Generalizing the Black and Scholes Equation Assuming Differentiable Noise
This article develops probability equations for an asset value through time, assuming continuous correlated differentiable Gaussian distributed noise. Ito’s (1944) stochastic integral and a generalized Novikov’s (1919) theorem are used. As an example, the mathematical model is used to generalize the...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/8906248 |
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| _version_ | 1832543375018950656 |
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| author | Kjell Hausken John F. Moxnes |
| author_facet | Kjell Hausken John F. Moxnes |
| author_sort | Kjell Hausken |
| collection | DOAJ |
| description | This article develops probability equations for an asset value through time, assuming continuous correlated differentiable Gaussian distributed noise. Ito’s (1944) stochastic integral and a generalized Novikov’s (1919) theorem are used. As an example, the mathematical model is used to generalize the Black and Scholes’ (1973) equation for pricing financial instruments. The article connects the Kolmogorov (1931) probability equation to arbitrage and to how financial instruments are priced, where more generally, the mathematical model based on differentiable noise may improve or be an alternative for forecasts. The article contrasts with much of the literature which assumes continuous nondifferentiable uncorrelated Gaussian distributed white noise. |
| format | Article |
| id | doaj-art-8d426a42f32a4ad199d2bd33699fea7f |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-8d426a42f32a4ad199d2bd33699fea7f2025-02-03T11:49:34ZengWileyJournal of Applied Mathematics1687-00422024-01-01202410.1155/2024/8906248Generalizing the Black and Scholes Equation Assuming Differentiable NoiseKjell Hausken0John F. Moxnes1Faculty of Science and TechnologyDefence SystemsThis article develops probability equations for an asset value through time, assuming continuous correlated differentiable Gaussian distributed noise. Ito’s (1944) stochastic integral and a generalized Novikov’s (1919) theorem are used. As an example, the mathematical model is used to generalize the Black and Scholes’ (1973) equation for pricing financial instruments. The article connects the Kolmogorov (1931) probability equation to arbitrage and to how financial instruments are priced, where more generally, the mathematical model based on differentiable noise may improve or be an alternative for forecasts. The article contrasts with much of the literature which assumes continuous nondifferentiable uncorrelated Gaussian distributed white noise.http://dx.doi.org/10.1155/2024/8906248 |
| spellingShingle | Kjell Hausken John F. Moxnes Generalizing the Black and Scholes Equation Assuming Differentiable Noise Journal of Applied Mathematics |
| title | Generalizing the Black and Scholes Equation Assuming Differentiable Noise |
| title_full | Generalizing the Black and Scholes Equation Assuming Differentiable Noise |
| title_fullStr | Generalizing the Black and Scholes Equation Assuming Differentiable Noise |
| title_full_unstemmed | Generalizing the Black and Scholes Equation Assuming Differentiable Noise |
| title_short | Generalizing the Black and Scholes Equation Assuming Differentiable Noise |
| title_sort | generalizing the black and scholes equation assuming differentiable noise |
| url | http://dx.doi.org/10.1155/2024/8906248 |
| work_keys_str_mv | AT kjellhausken generalizingtheblackandscholesequationassumingdifferentiablenoise AT johnfmoxnes generalizingtheblackandscholesequationassumingdifferentiablenoise |