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Invariance properties in the dynamic gaussian copula model

Author

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  • Stéphane Crépey

    (LaMME - 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)

  • Shiqi Song

    (LaMME - 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

We prove that the default times (or any of their minima) in the dynamic Gaussian copula model of Crépey, Jeanblanc, and Wu (2013) are invariance times in the sense of Crépey and Song (2017), with related invariance probability measures different from the pricing measure. This reflects a departure from the immersion property, whereby the default intensities of the surviving names and therefore the value of credit protection spike at default times. These properties are in line with the wrong-way risk feature of counterparty risk embedded in credit derivatives, i.e. the adverse dependence between the default risk of a counterparty and an underlying credit derivative exposure.

Suggested Citation

  • Stéphane Crépey & Shiqi Song, 2017. "Invariance properties in the dynamic gaussian copula model ," Working Papers hal-01455424, HAL.
    • Handle: RePEc:hal:wpaper:hal-01455424
    Note: View the original document on HAL open archive server: https://hal.science/hal-01455424
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    References listed on IDEAS

    as
    1. Stéphane Crépey & Shiqi Song, 2017. "Invariance Times ," Working Papers hal-01455414, HAL.
    2. 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.
    3. Stéphane Crépey & Shiqi Song, 2016. "Counterparty risk and funding: immersion and beyond," Finance and Stochastics, Springer, vol. 20(4), pages 901-930, October.
    4. El Karoui, Nicole & Jeanblanc, Monique & Jiao, Ying, 2010. "What happens after a default: The conditional density approach," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1011-1032, July.
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    Cited by:

    1. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," Papers 1710.07030, arXiv.org, revised Mar 2019.
    2. Marc Chataigner & Stéphane Crépey, 2019. "Credit Valuation Adjustment Compression by Genetic Optimization," Risks, MDPI, vol. 7(4), pages 1-21, September.
    3. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," CIRJE F-Series CIRJE-F-1069, CIRJE, Faculty of Economics, University of Tokyo.
    4. Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2017. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs," CARF F-Series CARF-F-423, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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    More about this item

    Keywords

    immersion property; dynamic copula; counterparty credit risk; wrong-way risk; Gaussian copula; invariance; time; CDS;
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