WIAS Preprint No. 1614, (2011)

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



Authors

  • Papapantoleon, Antonis
  • Schoenmakers, John G. M.
    ORCID: 0000-0002-4389-8266
  • Skovmand, David

2010 Mathematics Subject Classification

  • 91G30 91G60 60G51

Keywords

  • LIBOR market model, Levy processes, drift term, Picard approximation, option pricing, caps, swaptions, annuities

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.

Appeared in

  • J. Comput. Finance, 15 (2012) pp. 3--44.

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