A hierarchical copula-based world-wide valuation of sovereign risk

We propose a new model for the aggregation of risks that is very flexible and useful in high dimensional problems. We propose a copula-based model that is both hierarchical and hybrid (HYC for short), because: (i) the dependence structure is modeled as a hierarchical copula, (ii) it unifies the idea of the clusterized homogeneous copula-based approach (CHC for short) and its limiting version (LHC for short) proposed in Bernardi and Romagnoli (2012, 2013). Based on this, we compute the loss function of a world-wide sovereign debt portfolio which accounts for a systemic dependence of all countries, in line with a global valuation of financial risks. Our approach enables us to take into account the non-exchangeable behavior of a sovereign debts' portfolio clustered into several classes with homogeneous risk and to recover a possible risks' hierarchy. A comparison between the HYC loss surface and those computed through a pure limiting approach, which is commonly used in high dimensional problems, is presented and the impact of the concentration and the granularity errors is appreciated. Finally the impact of an enlargement of the dependence structure is discussed, in the contest of a geographical area sub-portfolios analysis now relevant to determine the risk contributions of subgroups under the presence of a wider dependence structure. This argument is presented in relation to the evaluation of the insurance premium and the collateral related to the designed project of an euro-insurance-bond.