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A jump-diffusion Libor model and its robust calibration

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Author Info

  • Denis Belomestny
  • John Schoenmakers

Abstract

In this paper we propose a jump-diffusion Libor model with jumps in a high-dimensional space (Rm) and test a stable non-parametric calibration algorithm which takes into account a given local covariance structure. The algorithm returns smooth and simply structured Lévy densities, and penalizes the deviation from the Libor market model. In practice, the procedure is FFT based, thus fast, easy to implement, and yields good results, particularly in view of the severe ill-posedness of the underlying inverse problem.

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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-037.pdf
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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-037.

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Length: 33 pages
Date of creation: Apr 2006
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2006-037

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Keywords: Libor market model; calibration; correlation; jump-diffusion;

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References

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  1. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 13(3), pages 383-410.
  2. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, Springer, vol. 1(4), pages 293-330.
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Citations

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Cited by:
  1. Mathias Trabs, 2011. "Calibration of selfdecomposable Lévy models," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2011-073, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2011. "Efficient and accurate log-L\'evy approximations to L\'evy driven LIBOR models," Papers 1106.0866, arXiv.org, revised Jan 2012.
  3. Marcel Ladkau & John G. M. Schoenmakers & Jianing Zhang, 2012. "Libor model with expiry-wise stochastic volatility and displacement," Papers 1204.5698, arXiv.org.
  4. Denis Belomestny & Stanley Matthew & John Schoenmakers, 2007. "A stochastic volatility Libor model and its robust calibration," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2007-067, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  5. Antonis Papapantoleon, 2009. "Old and new approaches to LIBOR modeling," Papers 0910.4941, arXiv.org, revised Apr 2010.

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