An Unconditionally Stable, Positivity-Preserving Splitting Scheme for Nonlinear Black-Scholes Equation with Transaction Costs
This paper deals with the numerical analysis of nonlinear Black-Scholes equation with transaction costs. An unconditionally stable and monotone splitting method, ensuring positive numerical solution and avoiding unstable oscillations, is proposed. This numerical method is based on the LOD-Backward E...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/525207 |
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| _version_ | 1832563109598855168 |
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| author | Jianqiang Guo Wansheng Wang |
| author_facet | Jianqiang Guo Wansheng Wang |
| author_sort | Jianqiang Guo |
| collection | DOAJ |
| description | This paper deals with the numerical analysis of nonlinear Black-Scholes equation with transaction costs. An unconditionally stable and monotone splitting method, ensuring positive numerical solution and avoiding unstable oscillations, is proposed. This numerical method is based on the LOD-Backward Euler method which allows us to solve the discrete equation explicitly. The numerical results for vanilla call option and for European butterfly spread are provided. It turns out that the proposed scheme is efficient and reliable. |
| format | Article |
| id | doaj-art-a85aa3049f494fbb8507efa7c74c5e51 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-a85aa3049f494fbb8507efa7c74c5e512025-02-03T01:20:57ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/525207525207An Unconditionally Stable, Positivity-Preserving Splitting Scheme for Nonlinear Black-Scholes Equation with Transaction CostsJianqiang Guo0Wansheng Wang1Law School, Hunan University, Hunan 410082, ChinaSchool of Mathematics and Computational Science, Changsha University of Science and Technology, Hunan 410114, ChinaThis paper deals with the numerical analysis of nonlinear Black-Scholes equation with transaction costs. An unconditionally stable and monotone splitting method, ensuring positive numerical solution and avoiding unstable oscillations, is proposed. This numerical method is based on the LOD-Backward Euler method which allows us to solve the discrete equation explicitly. The numerical results for vanilla call option and for European butterfly spread are provided. It turns out that the proposed scheme is efficient and reliable.http://dx.doi.org/10.1155/2014/525207 |
| spellingShingle | Jianqiang Guo Wansheng Wang An Unconditionally Stable, Positivity-Preserving Splitting Scheme for Nonlinear Black-Scholes Equation with Transaction Costs The Scientific World Journal |
| title | An Unconditionally Stable, Positivity-Preserving Splitting Scheme for Nonlinear Black-Scholes Equation with Transaction Costs |
| title_full | An Unconditionally Stable, Positivity-Preserving Splitting Scheme for Nonlinear Black-Scholes Equation with Transaction Costs |
| title_fullStr | An Unconditionally Stable, Positivity-Preserving Splitting Scheme for Nonlinear Black-Scholes Equation with Transaction Costs |
| title_full_unstemmed | An Unconditionally Stable, Positivity-Preserving Splitting Scheme for Nonlinear Black-Scholes Equation with Transaction Costs |
| title_short | An Unconditionally Stable, Positivity-Preserving Splitting Scheme for Nonlinear Black-Scholes Equation with Transaction Costs |
| title_sort | unconditionally stable positivity preserving splitting scheme for nonlinear black scholes equation with transaction costs |
| url | http://dx.doi.org/10.1155/2014/525207 |
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