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Hedging of Credit Derivatives in Models with Totally Unexpected Default

In: Stochastic Processes And Applications To Mathematical Finance

Author

Listed:
  • Tomasz R. Bielecki

    (Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA)

  • Monique Jeanblanc

    (Département de Mathématiques, Université d'Évry Val d'Essonne, 91025 Évry Cedex, France)

  • Marek Rutkowski

    (School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia and Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-661 Warszawa, Poland)

Abstract
The paper analyzes alternative mathematical techniques, which can be used to derive hedging strategies for credit derivatives in models with totally unexpected default. The stochastic calculus approach is used to establish abstract characterization results for hedgeable contingent claims in a fairly general set-up. In the Markovian framework, we use the PDE approach to show that the arbitrage price and the hedging strategy for an attainable contingent claim can be described in terms of solutions of a pair of coupled PDEs.

Suggested Citation

  • Tomasz R. Bielecki & Monique Jeanblanc & Marek Rutkowski, 2006. "Hedging of Credit Derivatives in Models with Totally Unexpected Default," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 2, pages 35-100, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812774637_0002
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    Citations

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    Cited by:

    1. Tomasz Bielecki & Monique Jeanblanc & Marek Rutkowski, 2011. "Hedging of a credit default swaption in the CIR default intensity model," Finance and Stochastics, Springer, vol. 15(3), pages 541-572, September.
    2. Dharmaraja Selvamuthu & Paola Tardelli, 2022. "Infinite-server systems with Hawkes arrivals and Hawkes services," Queueing Systems: Theory and Applications, Springer, vol. 101(3), pages 329-351, August.
    3. Ma, Jin & Yun, Youngyun, 2010. "Correlated intensity, counter party risks, and dependent mortalities," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 337-351, December.
    4. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2017. "Unit-linked life insurance policies: Optimal hedging in partially observable market models," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 149-163.
    5. Tomasz R. Bielecki & Igor Cialenco & Marek Rutkowski, 2017. "Arbitrage-Free Pricing Of Derivatives In Nonlinear Market Models," Papers 1701.08399, arXiv.org, revised Apr 2018.
    6. Damien Ackerer & Damir Filipovi'c, 2016. "Linear Credit Risk Models," Papers 1605.07419, arXiv.org, revised Jul 2019.
    7. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2016. "Unit-linked life insurance policies: optimal hedging in partially observable market models," Papers 1608.07226, arXiv.org, revised Dec 2016.
    8. Elhiwi, Majdi, 2014. "Default barrier intensity model for credit risk evaluation," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 125-131.

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