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.
展开▼
机译：在本文中，我们用动力学边界条件对退化的抛物方程进行数值求解，以对零息债券定价，并将数值解与渐近解析解进行了比较。首先，我们讨论该模型的近似解析解及其准确性顺序。然后，从方程的发散形式开始，我们采用Song Wang（IMA J Numer Anal 24：699–720，2004）的有限体积方法来离散化微分问题。我们表明离散化方案的系统矩阵是一个M矩阵，因此离散化是单调的。如果初始分布为非负数，则这将提供价格相对于时间的非负数。数值实验证明了当节点不太接近退化点时差分方案的二阶收敛性。
展开▼
