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

Author

Listed:
  • Zhiqiang Zhou
  • Hongying Wu
  • Caijuan Kang
  • You Wu
  • Chun Wei

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.

Suggested Citation

  • Zhiqiang Zhou & Hongying Wu & Caijuan Kang & You Wu & Chun Wei, 2024. "Using Time-Space Double Radial Basis Function Method to Solve High-Dimensional PDEs Arising from Multiasset Option Pricing," Discrete Dynamics in Nature and Society, Hindawi, vol. 2024, pages 1-20, September.
    • Handle: RePEc:hin:jnddns:5226282
    DOI: 10.1155/2024/5226282
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