two other structures.