Fadugba, S.E. ORCID: https://orcid.org/0000-0003-0911-6838, Udoye, A.M. ORCID: https://orcid.org/0000-0001-9402-5804, Zelibe, S.C. ORCID: https://orcid.org/0000-0002-8722-4343, Edeki, S.O. ORCID: https://orcid.org/0000-0002-7921-3492, Achudume, C. ORCID: https://orcid.org/0000-0003-1689-980X, Adeyanju, A.A. ORCID: https://orcid.org/0000-0002-9013-6002, Makinde, O. ORCID: https://orcid.org/0009-0003-7535-7987, Bankole, P.A. ORCID: https://orcid.org/0000-0003-4606-2349 and Kekana, M.C. ORCID: https://orcid.org/0000-0001-6214-7495 (2025) Solving the Black–Scholes European options model using the reduced differential transform method with powered modified log-payoff function. Partial Differential Equations in Applied Mathematics, 13 (1):101087. ISSN 2666-8181 (doi:10.1016/j.padiff.2025.101087)

Preview

PDF (Open Access Article) 51729 ZELIBE_Solving_the_Black–Scholes_European_Options_Model_Using_the_Reduced_Differential_Transform_Method_(OA)_2025.pdf - Published Version Available under License Creative Commons Attribution Non-commercial No Derivatives. Download (1MB) | Preview

Abstract

This study introduces a novel analytical method for the Black–Scholes European options model, employing modified log-payoff functions raised to a power. The main motivation for this study stems from the need to develop more efficient and accurate analytical techniques for option pricing, particularly under the assumptions of the Black–Scholes framework. The proposed method utilizes the reduced differential transform method (RDTM), which provides a straightforward, flexible, and precise approach for solving the model. A significant contribution of this work is the ability to swiftly obtain explicit solutions with reduced computational time compared to traditional methods. The research also demonstrates that the sensitivities of the European call and put option prices, commonly known as the “Greeks,” can be effectively captured using this approach. Importantly, this model operates under the assumption that assets follow geometric Brownian motion and do not yield dividends. The findings from this study highlight the potential of RDTM as a powerful tool in the realm of financial mathematics, offering substantial improvements in the computational efficiency and accuracy of option pricing models.

Item Type:	Article
Uncontrolled Keywords:	European option model, non-dividend, non-linear return, semi-analytical method, sensitivity analysis
Subjects:	Q Science > Q Science (General) Q Science > QA Mathematics
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science Faculty of Engineering & Science > School of Computing & Mathematical Sciences (CMS)
Last Modified:	24 Nov 2025 16:45
URI:	https://gala.gre.ac.uk/id/eprint/51729

Actions (login required)

View Item

Downloads