A Cubic B-Spline Collocation Method for Barrier Options under the CEV Model
In this paper, we construct a new numerical algorithm for the partial differential equation of up-and-out put barrier options under the CEV model. In this method, we use the Crank-Nicolson scheme to discrete temporal variables and the cubic B-spline collocation method to discrete spatial variables....
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/18/3979 |
| _version_ | 1797578946864218112 |
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| author | Xiwei Yu Qing Hu Yudong Sun |
| author_facet | Xiwei Yu Qing Hu Yudong Sun |
| author_sort | Xiwei Yu |
| collection | DOAJ |
| description | In this paper, we construct a new numerical algorithm for the partial differential equation of up-and-out put barrier options under the CEV model. In this method, we use the Crank-Nicolson scheme to discrete temporal variables and the cubic B-spline collocation method to discrete spatial variables. The method is stable and has second-order convergence for both time and space variables. The convergence analysis of the proposed method is discussed in detail. Finally, numerical examples verify the stability and accuracy of the method. |
| first_indexed | 2024-03-10T22:29:50Z |
| format | Article |
| id | doaj.art-487e06a843d044778f0c3b19698b4f9a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T22:29:50Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-487e06a843d044778f0c3b19698b4f9a2023-11-19T11:50:13ZengMDPI AGMathematics2227-73902023-09-011118397910.3390/math11183979A Cubic B-Spline Collocation Method for Barrier Options under the CEV ModelXiwei Yu0Qing Hu1Yudong Sun2College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, ChinaCollege of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, ChinaDepartment of Finance, Guizhou Minzu University, Guiyang 550025, ChinaIn this paper, we construct a new numerical algorithm for the partial differential equation of up-and-out put barrier options under the CEV model. In this method, we use the Crank-Nicolson scheme to discrete temporal variables and the cubic B-spline collocation method to discrete spatial variables. The method is stable and has second-order convergence for both time and space variables. The convergence analysis of the proposed method is discussed in detail. Finally, numerical examples verify the stability and accuracy of the method.https://www.mdpi.com/2227-7390/11/18/3979CEV modelbarrier optionscubic B-splineCrank-Nicolson method |
| spellingShingle | Xiwei Yu Qing Hu Yudong Sun A Cubic B-Spline Collocation Method for Barrier Options under the CEV Model Mathematics CEV model barrier options cubic B-spline Crank-Nicolson method |
| title | A Cubic B-Spline Collocation Method for Barrier Options under the CEV Model |
| title_full | A Cubic B-Spline Collocation Method for Barrier Options under the CEV Model |
| title_fullStr | A Cubic B-Spline Collocation Method for Barrier Options under the CEV Model |
| title_full_unstemmed | A Cubic B-Spline Collocation Method for Barrier Options under the CEV Model |
| title_short | A Cubic B-Spline Collocation Method for Barrier Options under the CEV Model |
| title_sort | cubic b spline collocation method for barrier options under the cev model |
| topic | CEV model barrier options cubic B-spline Crank-Nicolson method |
| url | https://www.mdpi.com/2227-7390/11/18/3979 |
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