1 Department of Business Studies, Aarhus School of Business, Aarhus BSS, Aarhus University2 Finance Research Group, Aarhus School of Business, Aarhus BSS, Aarhus University3 Institute of Mathematics, TU Berlin and Deutsche Bank AG4 Department of Economics and Business Economics, Aarhus BSS, Aarhus University5 Department of Economics and Business Economics, Aarhus BSS, Aarhus University
The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the Lévy LIBOR model of Eberlein and Özkan (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.