Financial Dependence Analysis: Applications of Vine Copulae

This paper features the application of a novel and recently developed method of statistical and mathe- matical analysis to the assessment of financial risk: namely Regular Vine copulas. Dependence modelling using copulas is a popular tool in financial applications, but is usually applied to pairs of securities. Vine copulas offer greater flexibility and permit the modelling of complex dependency patterns using the rich variety of bivariate copulas which can be arranged and analysed in a tree structure to facilitate the anal- ysis of multiple dependencies. We apply Regular Vine copula analysis to a sample of stocks comprising the Dow Jones Index to assess their interdependencies and to assess how their correlations change in different economic circumstances using three different sample periods: pre-GFC (Jan 2005- July 2007), GFC (July 2007-Sep 2009), and post-GFC periods (Sep 2009 - Dec 2011). The empirical results suggest that the dependencies change in a complex manner, and there is evidence of greater reliance on the Student t copula in the copula choice within the tree structures for the GFC period, which is consistent with the existence of larger tails in the distributions of returns for this period. One of the attractions of this approach to risk modelling is the flexibility in the choice of distributions used to model co-dependencies.