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Efficient and accurate log-L\'evy approximations to L\'evy driven LIBOR models

Author

Listed:
  • Antonis Papapantoleon
  • John Schoenmakers
  • David Skovmand

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 L\'evy-driven LIBOR model and aim at developing accurate and efficient log-L\'evy 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, swaptions and sticky ratchet caps show that the approximations perform very well. In addition, we also consider the log-L\'evy approximation of annuities, which offers good approximations for high volatility regimes.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1106.0866
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    References listed on IDEAS

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    12. 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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    Cited by:

    1. Zorana Grbac & David Krief & Peter Tankov, 2015. "Approximate Option Pricing in the L\'evy Libor Model," Papers 1511.08466, arXiv.org, revised Jul 2016.

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