Abstract
The purpose of this article is to give a closed Fourier-based valuation formula for a caplet in the framework of the Levy forward process model which was introduced in Eberlein and Ozkan, Financ. Stochast. 9:327-348, 2005, [5]. Afterwards, we compute Greeks by two approaches which come from totally different mathematical fields. The first is based on the integration-by-parts formula, which lies at the core of the application of the Malliavin calculus to finance. The second consists in using Fourier-based methods for pricing derivatives as exposed in Eberlein, Quantitative Energy Finance, 2014, [3]. We illustrate the results in the case where the jump part of the underlying model is driven by a time-inhomogeneous Gamma process and alternatively by a Variance Gamma process.