Extreme risk interdependence

We define tail interdependence as a situation where extreme outcomes for some variables are informative about such outcomes for other variables. We extend the concept of multiinformation to quantify tail interdependence, decompose it into systemic and residual interdependence and measure the contribution of a constituent to the interdependence of a system. Further, we devise statistical procedures to test: a) tail independence, b) whether an empirical interdependence structure is generated by a theoretical model and c) symmetry of the interdependence structure in the tails. We outline some additional extensions and illustrate this framework by applying it to several datasets.