A Collocation Method Using Diagonal Polynomials for Pricing Geometric Asian Options Under the Mixed Fractional Heston Model

In this paper, we introduce an efficient computational framework for pricing geometric Asian options based on a collocation method. The approach employs a collocation scheme utilizing a specific class of diagonal polynomials to construct operational matrices. The sparse structure of these matrices, containing a significant number of zeros, enhances computational efficiency. We solve the governing partial differential equation (PDE) by representing the solution as a series of multivariate diagonal functions with unknown coefficients. Subsequently, we derive the operational matrices for the differential operators and their associated partial derivatives, demonstrating how this formalism transforms the original pricing problem into a tractable system of nonlinear algebraic equations. Furthermore, we provide a rigorous convergence analysis of the proposed collocation method. Finally, we present numerical examples that demonstrate the method’s applicability, robustness, and computational effectiveness. The obtained results, supported by a strong theoretical foundation, indicate the considerable potential of this approach for practical financial applications.