The Fractional Soliton Wave Propagation of Non-Linear Volatility and Option Pricing Systems with a Sensitive Demonstration
In this study, we explore a fractional non-linear coupled option pricing and volatility system. The model under consideration can be viewed as a fractional non-linear coupled wave alternative to the Black–Scholes option pricing governing system, introducing a leveraging effect where stock volatility...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/11/809 |
| _version_ | 1797459287432232960 |
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| author | Muhammad Bilal Riaz Ali Raza Ansari Adil Jhangeer Muddassar Imran Choon Kit Chan |
| author_facet | Muhammad Bilal Riaz Ali Raza Ansari Adil Jhangeer Muddassar Imran Choon Kit Chan |
| author_sort | Muhammad Bilal Riaz |
| collection | DOAJ |
| description | In this study, we explore a fractional non-linear coupled option pricing and volatility system. The model under consideration can be viewed as a fractional non-linear coupled wave alternative to the Black–Scholes option pricing governing system, introducing a leveraging effect where stock volatility corresponds to stock returns. Employing the inverse scattering transformation, we find that the Cauchy problem for this model is insolvable. Consequently, we utilize the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mo>Φ</mo><mn>6</mn></msup></semantics></math></inline-formula>-expansion algorithm to generate generalized novel solitonic analytical wave structures within the system. We present graphical representations in contour, 3D, and 2D formats to illustrate how the system’s behavior responds to the propagation of pulses, enabling us to predict suitable parameter values that align with the data. Finally, a conclusion is given. |
| first_indexed | 2024-03-09T16:49:18Z |
| format | Article |
| id | doaj.art-d33ea328e83b4130b7723d7b7a16c884 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T16:49:18Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-d33ea328e83b4130b7723d7b7a16c8842023-11-24T14:43:03ZengMDPI AGFractal and Fractional2504-31102023-11-0171180910.3390/fractalfract7110809The Fractional Soliton Wave Propagation of Non-Linear Volatility and Option Pricing Systems with a Sensitive DemonstrationMuhammad Bilal Riaz0Ali Raza Ansari1Adil Jhangeer2Muddassar Imran3Choon Kit Chan4Faculty of Engineering and Quantity Surveying, INTI International University, Putra Nilai, Nilai 71800, MalaysiaCentre for Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology, Hawally 32093, KuwaitDepartment of Mathematics, Namal University, 30KM Talagang Road, Mianwali 42250, PakistanCollege of Humanities and Sciences, Ajman University, Ajman P.O. Box 346, United Arab EmiratesFaculty of Engineering and Quantity Surveying, INTI International University, Putra Nilai, Nilai 71800, MalaysiaIn this study, we explore a fractional non-linear coupled option pricing and volatility system. The model under consideration can be viewed as a fractional non-linear coupled wave alternative to the Black–Scholes option pricing governing system, introducing a leveraging effect where stock volatility corresponds to stock returns. Employing the inverse scattering transformation, we find that the Cauchy problem for this model is insolvable. Consequently, we utilize the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mo>Φ</mo><mn>6</mn></msup></semantics></math></inline-formula>-expansion algorithm to generate generalized novel solitonic analytical wave structures within the system. We present graphical representations in contour, 3D, and 2D formats to illustrate how the system’s behavior responds to the propagation of pulses, enabling us to predict suitable parameter values that align with the data. Finally, a conclusion is given.https://www.mdpi.com/2504-3110/7/11/809Φ6-model expansion schemeM-truncated fractional operatoranalytical solutioncoupled nonlinear volatilityoption pricing model |
| spellingShingle | Muhammad Bilal Riaz Ali Raza Ansari Adil Jhangeer Muddassar Imran Choon Kit Chan The Fractional Soliton Wave Propagation of Non-Linear Volatility and Option Pricing Systems with a Sensitive Demonstration Fractal and Fractional Φ6-model expansion scheme M-truncated fractional operator analytical solution coupled nonlinear volatility option pricing model |
| title | The Fractional Soliton Wave Propagation of Non-Linear Volatility and Option Pricing Systems with a Sensitive Demonstration |
| title_full | The Fractional Soliton Wave Propagation of Non-Linear Volatility and Option Pricing Systems with a Sensitive Demonstration |
| title_fullStr | The Fractional Soliton Wave Propagation of Non-Linear Volatility and Option Pricing Systems with a Sensitive Demonstration |
| title_full_unstemmed | The Fractional Soliton Wave Propagation of Non-Linear Volatility and Option Pricing Systems with a Sensitive Demonstration |
| title_short | The Fractional Soliton Wave Propagation of Non-Linear Volatility and Option Pricing Systems with a Sensitive Demonstration |
| title_sort | fractional soliton wave propagation of non linear volatility and option pricing systems with a sensitive demonstration |
| topic | Φ6-model expansion scheme M-truncated fractional operator analytical solution coupled nonlinear volatility option pricing model |
| url | https://www.mdpi.com/2504-3110/7/11/809 |
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