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...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2024/5226282 |
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| Summary: | 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. |
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| ISSN: | 1607-887X |