Efficient and accurate log-Lévi approximations to Lévi driven LIBOR models
AbstractThe 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.
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Bibliographic InfoPaper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2011-22.
Date of creation: 04 Jun 2011
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Web page: http://www.econ.au.dk/afn/
LIBOR market model; Lévy processes; drift term; Picard approximation; option pricing; caps; swaptions; annuities.;
Find related papers by JEL classification:
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-06-25 (All new papers)
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