Enhancing the COS method with machine learning

Brignone, Riccardo; Stier, Hauke und Junike, Gero (2025): Enhancing the COS method with machine learning. In: International Journal of Computer Mathematics [Forthcoming]

Abstract

The Fourier-cosine (COS) method is a classic tool for pricing European options. The method is generally applicable to models where the characteristic function of log-returns is known. A major advantage of the COS method over competing Fourier pricing methods is an effective error control. However, implementing formulas for the tuning parameters of the COS method requires the calculation of higher-order moments of the log-returns. The scope of this paper is twofold: (i) We illustrate how to obtain fully explicit formulas for the high-order moments of the log-returns under affine stochastic volatility models, which is crucial for the efficient implementation of the COS method. (ii) Whenever it is not possible to obtain explicit formulas for high order moments, e.g. for the 3/2 stochastic volatility model, we propose to learn high order moments using machine learning techniques. As a result, we obtain very fast algorithms with almost complete error control.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0020-7160
• Language: English