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

Antonis Papapantoleon, John Schoenmakers and David Skovmand

Papers from arXiv.org

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.

New Economics Papers: this item is included in nep-cmp
Date: 2011-06, Revised 2012-01
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Published in Journal of Computational Finance 2012, Vol. 15, No. 4, 3-44

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1106.0866

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