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EFFICIENT AND ACCURATE LOG-LEVY APPROXIMATIONS TO LEVY DRIVEN LIBOR MODELS

Please always quote using this URN:urn:nbn:de:0296-matheon-8426
  • The LIBOR market model is very popular for pricing inter- est 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 Levy-driven LIBOR model and aim at developing accurate and efficient log-Levy 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-Levy approximation of annuities, which offers good approximations for high volatility regimes.

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Metadaten
Author:Antonis Papapantoleon, John Schoenmakers, David Skovmand
URN:urn:nbn:de:0296-matheon-8426
Referee:Dirk Becherer
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/01/27
Release Date:2012/01/27
Tag:
Institute:Research Center Matheon
Technische Universität Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G51 Processes with independent increments; Lévy processes
91-XX GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES / 91Gxx Mathematical finance / 91G30 Interest rates (stochastic models)
91-XX GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES / 91Gxx Mathematical finance / 91G60 Numerical methods (including Monte Carlo methods)
Preprint Number:885
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