Singularity Bias, Systemic Risk and Credit Indexes

Abstract

Singular distributions, such as the Marshall-Olkin one, assign a probability mass to the simultaneous occurrence of events. Aim of this paper is to: i) provide systemic risk measures based on singular distributions; ii) evaluate the presence of a singular component in the joint default distribution of financial institutions; iii) evaluate the impact on the systemic measure of the use of absolutely continuous distributions if the true distribution is singular (we call this singularity bias). The analysis is carried out in a set of hidden common shocks models with Archimedean dependence for which the simultaneous shock intensity is proportional to the CDS credit index of the banks involved, a key feature to define a test of the presence of a singularity. The model is applied to a panel of European banks in the sovereign crisis period and after the crisis, and the specification test based on credit indexes shows clear evidence of the presence of a singular component during the crisis, while this hypothesis is rejected at the 10% probability level in the post crisis period. In the crisis period we evaluate the impact of the singularity bias on two measures representative of the actuarial approach to systemic risk. The singularity bias induces a severe underestimation of last-to-default systemic risk measures, while the sign and magnitude of the effect is more difficult to predict for measures that take into account the default of all subsets of banks.

Keywords: Systemic Risk, Credit Indexes, Marshall Olkin Models, Copula Functions

JEL Classification: G01, G21, G22, C23, C38, C43, C58