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A tractable LIBOR model with default risk

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  • Zorana Grbac
  • Antonis Papapantoleon

Abstract

We develop a model for the dynamic evolution of default-free and defaultable interest rates in a LIBOR framework. Utilizing the class of affine processes, this model produces positive LIBOR rates and spreads, while the dynamics are analytically tractable under defaultable forward measures. This leads to explicit formulas for CDS spreads, while semi-analytical formulas are derived for other credit derivatives. Finally, we give an application to counterparty risk.

Suggested Citation

  • Zorana Grbac & Antonis Papapantoleon, 2012. "A tractable LIBOR model with default risk," Papers 1202.0587, arXiv.org, revised Oct 2012.
  • Handle: RePEc:arx:papers:1202.0587
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    File URL: http://arxiv.org/pdf/1202.0587
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    References listed on IDEAS

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    1. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
    2. Antonis Papapantoleon, 2009. "Old and new approaches to LIBOR modeling," Papers 0910.4941, arXiv.org, revised Apr 2010.
    3. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195.
    4. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    5. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409 World Scientific Publishing Co. Pte. Ltd..
    6. Thomas Kokholm & Elisa Nicolato, 2010. "Sato Processes in Default Modelling," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(5), pages 377-397.
    7. Hull, John & White, Alan, 1995. "The impact of default risk on the prices of options and other derivative securities," Journal of Banking & Finance, Elsevier, vol. 19(2), pages 299-322, May.
    8. Antonis Papapantoleon, 2010. "Old and new approaches to LIBOR modeling," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 257-275.
    9. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2010. "Analysis of Fourier Transform Valuation Formulas and Applications," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(3), pages 211-240.
    10. Johnson, Herb & Stulz, Rene, 1987. " The Pricing of Options with Default Risk," Journal of Finance, American Finance Association, vol. 42(2), pages 267-280, June.
    11. Lotz, Christopher & Schlogl, Lutz, 2000. "Default risk in a market model," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 301-327, January.
    12. Philipp J. Schönbucher, 2000. "A Libor Market Model with Default Risk," Bonn Econ Discussion Papers bgse15_2001, University of Bonn, Germany.
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    Cited by:

    1. Da Fonseca, José & Gnoatto, Alessandro & Grasselli, Martino, 2013. "A flexible matrix Libor model with smiles," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 774-793.

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