Failure of Fourier pricing techniques to approximate the Greeks

Behrens, Tobias; Junike, Gero und Schoutens, Wim (März 2025): Failure of Fourier pricing techniques to approximate the Greeks. In: Frontiers of Mathematical Finance, Bd. 4: S. 102-113

Abstract

The Greeks Delta and Gamma of plain vanilla options play a fundamental role in finance, e.g., in hedging or risk management. These Greeks were approximated in many models such as the widely used Variance Gamma model by Fourier techniques such as the Carr-Madan formula, or the Fourier cosine expansion (COS) method method or the Lewis formula. However, for some realistic market parameters, we show empirically that these three Fourier methods completely fail to approximate the Greeks. As an application we show that the Delta-Gamma value at risk is severely underestimated in realistic market environments. As a solution, we propose to use finite differences instead to obtain the Greeks.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik ; Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 2769-6715
• Sprache: Englisch