An efficient numerical technique based on the extended cubic B-spline functions for solving time fractional Black–Scholes model
Financial theory could introduce a fractional differential equation (FDE) that presents new theoretical research concepts, methods and practical implementations. Due to the memory factor of fractional derivatives, physical pathways with storage and inherited properties can be best represented by FDE...
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| Veröffentlicht in: | Engineering with computers 2022-06, Vol.38 (Suppl 2), p.1705-1716 |
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| creator | Akram, Tayyaba Abbas, Muhammad Abualnaja, Khadijah M. Iqbal, Azhar Majeed, Abdul |
| description | Financial theory could introduce a fractional differential equation (FDE) that presents new theoretical research concepts, methods and practical implementations. Due to the memory factor of fractional derivatives, physical pathways with storage and inherited properties can be best represented by FDEs. For that purpose, reliable and effective techniques are required for solving FDEs. Our objective is to generalize the collocation method for solving time fractional Black–Scholes European option pricing model using the extended cubic B-spline. The key feature of the strategy is that it turns these type of problems into a system of algebraic equations which can be appropriate for computer programming. This is not only streamlines the problems but speed up the computations as well. The Fourier stability and convergence analysis of the scheme are examined. A proposed numerical scheme having second-order accuracy via spatial direction is also constructed. The numerical and graphical results indicate that the suggested approach for the European option prices agree well with the analytical solutions. |
| doi_str_mv | 10.1007/s00366-021-01436-1 |
| format | Article |
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Due to the memory factor of fractional derivatives, physical pathways with storage and inherited properties can be best represented by FDEs. For that purpose, reliable and effective techniques are required for solving FDEs. Our objective is to generalize the collocation method for solving time fractional Black–Scholes European option pricing model using the extended cubic B-spline. The key feature of the strategy is that it turns these type of problems into a system of algebraic equations which can be appropriate for computer programming. This is not only streamlines the problems but speed up the computations as well. The Fourier stability and convergence analysis of the scheme are examined. A proposed numerical scheme having second-order accuracy via spatial direction is also constructed. 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Applications in Chemistry</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Original Article</topic><topic>Partial differential equations</topic><topic>Securities prices</topic><topic>Stability analysis</topic><topic>Systems Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Akram, Tayyaba</creatorcontrib><creatorcontrib>Abbas, Muhammad</creatorcontrib><creatorcontrib>Abualnaja, Khadijah M.</creatorcontrib><creatorcontrib>Iqbal, Azhar</creatorcontrib><creatorcontrib>Majeed, Abdul</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Engineering with computers</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Akram, Tayyaba</au><au>Abbas, Muhammad</au><au>Abualnaja, Khadijah M.</au><au>Iqbal, Azhar</au><au>Majeed, Abdul</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An efficient numerical technique based on the extended cubic B-spline functions for solving time fractional Black–Scholes model</atitle><jtitle>Engineering with computers</jtitle><stitle>Engineering with Computers</stitle><date>2022-06-01</date><risdate>2022</risdate><volume>38</volume><issue>Suppl 2</issue><spage>1705</spage><epage>1716</epage><pages>1705-1716</pages><issn>0177-0667</issn><eissn>1435-5663</eissn><abstract>Financial theory could introduce a fractional differential equation (FDE) that presents new theoretical research concepts, methods and practical implementations. Due to the memory factor of fractional derivatives, physical pathways with storage and inherited properties can be best represented by FDEs. For that purpose, reliable and effective techniques are required for solving FDEs. Our objective is to generalize the collocation method for solving time fractional Black–Scholes European option pricing model using the extended cubic B-spline. The key feature of the strategy is that it turns these type of problems into a system of algebraic equations which can be appropriate for computer programming. This is not only streamlines the problems but speed up the computations as well. The Fourier stability and convergence analysis of the scheme are examined. A proposed numerical scheme having second-order accuracy via spatial direction is also constructed. 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| subjects | Approximation B spline functions CAE) and Design Calculus of Variations and Optimal Control Optimization Classical Mechanics Collocation methods Computer programming Computer Science Computer-Aided Engineering (CAD Computers Control Differential equations Exact solutions Fractional calculus Math. Applications in Chemistry Mathematical and Computational Engineering Mathematical models Mathematics Original Article Partial differential equations Securities prices Stability analysis Systems Theory |
| title | An efficient numerical technique based on the extended cubic B-spline functions for solving time fractional Black–Scholes model |
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