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Informationally Dynamized Gaussian Copula

Author

Listed:
  • S. CRÉPEY

    (Laboratoire Analyse et Probabilités, Université d'Évry Val d'Essonne, 91037 Évry Cedex, France)

  • M. JEANBLANC

    (Laboratoire Analyse et Probabilités, Université d'Évry Val d'Essonne, 91037 Évry Cedex, France)

  • D. WU

    (Laboratoire Analyse et Probabilités, Université d'Évry Val d'Essonne, 91037 Évry Cedex, France)

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.

Suggested Citation

  • S. Crépey & M. Jeanblanc & D. Wu, 2013. "Informationally Dynamized Gaussian Copula," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 1-29.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:02:n:s0219024913500088
    DOI: 10.1142/S0219024913500088
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    Citations

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    Cited by:

    1. St'ephane Cr'epey & Shiqi Song, 2017. "Invariance properties in the dynamic gaussian copula model ," Papers 1702.03232, arXiv.org.
    2. Tomasz R. Bielecki & Areski Cousin & Stéphane Crépey & Alexander Herbertsson, 2014. "Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 90-102, April.
    3. Frédéric Vrins, 2017. "Wrong-Way Risk Cva Models With Analytical Epe Profiles Under Gaussian Exposure Dynamics," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-35, November.
    4. Cheikh Mbaye & Fr'ed'eric Vrins, 2019. "An arbitrage-free conic martingale model with application to credit risk," Papers 1909.02474, arXiv.org.
    5. Stéphane Crépey & Shiqi Song, 2017. "Invariance properties in the dynamic gaussian copula model ," Working Papers hal-01455424, HAL.

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