A Computational Scheme for a Problem in the Zero-coupon Bond Pricing

In this paper we derive a finite volume difference scheme for a degenerate parabolic equation with dynamical boundary conditions of zero-coupon bond pricing. We show that the system matrix of the discretization scheme is an M-matrix, so that the discretization is monotone. This provides the non-negativity of the price whit respect to time if the initial distribution is nonnegative. Then one can prove convergence of the numerical solution with rate of convergence O(h), where h denotes the mesh parameter [2]. Several numerical experiments show higher accuracy with comparison of known difference schemes near the boundary (degeneration).