Graphical Models for Commodities: A Quantile Approach

The high level of integration of international financial markets highlights the need to accurately assess contagion and systemic risk under different market conditions. To this end, we develop a quantile graphical model to identify the tail conditional dependence structure in multivariate data across different quantiles of the marginal distributions of the variables of interest. To implement the procedure, we consider the Multivariate Asymmetric Laplace distribution and exploit its location-scale mixture representation to build a penalized EM algorithm for estimating the sparse precision matrix of the distribution by means of an L1 penalty. The empirical application is performed on a large set of commodities representative of the energy, agricultural and metal sectors.