Computation of Greeks in LIBOR models driven by time-inhomogeneous Lévy processes

Journal Article

Eddahbi, M. . 2016

• Publication Work Type: Research paper
• Publication Online URL: Applied Mathematical Finance (AMF)
• Issue Number: 3
• Volume Number: 23
• Pages: 236 to 260

Publication Abstract

The aim of this paper is to compute Greeks, i.e. price sensitivities in the framework of
the Lévy LIBOR model (LLM) which was introduced in Eberlein and Özkan (2005). Two approaches
are discussed. The first approach is based on the integration–by–parts formula, which lies at the core
of the application of the Malliavin calculus to finance as developed in Fournié et al. (1999). The
second approach consists in using Fourier based methods for pricing derivatives. A recent survey on
these methods is presented in Eberlein (2014). We illustrate the result by applying the formula to
a caplet price where the underlying model is driven by a time–inhomogeneous Gamma process and
alternatively by a Variance Gamma process. A comparison between the two approaches which come
from totally different mathematical fields is made.