Levy-Driven Libor Model and its Numerical Approximation

Abstract

This paper studies numerical method for approximation of the Libor rate model driven by the Levy noise. We start with the Libor model based directly on the forward rate process. Within this modeling approach we can derive the explicit prices for swaps and swaptions. We use the implicit Euler scheme for the numerical approximation of the SDE corresponding to the log-Libor model. Using the Euler method for the numerical solution to the corresponding L ́evy-process driven SDE requires efficient approximation of the Levy measure. Here, we use the methodology of truncation and discretization of the Levy measure. Then, the truncated small jumps are replaced by the Wiener process as suggested in [23]. We study the performance of our method In several numerical experiments.