A meshless method for numerical solutions of linear and nonlinear time-fractional Black-Scholes models

The numerical solution of the time-fractional Black-Scholes model for European and American options is presented using a local meshless collocation approach based on hybrid Gaussian-cubic radial basis functions with polynomials is presented. The approach is then expanded to a nonlinear time-fraction...

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Main Authors: Ahmad H., Khan M.N., Ahmad I., Omri M., Alotaibi M.F.
其他作者: 57220768187
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出版: American Institute of Mathematical Sciences 2024
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spelling my.uniten.dspace-345572024-10-14T11:20:38Z A meshless method for numerical solutions of linear and nonlinear time-fractional Black-Scholes models Ahmad H. Khan M.N. Ahmad I. Omri M. Alotaibi M.F. 57220768187 57205304990 57220824630 56973969500 57194206309 hybrid local meshless method polynomial radial basis functions time-fractional Black-Scholes model The numerical solution of the time-fractional Black-Scholes model for European and American options is presented using a local meshless collocation approach based on hybrid Gaussian-cubic radial basis functions with polynomials is presented. The approach is then expanded to a nonlinear time-fractional model for an option with transaction costs in a market with low liquidity. The spatial derivatives of the models are discretized using the proposed meshless technique. Numerical experiments are carried out for the American option, European option, and nonlinear transaction cost option models. In order to evaluate the effectiveness and precision of the suggested meshless approach, L? and Lrel error norms are utilized. Both call and put option volatility is explored. A non-uniform grid customized around the strike price region is also used to determine the prices of European call and American put options. The methods described in literature are compared with the numerical results. � 2023 the Author(s), licensee AIMS Press. Final 2024-10-14T03:20:38Z 2024-10-14T03:20:38Z 2023 Article 10.3934/math.20231003 2-s2.0-85163127496 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85163127496&doi=10.3934%2fmath.20231003&partnerID=40&md5=5e094803e93b912cc0be62268838d4e5 https://irepository.uniten.edu.my/handle/123456789/34557 8 8 19677 19698 All Open Access Gold Open Access American Institute of Mathematical Sciences Scopus
institution Universiti Tenaga Nasional
building UNITEN Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Tenaga Nasional
content_source UNITEN Institutional Repository
url_provider http://dspace.uniten.edu.my/
topic hybrid local meshless method
polynomial
radial basis functions
time-fractional Black-Scholes model
spellingShingle hybrid local meshless method
polynomial
radial basis functions
time-fractional Black-Scholes model
Ahmad H.
Khan M.N.
Ahmad I.
Omri M.
Alotaibi M.F.
A meshless method for numerical solutions of linear and nonlinear time-fractional Black-Scholes models
description The numerical solution of the time-fractional Black-Scholes model for European and American options is presented using a local meshless collocation approach based on hybrid Gaussian-cubic radial basis functions with polynomials is presented. The approach is then expanded to a nonlinear time-fractional model for an option with transaction costs in a market with low liquidity. The spatial derivatives of the models are discretized using the proposed meshless technique. Numerical experiments are carried out for the American option, European option, and nonlinear transaction cost option models. In order to evaluate the effectiveness and precision of the suggested meshless approach, L? and Lrel error norms are utilized. Both call and put option volatility is explored. A non-uniform grid customized around the strike price region is also used to determine the prices of European call and American put options. The methods described in literature are compared with the numerical results. � 2023 the Author(s), licensee AIMS Press.
author2 57220768187
author_facet 57220768187
Ahmad H.
Khan M.N.
Ahmad I.
Omri M.
Alotaibi M.F.
format Article
author Ahmad H.
Khan M.N.
Ahmad I.
Omri M.
Alotaibi M.F.
author_sort Ahmad H.
title A meshless method for numerical solutions of linear and nonlinear time-fractional Black-Scholes models
title_short A meshless method for numerical solutions of linear and nonlinear time-fractional Black-Scholes models
title_full A meshless method for numerical solutions of linear and nonlinear time-fractional Black-Scholes models
title_fullStr A meshless method for numerical solutions of linear and nonlinear time-fractional Black-Scholes models
title_full_unstemmed A meshless method for numerical solutions of linear and nonlinear time-fractional Black-Scholes models
title_sort meshless method for numerical solutions of linear and nonlinear time-fractional black-scholes models
publisher American Institute of Mathematical Sciences
publishDate 2024
_version_ 1814061185103822848
score 13.250246