Efficient and accurate log-Lévy approximations of Lévy-driven LIBOR models

Antonis Papapantoleon, John Schoenmakers and David Skovmand

Abstract

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 grows exponentially fast (as a function of the tenor length). We consider a Lévy-driven LIBOR model and aim to develop accurate and efficient log-Lévy approximations for the dynamics of the rates. The approximations are based on the truncation of the drift term and on Picard approximation of suitable processes. Numerical experiments for forward-rate agreements, caps, swaptions and sticky ratchet caps show that the approximations perform very well. In addition, we also consider the log-Lévy approximation of annuities, which offers good approximations for high-volatility regimes.