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First-to-default and second-to-default options in models with various information flows

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  • Gapeev, Pavel V.
  • Jeanblanc, Monique

Abstract

We continue to study a credit risk model of a financial market introduced recently by the authors, 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 that are not independent of the ones describing the default intensity rates. We obtain closed form expressions for the no-arbitrage prices of some first-to-default and second-to-default European style contingent claims given the reference filtration initially and progressively enlarged by the two successive default times. The accessible default-free reference filtration is generated by the standard Brownian motions driving the model.

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:110750
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    File URL: http://eprints.lse.ac.uk/110750/
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    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195, April.
    8. 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.
    9. Gapeev, P.V. & Peskir, G., 2006. "The Wiener disorder problem with finite horizon," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1770-1791, December.
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    More about this item

    Keywords

    successive default times; first-to-default and second-to-default options; geometric Brownian motion; initial and progressive enlargements of filtrations;
    All these keywords.

    JEL classification:

    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance

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