Construction of multivariate distributions wits asymmetric dependence: hierarchical arquimedean copula, pair-copula and t-student copula

Author(s)

Caroline de Freitas Sakamoto

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Ciência da Computação
• Defense date: 2012-02-28

Examining board members

Luiz Koodi Hotta; Mauricio Enrique Zevallos Herencia; Pedro Luiz Valls Pereira

• Advisor: Luiz Koodi Hotta

Abstract

The construction of multivariate distributions with asymmetric dependencies, especially with complex dependencies in the tails, 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 the Archimedean hierarchical models, Pair-Copula models and asymmetric t-Student copula. This dissertation is focused on the study and application of models of more than three dimensions through the Pair-Copula models, which have been essential to extend the concept of dependence of bivariate case to the multivariate case. The Pair-Copula methodology proposes the use of vine tree for the organization the possible models. Emphasis is given to the D-vine tree, which allows permutation among the variables. The influence and the importance of the order of the variables in the D-vine in the estimation of the Value at Risk (VaR) is investigated by simulation. The pair-copula model is compared with the t-Student multivariate distribution, the multivariate Archimedean copula, and paircopula models using different copula functions. The model is also applied to estimate the VaR of a portfolio with four assets (AU)

• FAPESP's process: 09/11104-6 - Construction of Multivariate Distributions With Asymmetric Dependence: Hierarchical Arquimedean Copula, Pair-Copula and Students t Copula.
• Grantee: Caroline de Freitas Sakamoto
• Support Opportunities: Scholarships in Brazil - Master