Investigation of Higher Order Localized Approximations for a Fractional Pricing Model in Finance
In this work, by considering spatial uniform meshes and stencils having five adjacent discretization nodes, we furnish a numerical scheme to solve the time-fractional Black–Scholes (partial differential equation) PDE to price financial options under the generalized multiquadric radial basis function...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/12/2641 |
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| author | Malik Zaka Ullah Abdullah Khamis Alzahrani Hashim Mohammed Alshehri Stanford Shateyi |
| author_facet | Malik Zaka Ullah Abdullah Khamis Alzahrani Hashim Mohammed Alshehri Stanford Shateyi |
| author_sort | Malik Zaka Ullah |
| collection | DOAJ |
| description | In this work, by considering spatial uniform meshes and stencils having five adjacent discretization nodes, we furnish a numerical scheme to solve the time-fractional Black–Scholes (partial differential equation) PDE to price financial options under the generalized multiquadric radial basis function (RBF). The time-fractional derivative is estimated by an L1-scheme but the spatial variable is discretized using fourth-order RBF-FD methodology. As a matter of fact, the PDE problem is transformed in the form of a linear set of algebraic equations. To support analytical discussions, numerical tests are furnished and reveal the efficacy of the presented solver. |
| first_indexed | 2024-03-11T02:12:20Z |
| format | Article |
| id | doaj.art-5bdb2effb09d46e0bbd082f4fadded65 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T02:12:20Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5bdb2effb09d46e0bbd082f4fadded652023-11-18T11:27:44ZengMDPI AGMathematics2227-73902023-06-011112264110.3390/math11122641Investigation of Higher Order Localized Approximations for a Fractional Pricing Model in FinanceMalik Zaka Ullah0Abdullah Khamis Alzahrani1Hashim Mohammed Alshehri2Stanford Shateyi3Mathematical Modelling and Applied Computation (MMAC) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaMathematical Modelling and Applied Computation (MMAC) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaMathematical Modelling and Applied Computation (MMAC) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South AfricaIn this work, by considering spatial uniform meshes and stencils having five adjacent discretization nodes, we furnish a numerical scheme to solve the time-fractional Black–Scholes (partial differential equation) PDE to price financial options under the generalized multiquadric radial basis function (RBF). The time-fractional derivative is estimated by an L1-scheme but the spatial variable is discretized using fourth-order RBF-FD methodology. As a matter of fact, the PDE problem is transformed in the form of a linear set of algebraic equations. To support analytical discussions, numerical tests are furnished and reveal the efficacy of the presented solver.https://www.mdpi.com/2227-7390/11/12/2641option pricingfractional Black–Scholesradial basis function (RBF)RBF-FDnumerical method |
| spellingShingle | Malik Zaka Ullah Abdullah Khamis Alzahrani Hashim Mohammed Alshehri Stanford Shateyi Investigation of Higher Order Localized Approximations for a Fractional Pricing Model in Finance Mathematics option pricing fractional Black–Scholes radial basis function (RBF) RBF-FD numerical method |
| title | Investigation of Higher Order Localized Approximations for a Fractional Pricing Model in Finance |
| title_full | Investigation of Higher Order Localized Approximations for a Fractional Pricing Model in Finance |
| title_fullStr | Investigation of Higher Order Localized Approximations for a Fractional Pricing Model in Finance |
| title_full_unstemmed | Investigation of Higher Order Localized Approximations for a Fractional Pricing Model in Finance |
| title_short | Investigation of Higher Order Localized Approximations for a Fractional Pricing Model in Finance |
| title_sort | investigation of higher order localized approximations for a fractional pricing model in finance |
| topic | option pricing fractional Black–Scholes radial basis function (RBF) RBF-FD numerical method |
| url | https://www.mdpi.com/2227-7390/11/12/2641 |
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