Adaptive Wavelet Precise Integration Method for Nonlinear Black-Scholes Model Based on Variational Iteration Method
An adaptive wavelet precise integration method (WPIM) based on the variational iteration method (VIM) for Black-Scholes model is proposed. Black-Scholes model is a very useful tool on pricing options. First, an adaptive wavelet interpolation operator is constructed which can transform the nonlinear...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/735919 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850209352832516096 |
|---|---|
| author | Huahong Yan |
| author_facet | Huahong Yan |
| author_sort | Huahong Yan |
| collection | DOAJ |
| description | An adaptive wavelet precise integration method (WPIM) based on the variational iteration method (VIM) for Black-Scholes model is proposed. Black-Scholes model is a very useful tool on pricing options. First, an adaptive wavelet interpolation operator is constructed which can transform the nonlinear partial differential equations into a matrix ordinary differential equations. Next, VIM is developed to solve the nonlinear matrix differential equation, which is a new asymptotic analytical method for the nonlinear differential equations. Third, an adaptive precise integration method (PIM) for the system of ordinary differential equations is constructed, with which the almost exact numerical solution can be obtained. At last, the famous Black-Scholes model is taken as an example to test this new method. The numerical result shows the method's higher numerical stability and precision. |
| format | Article |
| id | doaj-art-91ef2965e2964954a26a52fd56342862 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-91ef2965e2964954a26a52fd563428622025-08-20T02:10:02ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/735919735919Adaptive Wavelet Precise Integration Method for Nonlinear Black-Scholes Model Based on Variational Iteration MethodHuahong Yan0School of Accounting, Capital University of Economics and Business, 121 Zhangjialukou, Huaxiang Fengtai District, Beijing 100070, ChinaAn adaptive wavelet precise integration method (WPIM) based on the variational iteration method (VIM) for Black-Scholes model is proposed. Black-Scholes model is a very useful tool on pricing options. First, an adaptive wavelet interpolation operator is constructed which can transform the nonlinear partial differential equations into a matrix ordinary differential equations. Next, VIM is developed to solve the nonlinear matrix differential equation, which is a new asymptotic analytical method for the nonlinear differential equations. Third, an adaptive precise integration method (PIM) for the system of ordinary differential equations is constructed, with which the almost exact numerical solution can be obtained. At last, the famous Black-Scholes model is taken as an example to test this new method. The numerical result shows the method's higher numerical stability and precision.http://dx.doi.org/10.1155/2013/735919 |
| spellingShingle | Huahong Yan Adaptive Wavelet Precise Integration Method for Nonlinear Black-Scholes Model Based on Variational Iteration Method Abstract and Applied Analysis |
| title | Adaptive Wavelet Precise Integration Method for Nonlinear Black-Scholes Model Based on Variational Iteration Method |
| title_full | Adaptive Wavelet Precise Integration Method for Nonlinear Black-Scholes Model Based on Variational Iteration Method |
| title_fullStr | Adaptive Wavelet Precise Integration Method for Nonlinear Black-Scholes Model Based on Variational Iteration Method |
| title_full_unstemmed | Adaptive Wavelet Precise Integration Method for Nonlinear Black-Scholes Model Based on Variational Iteration Method |
| title_short | Adaptive Wavelet Precise Integration Method for Nonlinear Black-Scholes Model Based on Variational Iteration Method |
| title_sort | adaptive wavelet precise integration method for nonlinear black scholes model based on variational iteration method |
| url | http://dx.doi.org/10.1155/2013/735919 |
| work_keys_str_mv | AT huahongyan adaptivewaveletpreciseintegrationmethodfornonlinearblackscholesmodelbasedonvariationaliterationmethod |