Bayesian Model Selection of Regular Vine Copulas

• Activity Number: 541
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Lutz Gruber*+ and Claudia Czado
• Companies: Munich University of Technology and Munich University of Technology
• Keywords: Model Selection ; Dependence Modeling ; Vine Copula ; Financial Data

Abstract

Regular vine copulas can describe a wider array of dependency patterns than the multivariate Gaussian copula or the multivariate Student's t copula. We present two contributions related to model selection of regular vine copulas. First is a reversible jump Markov chain Monte Carlo algorithm to estimate the joint posterior distribution of the density factorization, pair copula families and parameters of a regular vine copula. In a second step, we reduce the algorithm to a tree-by-tree stepwise Bayesian procedure that allows for faster computation. A simulation study shows that our algorithm outperforms the model selection methods suggested in current literature and succeeds in recovering the true model when other methods fail. Furthermore, we present an application study that shows how a vine copula-based approach can improve the pricing of exotic financial derivatives using real-life data.