Error and stability estimates of a time-fractional option pricing model under fully spatial-temporal graded meshes

作者：Soleymani, Fazlollah^*; Zhu, Shengfeng

来源：Journal of Computational and Applied Mathematics, 2023, 425: 115075.

DOI：10.1016/j.cam.2023.115075

• Caputo fractional derivative
• Graded mesh
• Radial basis function
• Memory
• Option pricing
• Convergence analysis

To price vanilla European and American options via the fractional Black-Scholes model, first a (2-alpha)-order discretization scheme for the Caputo fractional derivative based upon graded meshes along time is presented. This is fruitful for problems having nonsmooth data at the initial time. Second, a nonuniform discretization of space is also considered and the coefficient weights based upon meshless radial basis function generated finite difference (RBF-FD) methodology are contributed under the inverse quadratic function. The fully space-time nonuniform solution method is then constructed via the presented discretization formulas. Numerical tests are given to show effectiveness and accuracy of our numerical scheme.