Numerical methods for the Lévy LIBOR model

Details Numerical methods for the Lévy LIBOR model Numerical methods for the Lévy LIBOR model

2010-06-16

arxiv.org/abs/1006.3340v1

In M.R. Guarracino et al. (Eds.), Euro-Par 2010 Workshops, LNCS 6586, pp. 463-470, Springer, 2011

Economy

Quantitative Finance

Computational Finance

10 pages, submitted to the Proceedings of the Conference on High-performance computing applied to Finance. A longer paper with

Scientific paper

The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the L\'evy LIBOR model of Eberlein and \"Ozkan (2005). Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates but the methods are generally slow. We propose an alternative approximation scheme based on Picard iterations. Our approach is similar in accuracy to the full numerical solution, but with the feature that each rate is, unlike the standard method, evolved independently of the other rates in the term structure. This enables simultaneous calculation of derivative prices of different maturities using parallel computing. We include numerical illustrations of the accuracy and speed of our method pricing caplets.

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