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Counterparty risk and funding: Immersion and beyond

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  • Stéphane Crépey

    (Laboratoire de Mathématiques et Modélisation d'Evry - INRA - Institut National de la Recherche Agronomique - UEVE - Université d'Évry-Val-d'Essonne - CNRS - Centre National de la Recherche Scientifique)

  • S. Song

    (Laboratoire de Mathématiques et Modélisation d'Evry - INRA - Institut National de la Recherche Agronomique - UEVE - Université d'Évry-Val-d'Essonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

A basic reduced-form counterparty risk modeling approach hinges on a standard immersion hypothesis between a reference filtration and the filtration progressively enlarged by the default times of the two parties, also involving the continuity of some of the data at default time. This basic approach is too restrictive for application to credit derivatives, which are characterized by strong wrong-way risk, i.e. adverse dependence between the exposure and the credit riskiness of the counterparties, and gap risk, i.e. slippage between the portfolio and its collateral during the so called cure period that separates default from liquidation. This paper shows how a suitable extension of the basic approach can be devised so that it can be applied in dynamic copula models of counterparty risk on credit derivatives. More generally, this method is applicable in any marked default times intensity setup satisfying a suitable integrability condition. The integrability condition expresses that no mass is lost in a related measure change. The changed probability measure is not needed algorithmically. All one needs in practice is an explicit expression for the intensities of the marked default times.

Suggested Citation

  • Stéphane Crépey & S. Song, 2014. "Counterparty risk and funding: Immersion and beyond," Working Papers hal-00989062, HAL.
  • Handle: RePEc:hal:wpaper:hal-00989062
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00989062v2
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    References listed on IDEAS

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    1. Claudio Albanese & Damiano Brigo & Frank Oertel, 2013. "Restructuring Counterparty Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 1-29.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    3. Tomasz R. Bielecki & Marek Rutkowski, 2014. "Valuation and Hedging of Contracts with Funding Costs and Collateralization," Papers 1405.4079, arXiv.org, revised Dec 2014.
    4. Jeanblanc, Monique & Le Cam, Yann, 2009. "Progressive enlargement of filtrations with initial times," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2523-2543, August.
    5. Dirk Becherer & Martin Schweizer, 2005. "Classical solutions to reaction-diffusion systems for hedging problems with interacting Ito and point processes," Papers math/0505208, arXiv.org.
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    Cited by:

    1. Masaaki Fujii, 2015. "Optimal Position Management for a Market Maker with Stochastic Price Impacts," Papers 1503.07007, arXiv.org, revised Sep 2015.
    2. Masaaki Fujii, 2015. "Optimal Position Management for a Market Maker with Stochastic Price Impacts," CARF F-Series CARF-F-360, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2015.
    3. Masaaki Fujii, 2015. "Optimal Position Management for a Market Maker with Stochastic Price Impacts," CIRJE F-Series CIRJE-F-963, CIRJE, Faculty of Economics, University of Tokyo.
    4. Cheikh Mbaye & Fr'ed'eric Vrins, 2019. "An arbitrage-free conic martingale model with application to credit risk," Papers 1909.02474, arXiv.org.

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