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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Main Authors: Rehman, Hamood Ur, Wong, Patricia Jia Yiing, Aljohani, A. F., Iqbal, Ifrah, Saleem, Muhammad Shoaib
Other Authors: School of Electrical and Electronic Engineering
Format: Article
Language:English
Published: 2024
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Online Access:https://hdl.handle.net/10356/180613
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Institution: Nanyang Technological University
Language: English
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spelling 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
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Mathematical Sciences
Black-Scholes equation
Option pricing modelling
spellingShingle 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
description 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.
author2 School of Electrical and Electronic Engineering
author_facet School of Electrical and Electronic Engineering
Rehman, Hamood Ur
Wong, Patricia Jia Yiing
Aljohani, A. F.
Iqbal, Ifrah
Saleem, Muhammad Shoaib
format Article
author Rehman, Hamood Ur
Wong, Patricia Jia Yiing
Aljohani, A. F.
Iqbal, Ifrah
Saleem, Muhammad Shoaib
author_sort 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
title_full The fractional soliton solutions: shaping future finances with innovativwave profiles in option pricing system
title_fullStr The fractional soliton solutions: shaping future finances with innovativwave profiles in option pricing system
title_full_unstemmed The fractional soliton solutions: shaping future finances with innovativwave profiles in option pricing system
title_sort fractional soliton solutions: shaping future finances with innovativwave profiles in option pricing system
publishDate 2024
url https://hdl.handle.net/10356/180613
_version_ 1814777779426689024