Numerical Methods for the Levy LIBOR Model

The aim of this work is to provide fast and accurate approximation schemes for the Monte Carlo pricing of derivatives in the Levy LIBOR model of Eberlein and Ozkan [4]. 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 approximations. Our approach is similar in accuracy to the full numerical solution, but with the feature that each rate is 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.