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

Author

Listed:
  • 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)

Abstract

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

    as
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    7. 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.
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    More about this item

    Keywords

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

    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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