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An enlargement of filtration formula with applications to multiple non-ordered default times

Author

Listed:
  • Monique Jeanblanc

    (Université Paris Saclay)

  • Libo Li

    (University of New South Wales)

  • Shiqi Song

    (Université Paris Saclay)

Abstract

In this work, for a reference filtration F $\mathbb {F}$ , we develop a method for computing the semimartingale decomposition of F $\mathbb {F}$ -martingales in a specific type of enlargement of F $\mathbb {F}$ . As an application, we study the progressive enlargement of F $\mathbb {F}$ with a sequence of non-ordered default times and show how to deduce results concerning the first-to-default, k $k$ th-to-default, k-out-of-n-to-default or all-to-default events. In particular, using this method, we compute explicitly the semimartingale decomposition of F $\mathbb {F}$ -martingales under the absolute continuity condition of Jacod.

Suggested Citation

  • Monique Jeanblanc & Libo Li & Shiqi Song, 2018. "An enlargement of filtration formula with applications to multiple non-ordered default times," Finance and Stochastics, Springer, vol. 22(1), pages 205-240, January.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:1:d:10.1007_s00780-017-0349-z
    DOI: 10.1007/s00780-017-0349-z
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    References listed on IDEAS

    as
    1. El Karoui, Nicole & Jeanblanc, Monique & Jiao, Ying, 2017. "Dynamics of multivariate default system in random environment," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3943-3965.
    2. repec:dau:papers:123456789/5717 is not listed on IDEAS
    3. Damiano Brigo & Andrea Pallavicini & Vasileios Papatheodorou, 2011. "Arbitrage-Free Valuation Of Bilateral Counterparty Risk For Interest-Rate Products: Impact Of Volatilities And Correlations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 773-802.
    4. 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.
    5. Jeanblanc, Monique & Song, Shiqi, 2015. "Martingale representation property in progressively enlarged filtrations," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4242-4271.
    6. 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.
    7. Stefan Ankirchner & Peter Imkeller, 2007. "Financial Markets with Asymmetric Information: Information Drift, Additional Utility and Entropy," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 1, pages 1-21, World Scientific Publishing Co. Pte. Ltd..
    8. Nicole El Karoui & Monique Jeanblanc & Ying Jiao, 2017. "Dynamics of multivariate default system in random environment," Post-Print hal-01205753, HAL.
    9. Song, Shiqi, 2016. "Drift operator in a viable expansion of information flow," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2297-2322.
    10. Caroline Hillairet & Ying Jiao, 2011. "Information Asymmetry In Pricing Of Credit Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(05), pages 611-633.
    11. Sebastien Choukroun & Stéphane Goutte & Armand Ngoupeyou, 2015. "Mean-variance hedging under multiple defaults risk," Post-Print hal-02879243, HAL.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Luke M. Bennett & Wei Hu, 2023. "Filtration enlargement‐based time series forecast in view of insider trading," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 112-140, February.
    2. Biagini, Francesca & Mazzon, Andrea & Oberpriller, Katharina, 2023. "Reduced-form framework for multiple ordered default times under model uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 1-43.

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    More about this item

    Keywords

    Enlargement of filtration; Non-ordered default times; Reduced form credit risk modeling; Semimartingale decomposition;
    All these keywords.

    JEL classification:

    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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