Analyzing the Correlation Structure of Financial Markets Using a Quantile Graphical Model

In this paper we develop a quantile graphical model to identify the tail conditional correlation 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 set of market indexes, cryptocurrencies and commodities.