Abstract
Counterparty risk on a portfolio of credit instruments between two parties poses some specific modeling challenges. On one hand, the model must be able to account for the wrong-way risk which is due to the potentially strong dependence between the credit risk of the two parties and that of the reference portfolio. On the other hand, the optional and therefore inherently dynamic nature of counterparty risk obliges one to cope with dynamic credit portfolio models, with the related combinatorial and computational issues. In particular a standard reduced-form approach for modeling the defaults of the two parties is not relevant in this case. To tackle these issues we resort to appropriately dynamized copula models. Specifically we consider first a dynamized Gaussian Copula model in which, in particular, the CDS spread deltas of a CDO tranche at time 0 coincide with the market Gaussian copula deltas; and second, a dynamized Gaussian Marshall-Olkin model in which dependence between credit names stems from the possibility of simultaneous defaults.