Qualitatively Stable Schemes for the Black–Scholes Equation
In this paper, the Black–Scholes equation is solved using a new technique. This scheme is derived by combining the Laplace transform method and the nonstandard finite difference (NSFD) strategy. The qualitative properties of the method are discussed, and it is shown that the new method is positive,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/2/154 |
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| author | Mohammad Mehdizadeh Khalsaraei Ali Shokri Yuanheng Wang Sohrab Bazm Giti Navidifar Pari Khakzad |
| author_facet | Mohammad Mehdizadeh Khalsaraei Ali Shokri Yuanheng Wang Sohrab Bazm Giti Navidifar Pari Khakzad |
| author_sort | Mohammad Mehdizadeh Khalsaraei |
| collection | DOAJ |
| description | In this paper, the Black–Scholes equation is solved using a new technique. This scheme is derived by combining the Laplace transform method and the nonstandard finite difference (NSFD) strategy. The qualitative properties of the method are discussed, and it is shown that the new method is positive, stable, and consistent when low volatility is assumed. The efficiency of the new method is demonstrated by a numerical example. |
| first_indexed | 2024-03-11T08:49:18Z |
| format | Article |
| id | doaj.art-d900141343ca4097a79d4e4505bdf2ff |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T08:49:18Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-d900141343ca4097a79d4e4505bdf2ff2023-11-16T20:36:44ZengMDPI AGFractal and Fractional2504-31102023-02-017215410.3390/fractalfract7020154Qualitatively Stable Schemes for the Black–Scholes EquationMohammad Mehdizadeh Khalsaraei0Ali Shokri1Yuanheng Wang2Sohrab Bazm3Giti Navidifar4Pari Khakzad5Faculty of Mathematical Science, University of Maragheh, Maragheh 83111-55181, IranFaculty of Mathematical Science, University of Maragheh, Maragheh 83111-55181, IranCollege of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, ChinaFaculty of Mathematical Science, University of Maragheh, Maragheh 83111-55181, IranFaculty of Mathematical Science, University of Maragheh, Maragheh 83111-55181, IranFaculty of Mathematical Science, University of Maragheh, Maragheh 83111-55181, IranIn this paper, the Black–Scholes equation is solved using a new technique. This scheme is derived by combining the Laplace transform method and the nonstandard finite difference (NSFD) strategy. The qualitative properties of the method are discussed, and it is shown that the new method is positive, stable, and consistent when low volatility is assumed. The efficiency of the new method is demonstrated by a numerical example.https://www.mdpi.com/2504-3110/7/2/154Black–Scholes equationLaplace transformnonstandard finite difference methodpositivity preserving |
| spellingShingle | Mohammad Mehdizadeh Khalsaraei Ali Shokri Yuanheng Wang Sohrab Bazm Giti Navidifar Pari Khakzad Qualitatively Stable Schemes for the Black–Scholes Equation Fractal and Fractional Black–Scholes equation Laplace transform nonstandard finite difference method positivity preserving |
| title | Qualitatively Stable Schemes for the Black–Scholes Equation |
| title_full | Qualitatively Stable Schemes for the Black–Scholes Equation |
| title_fullStr | Qualitatively Stable Schemes for the Black–Scholes Equation |
| title_full_unstemmed | Qualitatively Stable Schemes for the Black–Scholes Equation |
| title_short | Qualitatively Stable Schemes for the Black–Scholes Equation |
| title_sort | qualitatively stable schemes for the black scholes equation |
| topic | Black–Scholes equation Laplace transform nonstandard finite difference method positivity preserving |
| url | https://www.mdpi.com/2504-3110/7/2/154 |
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