Bayesian nonparametric copulas with tail dependence

We introduce a novel bivariate copula model able to capture both the central and tail dependence of the joint probability distribution. Model that can capture the dependence structure within the joint tail have important implications in many application areas where the focus is risk management (e.g. macroeconomics and finance). We use a Bayesian nonparametric approach to introduce a random copula based on infinite partitions of unity. We define a hierarchical prior over an infinite partition of the unit hypercube which has a stick breaking representation leading to an infinite mixture of products of independent beta densities. Capitalising on the stick breaking representation we introduce a Gibbs sample to proceed to inference. For our empirical analysis we consider both simulated and real data (insurance claims and portfolio returns). We compare both our model's ability to capture tail dependence and its out of sample predictive performance to competitive models (e.g. Joe and Clayton copulas) and show that in both simulated and real examples our model outperforms the competitive models.