Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods
Black–Scholes partial differential equation is a generally acceptable model in financial markets for option pricing. However, without variable transformations, the provision of symbolic solutions to the variable coefficient partial differential equation is not a straight-forward task. Moreover, the...
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Universidade Federal de Viçosa (UFV)
2022-06-01
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| Series: | The Journal of Engineering and Exact Sciences |
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| Online Access: | https://periodicos.ufv.br/jcec/article/view/15223 |
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| author | Zainab Olabisi Dere Gbeminiyi Musibau Sobamowo Antonio Marcos de Oliveira Siqueira |
| author_facet | Zainab Olabisi Dere Gbeminiyi Musibau Sobamowo Antonio Marcos de Oliveira Siqueira |
| author_sort | Zainab Olabisi Dere |
| collection | DOAJ |
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Black–Scholes partial differential equation is a generally acceptable model in financial markets for option pricing. However, without variable transformations, the provision of symbolic solutions to the variable coefficient partial differential equation is not a straight-forward task. Moreover, the coefficients of the Black–Scholes can depend on the time and the asset price which makes the analytical solution of the Black–Scholes model very difficult to develop. In this paper, analytical solutions of the model of valuations of financial options are presented using Laplace and differential transform methods. The results of the solutions of the Laplace and differential transformation methods are compared with the results of the exact analytical solutions. Moreover, numerical examples for different options pricing are presented to establish the applications, speed and accuracy of the hybrid methods.
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| format | Article |
| id | doaj-art-61b59819bd3b44a89550202d7e37f07e |
| institution | Kabale University |
| issn | 2527-1075 |
| language | English |
| publishDate | 2022-06-01 |
| publisher | Universidade Federal de Viçosa (UFV) |
| record_format | Article |
| series | The Journal of Engineering and Exact Sciences |
| spelling | doaj-art-61b59819bd3b44a89550202d7e37f07e2025-02-02T19:56:18ZengUniversidade Federal de Viçosa (UFV)The Journal of Engineering and Exact Sciences2527-10752022-06-018110.18540/jcecvl8iss1pp15223-01iAnalytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation MethodsZainab Olabisi Dere0Gbeminiyi Musibau Sobamowo1Antonio Marcos de Oliveira Siqueira2Department of Mathematics, Florida State University, USA Department of Mechanical Engineering, Faculty of Engineering, University of Lagos, Akoka Lagos, NigeriaFederal University of Viçosa, Brazil Black–Scholes partial differential equation is a generally acceptable model in financial markets for option pricing. However, without variable transformations, the provision of symbolic solutions to the variable coefficient partial differential equation is not a straight-forward task. Moreover, the coefficients of the Black–Scholes can depend on the time and the asset price which makes the analytical solution of the Black–Scholes model very difficult to develop. In this paper, analytical solutions of the model of valuations of financial options are presented using Laplace and differential transform methods. The results of the solutions of the Laplace and differential transformation methods are compared with the results of the exact analytical solutions. Moreover, numerical examples for different options pricing are presented to establish the applications, speed and accuracy of the hybrid methods. https://periodicos.ufv.br/jcec/article/view/15223Black–Scholes model; Partial differential Equation; Financial Market; Option pricing; Laplace-differential transformation method. |
| spellingShingle | Zainab Olabisi Dere Gbeminiyi Musibau Sobamowo Antonio Marcos de Oliveira Siqueira Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods The Journal of Engineering and Exact Sciences Black–Scholes model; Partial differential Equation; Financial Market; Option pricing; Laplace-differential transformation method. |
| title | Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods |
| title_full | Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods |
| title_fullStr | Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods |
| title_full_unstemmed | Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods |
| title_short | Analytical Solutions of Black-Scholes Partial Differential Equation of Pricing for Valuations of Financial Options using Hybrid Transformation Methods |
| title_sort | analytical solutions of black scholes partial differential equation of pricing for valuations of financial options using hybrid transformation methods |
| topic | Black–Scholes model; Partial differential Equation; Financial Market; Option pricing; Laplace-differential transformation method. |
| url | https://periodicos.ufv.br/jcec/article/view/15223 |
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