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Credit Default Swaps In Two-Dimensional Models With Various Informations Flows

Author

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  • PAVEL V. GAPEEV

    (Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, UK)

  • MONIQUE JEANBLANC

    (LaMME, Univ Evry-Université Paris Saclay, 23 Boulevard de France, 91037 Evry Cedex, France)

Abstract

We study a credit risk model of a financial market in which the dynamics of intensity rates of two default times are described by linear combinations of three independent geometric Brownian motions. The dynamics of two default-free risky asset prices are modeled by two geometric Brownian motions which are dependent of the ones describing the default intensity rates. We obtain closed form expressions for the no-arbitrage prices of both risk-free and risky credit default swaps given the reference filtration initially and progressively enlarged by the two default times. The accessible default-free reference filtration is generated by the standard Brownian motions driving the model.

Suggested Citation

  • Pavel V. Gapeev & Monique Jeanblanc, 2020. "Credit Default Swaps In Two-Dimensional Models With Various Informations Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 1-28, March.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:02:n:s0219024920500107
    DOI: 10.1142/S0219024920500107
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    References listed on IDEAS

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    1. T. R. Bielecki & S. Crépey & M. Jeanblanc & B. Zargari, 2012. "Valuation And Hedging Of Cds Counterparty Exposure In A Markov Copula Model," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 4, pages 75-113, World Scientific Publishing Co. Pte. Ltd..
    2. T. R. Bielecki & S. Crépey & M. Jeanblanc & B. Zargari, 2012. "Valuation And Hedging Of Cds Counterparty Exposure In A Markov Copula Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-39.
    3. Pavel V. Gapeev & Monique Jeanblanc, 2019. "Defaultable Claims In Switching Models With Partial Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-18, June.
    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.
    5. Damiano Brigo & Kyriakos Chourdakis, 2009. "Counterparty Risk For Credit Default Swaps: Impact Of Spread Volatility And Default Correlation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 1007-1026.
    6. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195, April.
    7. Damiano Brigo & Agostino Capponi & Andrea Pallavicini, 2014. "Arbitrage-Free Bilateral Counterparty Risk Valuation Under Collateralization And Application To Credit Default Swaps," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 125-146, January.
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    Cited by:

    1. Gapeev, Pavel V. & Jeanblanc, Monique, 2021. "First-to-default and second-to-default options in models with various information flows," LSE Research Online Documents on Economics 110750, London School of Economics and Political Science, LSE Library.

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