Solving the Black–Scholes European options model using the reduced differential transform method with powered modified log-payoff function
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, particularl...
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| Main Authors: | , , , , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125000154 |
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| author | S.E. Fadugba A.M. Udoye S.C. Zelibe S.O. Edeki C. Achudume A.A. Adeyanju O. Makinde P.A. Bankole M.C. Kekana |
| author_facet | S.E. Fadugba A.M. Udoye S.C. Zelibe S.O. Edeki C. Achudume A.A. Adeyanju O. Makinde P.A. Bankole M.C. Kekana |
| author_sort | S.E. Fadugba |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d517a8a1ce8144c5a4bc4348c8bfbf0b |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-d517a8a1ce8144c5a4bc4348c8bfbf0b2025-01-30T05:15:07ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101087Solving the Black–Scholes European options model using the reduced differential transform method with powered modified log-payoff functionS.E. Fadugba0A.M. Udoye1S.C. Zelibe2S.O. Edeki3C. Achudume4A.A. Adeyanju5O. Makinde6P.A. Bankole7M.C. Kekana8Department of Mathematics, Ekiti State University, Iworoko Road, PMB 5363, Ado Ekiti, 360001, Nigeria; Corresponding author.Department of Mathematics, Federal University Oye Ekiti, Ekiti State, NigeriaDepartment of Mathematics, Federal University of Petroleum Resources, Effurun, Delta State, NigeriaDepartment of Mathematics, Dennis Osadebay University, Asaba, Delta State, NigeriaDepartment of Computer Science and Mathematics, Evangel University, Akaeze, Abakaliki, 825001, Ebonyi State, NigeriaDepartment of Mathematics, Federal University of Agriculture, Abeokuta, Ogun State, NigeriaFederal College of Education, Abeokuta, Ogun State, NigeriaDepartment of Mathematics Education, Lagos State University of Education, Oto/Ijanikin, Lagos State, NigeriaDepartment of Mathematics, Tshwane University of Technology, 175 Nelson Mandela Drive, Pretoria, 0001, South AfricaThis 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.http://www.sciencedirect.com/science/article/pii/S2666818125000154European option modelNon-dividendNon-linear returnSemi-analytical methodSensitivity analysis |
| spellingShingle | S.E. Fadugba A.M. Udoye S.C. Zelibe S.O. Edeki C. Achudume A.A. Adeyanju O. Makinde P.A. Bankole M.C. Kekana 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 European option model Non-dividend Non-linear return Semi-analytical method Sensitivity analysis |
| title | Solving the Black–Scholes European options model using the reduced differential transform method with powered modified log-payoff function |
| title_full | Solving the Black–Scholes European options model using the reduced differential transform method with powered modified log-payoff function |
| title_fullStr | Solving the Black–Scholes European options model using the reduced differential transform method with powered modified log-payoff function |
| title_full_unstemmed | Solving the Black–Scholes European options model using the reduced differential transform method with powered modified log-payoff function |
| title_short | Solving the Black–Scholes European options model using the reduced differential transform method with powered modified log-payoff function |
| title_sort | solving the black scholes european options model using the reduced differential transform method with powered modified log payoff function |
| topic | European option model Non-dividend Non-linear return Semi-analytical method Sensitivity analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125000154 |
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