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CREDIT RISK PREMIA AND QUADRATIC BSDEs WITH A SINGLE JUMP

Author

Listed:
  • STEFAN ANKIRCHNER

    (Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universtät Bonn, Endenicher Allee 60, 53115 Bonn, Germany)

  • CHRISTOPHETTE BLANCHET-SCALLIET

    (Université de Lyon, CNRS, UMR 5208, Institut Camille Jordan, Ecole Centrale de Lyon, Université Lyon 1, INSA de Lyon, 36 Avenue Guy de Collongue, 69134 Ecully Cedex, France)

  • ANNE EYRAUD-LOISEL

    (Université de Lyon, Université Lyon 1, ISFA — Laboratoire SAF, 50 Avenue Tony Garnier, 69366 Lyon Cedex 07, France)

Abstract

This paper is concerned with the determination of credit risk premia of defaultable contingent claims by means of indifference valuation principles. Assuming exponential utility preferences we derive representations of indifference premia of credit risk in terms of solutions of Backward Stochastic Differential Equations (BSDE). The class of BSDEs needed for that representation allows for quadratic growth generators and jumps at random times. Since the existence and uniqueness theory for this class of BSDEs has not yet been developed to the required generality, the first part of the paper is devoted to fill that gap. By using a simple constructive algorithm, and known results on continuous quadratic BSDEs, we provide sufficient conditions for the existence and uniqueness of quadratic BSDEs with discontinuities at random times.

Suggested Citation

  • Stefan Ankirchner & Christophette Blanchet-Scalliet & Anne Eyraud-Loisel, 2010. "CREDIT RISK PREMIA AND QUADRATIC BSDEs WITH A SINGLE JUMP," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(07), pages 1103-1129.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:07:n:s0219024910006133
    DOI: 10.1142/S0219024910006133
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    Citations

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    Cited by:

    1. Idris Kharroubi & Thomas Lim, 2014. "Progressive Enlargement of Filtrations and Backward Stochastic Differential Equations with Jumps," Journal of Theoretical Probability, Springer, vol. 27(3), pages 683-724, September.
    2. Roxana Dumitrescu & Marie-Claire Quenez & Agn`es Sulem, 2016. "BSDEs with default jump," Papers 1612.05681, arXiv.org, revised Sep 2017.
    3. Lorenc Kapllani & Long Teng, 2020. "Deep learning algorithms for solving high dimensional nonlinear backward stochastic differential equations," Papers 2010.01319, arXiv.org, revised Jun 2022.
    4. Ludovic Tangpi & Shichun Wang, 2022. "Optimal Bubble Riding: A Mean Field Game with Varying Entry Times," Papers 2209.04001, arXiv.org, revised Jan 2024.
    5. Anna Aksamit & Libo Li & Marek Rutkowski, 2021. "Generalized BSDEs with random time horizon in a progressively enlarged filtration," Papers 2105.06654, arXiv.org.
    6. Yao, Song, 2017. "Lp solutions of backward stochastic differential equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3465-3511.
    7. Lorenc Kapllani & Long Teng, 2024. "A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations," Papers 2404.08456, arXiv.org.

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