Statistical analysis of multivariate dependence structures among financial time series

Abstract

In recent years copulas have become increasingly popular in .nancial applications however most of the empirical work in the .eld is focused on bivariate problems. The current thesis aims to .ll in some gaps in multivariate copulas by introducing to distinct methods that allow the researcher to use copulas in arbitrary dimensions. The thesis consists of .ve chapters, chapter one introduces the statistical theory behind copulas and provides a comprehensive review of the major applications of copulas in .nance. Chapter two introduces a novel way to estimate copulas in vast dimension based on the notion of composite likelihood. Chapter three introduces a multivariate non linear non normal CAPM model named the F - Vine. Chapter four describes in detail a MATLAB toolbox speci.cally designed by the author to .t copula based models and chapter .ve provides analytical derivatives of some of the most popular copula models used in .nance