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Informationally Dynamized Gaussian Copula

by Stéphane Crépey of University of Evry, France,
Monique Jeanblanc of University of Evry, France, and
Dominique Wu of University of Evry, France

April 22, 2013

Abstract: In order to dynamize the static Gaussian copula model of portfolio credit risk, we introduce a model filtration made of a reference Brownian filtration progressively enlarged by the default times. This yields a multidimensional density model of default times, where, as opposed to the classical situation of the Cox model, 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. From the point of view of financial interpretation this means default contagion, a good feature in the perspective of modeling counterparty wrong-way risk on credit derivatives. Computational tractability is ensured by invariance of multivariate Gaussian distributions through conditioning by some components, the ones corresponding to past defaults. Moreover the model is Markov in an augmented state-space including past default times. After a discussion of different notions of deltas, the model is applied to the valuation of counterparty risk on credit derivatives.

JEL Classification: G12, G13.

Keywords: Gaussian copula, dynamic copula, credit derivatives, counterparty risk, CVA, hedging.

Published in: International Journal of Theoretical and Applied Finance, Vol. 16, No. 2, (March 2013).

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