  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 S. Wang [16] to
discretize the differential problem. We show that the system matrix of the
discretization scheme is a 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 nonnegative. Numerical experiments demonstrate the
efficiency of our difference scheme near the ends of the interval where the
degeneration occurs.
