  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.
