Solving the Black–Scholes European options model using the reduced differential transform method with powered modified log-payoff function

作     者：Fadugba, S.E. Udoye, A.M. Zelibe, S.C. Edeki, S.O. Achudume, C. Adeyanju, A.A. Makinde, O. Bankole, P.A. Kekana, M.C. 

作者机构：Department of Mathematics Ekiti State University Iworoko Road PMB 5363 Ado Ekiti 360001 Nigeria Department of Mathematics Federal University Oye Ekiti Ekiti State Nigeria Department of Mathematics Federal University of Petroleum Resources Delta State Effurun Nigeria Department of Mathematics Dennis Osadebay University Delta State Asaba Nigeria Department of Computer Science and Mathematics Evangel University Akaeze Ebonyi State Abakaliki 825001 Nigeria Department of Mathematics Federal University of Agriculture Ogun State Abeokuta Nigeria Federal College of Education Ogun State Abeokuta Nigeria Department of Mathematics Education Lagos State University of Education Lagos State Oto/Ijanikin Nigeria Department of Mathematics Tshwane University of Technology 175 Nelson Mandela Drive Pretoria 0001 South Africa 

出 版 物：《Partial Differential Equations in Applied Mathematics》 (Partial Diff. Equ. Appl. Math.)

年 卷 期：2025年第13卷

基　　金：Tshwane University of Technology, TUT Department of Higher Education and Training, DHET 

主　　题：European option model Non-dividend Non-linear return Semi-analytical method Sensitivity analysis 

摘      要：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. © 2025 The Authors