We first derive representation formula for the Credit Value Adjustment (CVA) of a netted and collateralized portfolio. These results are This result is then specified to the case, most challenging from the modelling and numerical point of view, of counterparty credit risk. Our general results are essentially model free. Thus, although they are theoretically pleasing, they do not immediately lend themselves to any practical computations. We therefore subsequently introduce an underlying stochastic model, in order to to put the general results to work. We thus propose a Markovian model of portfolio credit risk in which dependence between defaults and the wrong way risk are represented by the possibility of simultaneous defaults among the underlying credit names. Specifically, single-name marginals in our model are themselves Markov, so that they can be pre-calibrated in the first stage, much like in the standard (static) copula approach. One can then calibrate the few model dependence parameters in the second stage. The numerical results show a good agreement of the behavior of EPE (Expected Positive Exposure) and CVA in the model with stylized features.

Bio:

After a PhD Thesis in Applied Mathematics from Ecole Polytechnique at INRIA Sophia Antipolis and the Caisse Autonome de Refinancement (group `Caisse des Dépôts'), Stéphane Crépey is now an Associate Professor at the Mathematics Department of Evry University. He is director of the Master program MSC Financial Engineering of Evry University. His current research interests are Financial Modeling, Credit Risk, Numerical Finance, as well as connected mathematical topics in the fields of Backward Stochastic Differential Equations and PDEs.Stéphane Crépey also had various consulting activities in the banking and financial engineering sector.