Modelling sovereign risks: from a hybrid model to the generalized density approach

Motivated by the European sovereign debt crisis, we study the sovereign risk by analyzing the solvency and the sovereign bond yield and propose a hybrid model which takes into account the movement of the sovereign solvency and the impact of critical political events. This model combines the structural and the reduced-form approaches in the credit risk modelling and the sovereign default time can be decomposed into an accessible part with predictable components and a totally inaccessible part. As a consequence, the probability of default at a critical political event date is nonzero and the probability law admits atoms. We study this model in a generalized density framework to deduce the compensator process of default and show that the intensity process does not necessarily exist. We also apply the model to the valuation of sovereign bond and explain the significant jumps in the long-term government bond yield during the sovereign crisis.