Hierarchical Graphical Models with Application to Systemic Risk

The latest financial crisis has stressed the need of understanding the world financial system as a network of interconnected institutions, where financial linkages play a fundamental role in the spread of systemic risks. In this paper we propose to enrich the topological perspective of network models with a more structured statistical framework, that of Bayesian graphical Gaussian models. From a statistical viewpoint, we propose a new class of hierarchical Bayesian graphical models, that can split correlations between institutions into country specific and idiosyncratic ones, in a way that parallels the decomposition of returns in the well-known Capital Asset Pricing Model. From a financial economics viewpoint, we suggest a way to model systemic risk that can explicitly take into account frictions between different financial markets, particularly suited to study the on-going banking union process in Europe. From a computational viewpoint, we develop a novel Markov Chain Monte Carlo algorithm based on Bayes factor thresholding.