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The Levy Swap Market Model

Author

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  • E. Eberlein
  • J. Liinev

Abstract

Models driven by Levy processes are attractive since they allow for better statistical fitting than classical diffusion models. The dynamics of the forward swap rate process is derived in a semimartingale setting and a Levy swap market model is introduced. In order to guarantee positive rates, the swap rates are modelled as ordinary exponentials. The model starts with the most distant rate, which is driven by a non-homogeneous Levy process. Via backward induction the remaining swap rates are constructed such that they become martingales under the corresponding forward swap measures. Finally it is shown how swaptions can be priced using bilateral Laplace transforms.

Suggested Citation

  • E. Eberlein & J. Liinev, 2007. "The Levy Swap Market Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(2), pages 171-196.
    • Handle: RePEc:taf:apmtfi:v:14:y:2007:i:2:p:171-196
    DOI: 10.1080/13504860600724950
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    Cited by:

    1. Ming-Chieh Wang & Li-Jhang Huang, 2019. "Pricing cross-currency interest rate swaps under the Levy market model," Review of Derivatives Research, Springer, vol. 22(2), pages 329-355, July.
    2. Leippold, Markus & Strømberg, Jacob, 2014. "Time-changed Lévy LIBOR market model: Pricing and joint estimation of the cap surface and swaption cube," Journal of Financial Economics, Elsevier, vol. 111(1), pages 224-250.

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