The fractional soliton solutions: shaping future finances with innovativwave profiles in option pricing system
Financial engineering problems hold considerable significance in the academic realm, where there remains a continued demand for efficient methods to scrutinize and analyze these models. Within this investigation, we delved into a fractional nonlinear coupled system for option pricing and volatility....
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sg-ntu-dr.10356-1806132024-10-18T15:41:55Z The fractional soliton solutions: shaping future finances with innovativwave profiles in option pricing system Rehman, Hamood Ur Wong, Patricia Jia Yiing Aljohani, A. F. Iqbal, Ifrah Saleem, Muhammad Shoaib School of Electrical and Electronic Engineering Mathematical Sciences Black-Scholes equation Option pricing modelling Financial engineering problems hold considerable significance in the academic realm, where there remains a continued demand for efficient methods to scrutinize and analyze these models. Within this investigation, we delved into a fractional nonlinear coupled system for option pricing and volatility. The model we examined can be conceptualized as a fractional nonlinear coupled wave alternative to the governing system of Black-Scholes option pricing. This introduced a leveraging effect, wherein stock volatility aligns with stock returns. To generate novel solitonic wave structures in the system, the present article introduced a generalized Ricatti mapping method and new Kudryashov method. Graphical representations, both in 3D and 2D formats, were employed to elucidate the system’s response to pulse propagation. These visualizations enabled the anticipation of appropriate parameter values that align with the observed data. Furthermore, a comparative analysis of solutions was presented for different fractional order values. Additionally, the article showcases the comparison of wave profiles through 2D graphs. The results of this investigation suggested that the proposed method served as a highly reliable and flexible alternative for problem-solving, preserving the physical attributes inherent in realistic processes. To sum up, the main objective of our work was to conceptualize a fractional nonlinear coupled wave system as an alternative to the Black-Scholes option pricing model and investigate its implications on stock volatility and returns. Additionally, we aimed to apply and analyze methods for generating solitonic wave structures and compare their solutions for different fractional order values. Published version 2024-10-15T02:32:29Z 2024-10-15T02:32:29Z 2024 Journal Article Rehman, H. U., Wong, P. J. Y., Aljohani, A. F., Iqbal, I. & Saleem, M. S. (2024). The fractional soliton solutions: shaping future finances with innovativwave profiles in option pricing system. AIMS Mathematics, 9(9), 24699-24721. https://dx.doi.org/10.3934/math.20241203 2473-6988 https://hdl.handle.net/10356/180613 10.3934/math.20241203 2-s2.0-85202544701 9 9 24699 24721 en AIMS Mathematics © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0). application/pdf |
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Mathematical Sciences Black-Scholes equation Option pricing modelling Rehman, Hamood Ur Wong, Patricia Jia Yiing Aljohani, A. F. Iqbal, Ifrah Saleem, Muhammad Shoaib The fractional soliton solutions: shaping future finances with innovativwave profiles in option pricing system |
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Financial engineering problems hold considerable significance in the academic realm, where there remains a continued demand for efficient methods to scrutinize and analyze these models. Within this investigation, we delved into a fractional nonlinear coupled system for option pricing and volatility. The model we examined can be conceptualized as a fractional nonlinear coupled wave alternative to the governing system of Black-Scholes option pricing. This introduced a leveraging effect, wherein stock volatility aligns with stock returns. To generate novel solitonic wave structures in the system, the present article introduced a generalized Ricatti mapping method and new Kudryashov method. Graphical representations, both in 3D and 2D formats, were employed to elucidate the system’s response to pulse propagation. These visualizations enabled the anticipation of appropriate parameter values that align with the observed data. Furthermore, a comparative analysis of solutions was presented for different fractional order values. Additionally, the article showcases the comparison of wave profiles through 2D graphs. The results of this investigation suggested that the proposed method served as a highly reliable and flexible alternative for problem-solving, preserving the physical attributes inherent in realistic processes. To sum up, the main objective of our work was to conceptualize a fractional nonlinear coupled wave system as an alternative to the Black-Scholes option pricing model and investigate its implications on stock volatility and returns. Additionally, we aimed to apply and analyze methods for generating solitonic wave structures and compare their solutions for different fractional order values. |
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School of Electrical and Electronic Engineering |
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School of Electrical and Electronic Engineering Rehman, Hamood Ur Wong, Patricia Jia Yiing Aljohani, A. F. Iqbal, Ifrah Saleem, Muhammad Shoaib |
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Article |
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Rehman, Hamood Ur Wong, Patricia Jia Yiing Aljohani, A. F. Iqbal, Ifrah Saleem, Muhammad Shoaib |
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Rehman, Hamood Ur |
title |
The fractional soliton solutions: shaping future finances with innovativwave profiles in option pricing system |
title_short |
The fractional soliton solutions: shaping future finances with innovativwave profiles in option pricing system |
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The fractional soliton solutions: shaping future finances with innovativwave profiles in option pricing system |
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The fractional soliton solutions: shaping future finances with innovativwave profiles in option pricing system |
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The fractional soliton solutions: shaping future finances with innovativwave profiles in option pricing system |
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fractional soliton solutions: shaping future finances with innovativwave profiles in option pricing system |
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2024 |
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https://hdl.handle.net/10356/180613 |
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