<p>In this article, we introduce an efficient numerical method designed for solving the partial differential equation associated with pricing two-dimensional Asian options. Our approach begins with applying the Crank-Nicolson scheme, which effectively discretizes the time derivative, while the central difference scheme is employed for discretizing the spatial derivative on uniform grids. This combination leads to solutions that are accurate to second-order. To enhance the accuracy further, we implement Richardson extrapolation, which allows us to achieve fourth-order accuracy in the spatial variable. We thoroughly investigate this numerical method’s stability and convergence properties, ensuring its reliability for practical applications. Additionally, we conduct numerical computations that validate our theoretical findings regarding convergence rates, confirming that our method performs effectively and meets the expected theoretical standards.</p>