Counterparty Risk on a CDS in a Model with Joint Defaults and Stochastic Spreads

by Stephane Crépey of the Université d'Évry Val d'Essonne,
Monique Jeanblanc of the Université d'Évry Val d'Essonne & Europlace Institute of Finance, and
Behnaz Zargari of the Université d'Évry Val d'Essonne

January 7, 2010

Abstract: A Markov model with simultaneous defaults and stochastic spreads is devised for modeling the counterparty risk on a CDS. The `wrong way risk' in this model is accounted for by the possibility of the common default of the reference name and the counterpart. Semi-explicit formulae are derived for most quantities of interest, such as Credit Valuation Adjustment (CVA) and Expected Positive Exposure (EPE). A dynamic copula property as well as appropriate specifications of the model make the calibration efficient. Numerical results are presented to show the adequation of the behavior of EPE and CVA in the model with stylized features. The spread risk in the model significantly increases the CVA in the cases of a low risk reference entity, or of a low correlation between the reference entity and the counterpart.

Keywords: Counterparty Credit Risk, CDS, CVA, EPE, Spread Risk.

Previously titled: Counterparty Risk on a CDS in a Markov Chain Copula Model with Joint Defaults

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