ABSTRACT
In this chapter, we “dynamize” the static Gaussian copula model of portfolio credit risk in order to make it suitable for counterparty risk computations. Toward this aim, we introduce a model filtration made of a reference Brownian filtration progressively enlarged by the default times. This results a multidimensional density model of default times, where the reference filtration is not immersed into the enlarged filtration. In mathematical terms, this lack of immersion means that martingales in the reference filtration are not martingales in the enlarged filtration. In the financial interpretation, this corresponds to a form of default contagion. Computational tractability is ensured by invariance of multivariate Gaussian distributions through conditioning by some components, the ones corresponding to past defaults. The model is also Markov in an augmented state-space that includes past default times.
