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Approximate Option Pricing in the L\'evy Libor Model


  • Zorana Grbac
  • David Krief
  • Peter Tankov


In this paper we consider the pricing of options on interest rates such as caplets and swaptions in the L\'evy Libor model developed by Eberlein and \"Ozkan (2005). This model is an extension to L\'evy driving processes of the classical log-normal Libor market model (LMM) driven by a Brownian motion. Option pricing is significantly less tractable in this model than in the LMM due to the appearance of stochastic terms in the jump part of the driving process when performing the measure changes which are standard in pricing of interest rate derivatives. To obtain explicit approximation for option prices, we propose to treat a given L\'evy Libor model as a suitable perturbation of the log-normal LMM. The method is inspired by recent works by Cern\'y, Denkl and Kallsen (2013) and M\'enass\'e and Tankov (2015). The approximate option prices in the L\'evy Libor model are given as the corresponding LMM prices plus correction terms which depend on the characteristics of the underlying L\'evy process and some additional terms obtained from the LMM model.

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  • Zorana Grbac & David Krief & Peter Tankov, 2015. "Approximate Option Pricing in the L\'evy Libor Model," Papers 1511.08466,, revised Jul 2016.
  • Handle: RePEc:arx:papers:1511.08466

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    References listed on IDEAS

    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. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
    3. repec:dau:papers:123456789/1380 is not listed on IDEAS
    4. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2007. "Self-Decomposability And Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 31-57.
    5. Alev{s} v{C}ern'y & Stephan Denkl & Jan Kallsen, 2013. "Hedging in L\'evy Models and the Time Step Equivalent of Jumps," Papers 1309.7833,, revised Jul 2017.
    6. Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2011. "Efficient and accurate log-L\'evy approximations to L\'evy driven LIBOR models," Papers 1106.0866,, revised Jan 2012.
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