Causal analysis of extreme risk in a network of industry portfolios

We provide a detailed review of causal dependence within the framework of max‐linear structural models. Such models express each node variable as a max‐linear function of its parental node variables in a directed acyclic graph (DAG) and some exogenous innovation. We reformulate results on structure learning and estimation, which we apply to a network of financial data. A new method, based on hard‐thresholding and on the Hamming distance, estimates a sparse DAG for extreme risk propagation.