Approximate Option Pricing in the L\'evy Libor Model

TL;DR

This paper develops an approximation method for pricing interest rate options in the Le9vy Libor model by treating it as a perturbation of the log-normal Libor market model, providing explicit correction terms.

Contribution

It introduces a novel approximation technique that simplifies option pricing in the complex Le9vy Libor model using perturbation methods based on the LMM.

Findings

Approximate option prices are expressed as LMM prices plus correction terms.

The correction terms depend on the Le9vy process characteristics.

The method offers explicit formulas for practical implementation.

Abstract

In this paper we consider the pricing of options on interest rates such as caplets and swaptions in the L\'evy Libor model developed by Eberlein and \"Ozkan (2005). This model is an extension to L\'evy driving processes of the classical log-normal Libor market model (LMM) driven by a Brownian motion. Option pricing is significantly less tractable in this model than in the LMM due to the appearance of stochastic terms in the jump part of the driving process when performing the measure changes which are standard in pricing of interest rate derivatives. To obtain explicit approximation for option prices, we propose to treat a given L\'evy Libor model as a suitable perturbation of the log-normal LMM. The method is inspired by recent works by Cern\'y, Denkl and Kallsen (2013) and M\'enass\'e and Tankov (2015). The approximate option prices in the L\'evy Libor model are given as the corresponding LMM prices plus correction terms which depend on the characteristics of the underlying L\'evy process and some additional terms obtained from the LMM model.