Strong Taylor approximation of stochastic differential equations and application to the L\'evy LIBOR model

TL;DR

This paper introduces a strong approximation method for SDEs driven by Lévy processes, using Taylor expansion techniques, and applies it to develop efficient algorithms for LIBOR market models, improving derivative valuation.

Contribution

The paper presents a novel Taylor-based approximation scheme for Lévy-driven SDEs and demonstrates its effectiveness in LIBOR model derivative pricing.

Findings

Developed fast, accurate algorithms for Lévy LIBOR models

Enhanced tractability of derivative valuation in LIBOR models

Numerical example confirms improved efficiency and precision

Abstract

In this article we develop a method for the strong approximation of stochastic differential equations (SDEs) driven by L\'evy processes or general semimartingales. The main ingredients of our method is the perturbation of the SDE and the Taylor expansion of the resulting parameterized curve. We apply this method to develop strong approximation schemes for LIBOR market models. In particular, we derive fast and precise algorithms for the valuation of derivatives in LIBOR models which are more tractable than the simulation of the full SDE. A numerical example for the L\'evy LIBOR model illustrates our method.