<p>In this work, we present a novel numerical scheme for addressing a degenerate parabolic equation pertinent to zero–coupon bond (ZCB) pricing. Zero–coupon bonds (ZCBs) are fundamental instruments in fixed–income markets and serve as underlying assets for various derivative contracts, including interest rate caps, swap options, and bond options. For the numerical solution, the time component is discretized using the backward Euler scheme, and the spatial derivatives are approximated using the weak Galerkin method. This study aims to establish stability and optimal-order error estimates, and we obtain these error estimates through rigorous theoretical analysis, proving the stability and convergence characteristics of the proposed weak Galerkin scheme. The theoretical results of this work are supported by numerical simulations. Furthermore, the model is calibrated using historical U.S. and European interest rate data, and the resulting numerical scheme is shown to accurately capture the fundamental inverse relationship between interest rates and bond prices.</p>