A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models
A positivity-preserving numerical method for nonlinear Black-Scholes models is developed in this paper. The numerical method is based on a nonstandard approximation of the second partial derivative. The scheme is not only unconditionally stable and positive, but also allows us to solve the discrete...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/205686 |
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| _version_ | 1832562593692123136 |
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| author | Shengwu Zhou Wei Li Yu Wei Cui Wen |
| author_facet | Shengwu Zhou Wei Li Yu Wei Cui Wen |
| author_sort | Shengwu Zhou |
| collection | DOAJ |
| description | A positivity-preserving numerical method for nonlinear Black-Scholes models is developed in this paper. The numerical method is based on a nonstandard approximation of the second partial derivative. The scheme is not only unconditionally stable and positive, but also allows us to solve the discrete equation explicitly. Monotone properties are studied in order to avoid unwanted oscillations of the numerical solution. The numerical results for European put option and European butterfly spread are compared to the standard finite difference scheme. It turns out that the proposed scheme is efficient and reliable. |
| format | Article |
| id | doaj-art-393c4b737ba046adab6ca96d6ae2c76a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-393c4b737ba046adab6ca96d6ae2c76a2025-02-03T01:22:13ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/205686205686A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing ModelsShengwu Zhou0Wei Li1Yu Wei2Cui Wen3College of Sciences, China University of Mining and Technology, Jiangsu, Xuzhou 221116, ChinaCollege of Sciences, China University of Mining and Technology, Jiangsu, Xuzhou 221116, ChinaCollege of Sciences, China University of Mining and Technology, Jiangsu, Xuzhou 221116, ChinaCollege of Sciences, China University of Mining and Technology, Jiangsu, Xuzhou 221116, ChinaA positivity-preserving numerical method for nonlinear Black-Scholes models is developed in this paper. The numerical method is based on a nonstandard approximation of the second partial derivative. The scheme is not only unconditionally stable and positive, but also allows us to solve the discrete equation explicitly. Monotone properties are studied in order to avoid unwanted oscillations of the numerical solution. The numerical results for European put option and European butterfly spread are compared to the standard finite difference scheme. It turns out that the proposed scheme is efficient and reliable.http://dx.doi.org/10.1155/2012/205686 |
| spellingShingle | Shengwu Zhou Wei Li Yu Wei Cui Wen A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models Journal of Applied Mathematics |
| title | A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models |
| title_full | A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models |
| title_fullStr | A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models |
| title_full_unstemmed | A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models |
| title_short | A Positivity-Preserving Numerical Scheme for Nonlinear Option Pricing Models |
| title_sort | positivity preserving numerical scheme for nonlinear option pricing models |
| url | http://dx.doi.org/10.1155/2012/205686 |
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