Option pricing and sensitivity analysis in the Lévy forward process model

Book Chapter

Eddahbi, M. . 2016

• نوع عمل المنشور: Research paper
• اسم الجهة الناشرة: Springer
• عنوان الكتاب: Innovations in Derivatives Markets Fixed Income Modeling, Valuation Adjustments, Risk Management, and Regulation

مستخلص المنشور

The purpose of this article is to give a closed Fourier-based valuation
formula for a caplet in the framework of the Lévy forward process model which was
introduced in Eberlein and Özkan (2005) [8]. 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 (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.