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

Antonis Papapantoleon (), John Schoenmakers () and David Skovmand ()
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Antonis Papapantoleon: TU Berlin, Institute of Mathematics, Postal: Strasse des 17. Juni 136, 10623 Berlin, Germany
John Schoenmakers: Weierstrass Institute for Applied Analysis and Stochastics, Postal: Mohrenstr. 39, 10117 Berlin, Germany
David Skovmand: Aarhus University, Department of Economics and Business and CREATES, Postal: Fuglesangs Allé 4, 8210 Aarhus V, Denmark

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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.

Keywords: LIBOR market model; Lévy processes; drift term; Picard approximation; option pricing; caps; swaptions; annuities. (search for similar items in EconPapers)
JEL-codes: C63 G12 G13 (search for similar items in EconPapers)
Pages: 33
Date: 2011-06-04
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