Construction of Multivariate Distributions With Asymmetric Dependence: Hierarchical Arquimedean Copula, Pair-Copula and Students t Copula.

Abstract

The construction of multivariate distributions with asymmetric dependencies, especially with complex tail dependence is a necessary requirement in many applications, particularly in finance. The theory of copulas can be very useful in this task. In this sense, some of the proposals suggested in the literature are Archimedean hierarchical models, pair-copula models and t-Student copula. The choice of appropriate methodology for each situation is still hampered by several issues. The project focuses on some of these issues: a comparison of the properties of the models, construction and estimation of copulas. In all models there is a difficulty to jointly estimating the parameters of the models. The project emphasizes the comparison of the dependencies in the tails and the joint estimation of parameters in the three classes of models.