For further disscussion of Copula families the readers are encouraged to refer to Nelsen (1999).

2.3 Pair-Copula Construction

Modelling bivariate distribution by means of copulas is relatively easy task, since there are a lot of work devoted to that topic. However, things get complicated as the dimension of the distribution gets higher. This project makes use of the hierarchial model called Pair-Copula construction, described in Aas, Czado, Frigessi, Bakken (2009). The main idea is to decompose a multivariate density into blocks of bivariate pair copulas, applied on original variables and on their conditional and unconditional distribution functions [6]. Details of algorithms described below can be found in [6].