The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs Method
In this paper, radial basis functions (RBFs) method was used to solve a fractional Black-Scholes-Schrodinger equation in an option pricing of financial problems. The RBFs method is applied in discretizing a spatial derivative process. The approximation of time fractional derivative is interpreted in...
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/1942762 |
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| author | Naravadee Nualsaard Anirut Luadsong Nitima Aschariyaphotha |
| author_facet | Naravadee Nualsaard Anirut Luadsong Nitima Aschariyaphotha |
| author_sort | Naravadee Nualsaard |
| collection | DOAJ |
| description | In this paper, radial basis functions (RBFs) method was used to solve a fractional Black-Scholes-Schrodinger equation in an option pricing of financial problems. The RBFs method is applied in discretizing a spatial derivative process. The approximation of time fractional derivative is interpreted in the Caputo’s sense by a simple quadrature formula. This RBFs approach was theoretically proved with different problems of two numerical examples: time step arbitrage bubble case and time linear arbitrage bubble case. Then, the numerical results were compared with the semiclassical solution in case of fractional order close to 1. As a result, both numerical examples showed that the option prices from RBFs method satisfy the semiclassical solution. |
| format | Article |
| id | doaj-art-111e2fa8d30844debff258a13e87b00d |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-111e2fa8d30844debff258a13e87b00d2025-02-03T05:49:29ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/19427621942762The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs MethodNaravadee Nualsaard0Anirut Luadsong1Nitima Aschariyaphotha2Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Bang Mod, Thung Khru, Bangkok 10140, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Bang Mod, Thung Khru, Bangkok 10140, ThailandRatchaburi Learning Park, King Mongkut’s University of Technology Thonburi (KMUTT), Rang Bua, Chom Bueng, Ratchaburi 70150, ThailandIn this paper, radial basis functions (RBFs) method was used to solve a fractional Black-Scholes-Schrodinger equation in an option pricing of financial problems. The RBFs method is applied in discretizing a spatial derivative process. The approximation of time fractional derivative is interpreted in the Caputo’s sense by a simple quadrature formula. This RBFs approach was theoretically proved with different problems of two numerical examples: time step arbitrage bubble case and time linear arbitrage bubble case. Then, the numerical results were compared with the semiclassical solution in case of fractional order close to 1. As a result, both numerical examples showed that the option prices from RBFs method satisfy the semiclassical solution.http://dx.doi.org/10.1155/2020/1942762 |
| spellingShingle | Naravadee Nualsaard Anirut Luadsong Nitima Aschariyaphotha The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs Method Advances in Mathematical Physics |
| title | The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs Method |
| title_full | The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs Method |
| title_fullStr | The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs Method |
| title_full_unstemmed | The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs Method |
| title_short | The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs Method |
| title_sort | numerical solution of fractional black scholes schrodinger equation using the rbfs method |
| url | http://dx.doi.org/10.1155/2020/1942762 |
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