Numerical methods for the L\'evy LIBOR model

TL;DR

This paper introduces a fast, accurate approximation scheme for pricing derivatives in the Le9vy LIBOR model using Picard iterations, enabling parallel computation of different maturities.

Contribution

It proposes a novel independent-rate evolution method based on Picard iterations, improving speed and enabling parallel pricing in the Le9vy LIBOR model.

Findings

Comparable accuracy to full numerical solutions

Significant speed improvements with parallel computation

Effective pricing of caplets demonstrated

Abstract

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.