Risk Measurement and risk modelling using applications of Vine Copulas

Abstract

This paper features an application of Regular Vine copulas which are a novel and recently developed statistical and mathematical tool which can be applied in the assessment of composite financial risk. Copula-based dependence modelling is a popular tool in financial applications, but is usually applied to pairs of securities. By contrast, Vine copulas provide greater flexibility and permit the modelling of complex dependency patterns using the rich variety of bivariate copulas which may be arranged and analysed in a tree structure to explore multiple dependencies. The paper features the use of Regular Vine copulas in an analysis of the co-dependencies of 10 major European Stock Markets, as represented by individual market indices and the composite STOXX 50 index. The sample runs from 2005 to the end of 2011 to permit an exploration of how correlations change indifferent economic circumstances using three different sample periods: pre-GFC 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 are subject to change in different economic circumstances. One of the attractions of this approach to risk modelling is the flexibility in the choice of distributions used to model co-dependencies. The practical application of Regular Vine metrics is demonstrated via an example of the calculation of the VaR of a portfolio made up of the indices.