Efficient and accurate log-L\'evy approximations to L\'evy driven LIBOR models

TL;DR

This paper develops efficient log-Lévy approximations for Lévydriven LIBOR models, enabling accurate pricing of interest rate derivatives with complex jump processes, and demonstrates their effectiveness through numerical experiments.

Contribution

It introduces novel truncation and Picard approximation methods for Lévydriven LIBOR models, improving computational efficiency and accuracy over existing approaches.

Findings

Approximations perform well for various derivatives.

Effective in high volatility regimes.

Numerical results validate the methods' accuracy.

Abstract

The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we consider a L\'evy-driven LIBOR model and aim at developing accurate and efficient log-L\'evy approximations for the dynamics of the rates. The approximations are based on truncation of the drift term and Picard approximation of suitable processes. Numerical experiments for FRAs, caps, swaptions and sticky ratchet caps show that the approximations perform very well. In addition, we also consider the log-L\'evy approximation of annuities, which offers good approximations for high volatility regimes.