Frost, Nageena and Lai, Choi-Hong ORCID: https://orcid.org/0000-0002-7558-6398 (2026) Data driven and numerical approaches with PDEs for option pricing. Abstract and Applied Analysis. ISSN 1085-3375 (Print), 1687-0409 (Online) (In Press)

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Abstract

This study examines the performance of various numerical and machine learning approaches in option pricing. The Black-Scholes equation is solved via finite difference methods and Laplace transform, and its numerical inversions then used to price European options where the volatility of the underlying asset is calculated through the statistical measure of stock markets’ historical data. In data driven approaches, calibrated via machine learning, some conventional and deep learning-based approaches are reviewed by utilising 50ETF European stock index options data. The efficiency and accuracy of the adapted methods is demonstrated by computing the conventional metrics for benchmark options. The results reveal that the numerical inversion techniques of Laplace transform with a direct solver such as Thomas algorithm are more efficient in pricing European options as compared to the classical time marching methods. When the dataset is sufficiently large the omission of some input parameters in a pricing model can still generate relatively accurate results using machine learning techniques.

Item Type:	Article
Uncontrolled Keywords:	Black-Scholes equation, European options, historical volatility, laplace transform, Thomas algorithm, pricing model, Machine Learning
Subjects:	Q Science > Q Science (General) Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science Faculty of Engineering & Science > School of Computing & Mathematical Sciences (CMS)
Last Modified:	02 Oct 2026 12:20
URI:	https://gala.gre.ac.uk/id/eprint/54607

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