A comparison of asymptotic analytical formulae with finite-difference approximations for pricing zero coupon bond

In this paper we solve numerically a degenerate parabolic equation with dynamical boundary condition for pricing zero coupon bond and compare numerical solution with asymptotic analytical solution. First, we discuss an approximate analytical solution of the model and its order of accuracy. Then, starting from the divergent form of the equation we implement the finite-volume method of Song Wang (IMA J Numer Anal 24:699–720, 2004) 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 second order of convergence for difference scheme when the node is not too close to the point of degeneration.