CVA Computation for Counterparty Risk Assessment in Credit Portfolios
by Samson Assefa of the Université d'Evry Val d'Essonne,
December 5, 2009
Abstract: We first derive a general counterparty risk representation formula for the Credit Value Adjustment (CVA) of a netted and collateralized portfolio. This result is then specified to the case, most challenging from the modeling 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 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.
Keywords: Counterparty Credit Risk, CVA, collateralization, Markov Copula, Joint Defaults, CDS.
This paper is Published as Ch. 12 in...