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.
Author: | Antonis Papapantoleon, John Schoenmakers, David Skovmand |
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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 |
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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 |