Truncated and Simplified Regular Vines for High-Dimensional Financial Risk Modeling

• Activity Number: 502
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Eike Christian Brechmann*+ and Claudia Czado and Kjersti Aas
• Companies: Technische Universität München and Technische Universität München and Norwegian Computing Center
• Keywords: multivariate copula ; regular vines ; truncated vines ; simplified vines

Abstract

Introduced by Bedford and Cooke (2001, Ann. Math. Artif. Intell.) and discussed in detail in Kurowicka and Cooke (2006, Wiley & Sons) regular vines (R-vines) are a flexible class of high-dimensional dependency models which use only bivariate copulas as building blocks. Each copula can be chosen arbitrarily and the full model exhibit complex dependence patterns such as asymmetry and tail dependence. The flexibility however comes along with a strongly increasing model complexity in higher dimensions. We therefore propose innovative efficient ways of constructing R-vines. This involves the choice of R-vine trees, selection of copula types and, in particular, possible simplifications after modeling a certain number of dependency levels with copulas. Regarding the latter issue we propose different new approaches using iterative Vuong tests, AIC and BIC as well as goodness-of-fit tests. All approaches are validated in extensive simulation studies and a substantial application to the returns of the Euro Stoxx 50 members is presented. In particular, we construct an extended version of the classical CAPM, the so-called Regular Vine Market Sector Model, which is based on a simplified R-vine.