Finite volume difference scheme for a degenerate parabolic equation in the zero-coupon bond pricing

In this paper we solve numerically a degenerate parabolic equation with dynamical boundary conditions of zero-coupon bond pricing. First, we discuss some properties of the differential equation. Then, starting from the divergent form of the equation we implement the finite volume method of Wang (2004) [6] to discretize the differential problem. 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 with respect to time if the initial distribution is non-negative. Numerical experiments demonstrate the efficiency of our difference scheme near the ends of the interval where the degeneration occurs.