Using Time-Space Double Radial Basis Function Method to Solve High-Dimensional PDEs Arising from Multiasset Option Pricing

Zhiqiang Zhou, Hongying Wu, Caijuan Kang, You Wu and Chun Wei

Discrete Dynamics in Nature and Society, 2024, vol. 2024, 1-20

Abstract: 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.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:5226282

DOI: 10.1155/2024/5226282

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