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Efficient and accurate log-Lévi approximations to Lévi driven LIBOR models


  • Antonis Papapantoleon

    () (TU Berlin, Institute of Mathematics)

  • John Schoenmakers

    () (Weierstrass Institute for Applied Analysis and Stochastics)

  • David Skovmand

    () (Aarhus University, Department of Economics and Business and CREATES)


The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we consider a Lévy-driven LIBOR model and aim at developing accurate and efficient log-Lévy approximations for the dynamics of the rates. The approximations are based on truncation of the drift term and Picard approximation of suitable processes. Numerical experiments for FRAs, caps and swaptions show that the approximations perform very well. In addition, we also consider the log-Lévy approximation of annuities, which offers good approximations for high volatility regimes.

Suggested Citation

  • Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2011. "Efficient and accurate log-Lévi approximations to Lévi driven LIBOR models," CREATES Research Papers 2011-22, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2011-22

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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. Denis Belomestny & John Schoenmakers, 2010. "A jump-diffusion Libor model and its robust calibration," Quantitative Finance, Taylor & Francis Journals, vol. 11(4), pages 529-546.
    3. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    4. 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.
    5. Jérémy Poirot & Peter Tankov, 2006. "Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(4), pages 327-344, December.
    6. Antonis Papapantoleon & David Skovmand, 2010. "Picard Approximation of Stochastic Differential Equations and Application to Libor Models," CREATES Research Papers 2010-40, Department of Economics and Business Economics, Aarhus University.
    7. Erik Schlögl, 2002. "A multicurrency extension of the lognormal interest rate Market Models," Finance and Stochastics, Springer, vol. 6(2), pages 173-196.
    8. Mark Joshi & Alan Stacey, 2008. "New and robust drift approximations for the LIBOR market model," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 427-434.
    9. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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    13. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410.
    14. Tim Dunn & Erik Schlögl & Geoff Barton, 2000. "Simulated Swaption Delta-Hedging in the Lognormal Forward Libor Model," Research Paper Series 40, Quantitative Finance Research Centre, University of Technology, Sydney.
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    More about this item


    LIBOR market model; Lévy processes; drift term; Picard approximation; option pricing; caps; swaptions; annuities.;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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