Efficient numerical method for pricing multi-asset options with the time-fractional Black-Scholes model: focus on American and digital options

This study presents a numerical solution for the two-asset time-fractional Black-Scholes model, which governs American and digital options, using a local meshless collocation method based on Gaussian radial basis functions. The proposed meshless approach effectively discretized the spatial derivatives of the model, while the Caputo derivative was employed to represent the time-fractional component, capturing the memory effects and non-local properties characteristic of fractional-order models. Numerical assessments were conducted to evaluate the method's performance across these option models. The study discusses the handling of interest rates, highlighting the method's capability to manage the complexities inherent in multi-asset options. The efficacy and accuracy of the proposed meshless approach were evaluated using the $L_{\mathrm{\infty }}$ error norms. In the absence of exact solutions for these option models, the double mesh technique was utilized to validate the accuracy and efficiency of the proposed method, ensuring the robustness and reliability of the numerical results.