Using Time-Space Double Radial Basis Function Method to Solve High-Dimensional PDEs Arising from Multiasset Option Pricing
This paper develops a time-space double radial basis function (TSDRBF) method to solve PDEs arising from multiasset option pricing. By TSDRBF discretization for the high-dimensional PDEs, a linear system (LS) is obtained. After solving the LS, multi-asset options of European and American style are r...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2024/5226282 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832568879035973632 |
|---|---|
| author | Zhiqiang Zhou Hongying Wu Caijuan Kang You Wu |
| author_facet | Zhiqiang Zhou Hongying Wu Caijuan Kang You Wu |
| author_sort | Zhiqiang Zhou |
| collection | DOAJ |
| description | This paper develops a time-space double radial basis function (TSDRBF) method to solve PDEs arising from multiasset option pricing. By TSDRBF discretization for the high-dimensional PDEs, a linear system (LS) is obtained. After solving the LS, multi-asset options of European and American style are restored, with number N of space discretization, number M¯ of time nodes, and number M of time RBF discretization. Numerical examples confirm that the TSDRBF method has exponentially convergent rates for the number N and number M, while the convergence is linear for the number M¯. Compared with finite difference, TSDRBF avoids the difficulty of space discretization, and the convergence is greatly improved. |
| format | Article |
| id | doaj-art-e3387df70de84e2ab3326ec657e7c0a1 |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e3387df70de84e2ab3326ec657e7c0a12025-02-03T00:08:39ZengWileyDiscrete Dynamics in Nature and Society1607-887X2024-01-01202410.1155/2024/5226282Using Time-Space Double Radial Basis Function Method to Solve High-Dimensional PDEs Arising from Multiasset Option PricingZhiqiang Zhou0Hongying Wu1Caijuan Kang2You Wu3School of Economics and ManagementSchool of Mathematics and Information ScienceSchool of Economics and ManagementSchool of Economics and ManagementThis paper develops a time-space double radial basis function (TSDRBF) method to solve PDEs arising from multiasset option pricing. By TSDRBF discretization for the high-dimensional PDEs, a linear system (LS) is obtained. After solving the LS, multi-asset options of European and American style are restored, with number N of space discretization, number M¯ of time nodes, and number M of time RBF discretization. Numerical examples confirm that the TSDRBF method has exponentially convergent rates for the number N and number M, while the convergence is linear for the number M¯. Compared with finite difference, TSDRBF avoids the difficulty of space discretization, and the convergence is greatly improved.http://dx.doi.org/10.1155/2024/5226282 |
| spellingShingle | Zhiqiang Zhou Hongying Wu Caijuan Kang You Wu Using Time-Space Double Radial Basis Function Method to Solve High-Dimensional PDEs Arising from Multiasset Option Pricing Discrete Dynamics in Nature and Society |
| title | Using Time-Space Double Radial Basis Function Method to Solve High-Dimensional PDEs Arising from Multiasset Option Pricing |
| title_full | Using Time-Space Double Radial Basis Function Method to Solve High-Dimensional PDEs Arising from Multiasset Option Pricing |
| title_fullStr | Using Time-Space Double Radial Basis Function Method to Solve High-Dimensional PDEs Arising from Multiasset Option Pricing |
| title_full_unstemmed | Using Time-Space Double Radial Basis Function Method to Solve High-Dimensional PDEs Arising from Multiasset Option Pricing |
| title_short | Using Time-Space Double Radial Basis Function Method to Solve High-Dimensional PDEs Arising from Multiasset Option Pricing |
| title_sort | using time space double radial basis function method to solve high dimensional pdes arising from multiasset option pricing |
| url | http://dx.doi.org/10.1155/2024/5226282 |
| work_keys_str_mv | AT zhiqiangzhou usingtimespacedoubleradialbasisfunctionmethodtosolvehighdimensionalpdesarisingfrommultiassetoptionpricing AT hongyingwu usingtimespacedoubleradialbasisfunctionmethodtosolvehighdimensionalpdesarisingfrommultiassetoptionpricing AT caijuankang usingtimespacedoubleradialbasisfunctionmethodtosolvehighdimensionalpdesarisingfrommultiassetoptionpricing AT youwu usingtimespacedoubleradialbasisfunctionmethodtosolvehighdimensionalpdesarisingfrommultiassetoptionpricing |