Numerical Investigation for the Temporal Fractional Financial Option Pricing Partial Differential Equation Utilizing a Multiquadric Function - Jia Li; Tao Liu; Jiaqi Xu; Xiaoxi Hu; Changan Xu; Yanlong Wei (Fractal and Fractional)
This paper proposes a computational procedure to resolve the temporal fractional financial option pricing partial differential equation (PDE) using a localized meshless approach via the multiquadric radial basis function (RBF). Given that financial market information is best characterized within a martingale framework, the resulting option pricing model follows a modified Black–Sholes (BS) equation, requiring efficient numerical techniques for practical implementation. The key innovation in this study is the derivation of analytical weights for approximating first and second derivatives, ensuring improved numerical stability and accuracy. The construction of these weights is grounded in the second integration of a variant of the multiquadric RBF, which enhances smoothness and convergence properties. The performance of the presented solver is analyzed through computational tests, where the analytical weights exhibit superior accuracy and stability in comparison to conventional numerical weights. The results confirm that the new approach reduces absolute errors, demonstrating its effectiveness for financial option pricing problems.