Finite Volume Difference Scheme for a Degenerate Parabolic Equation in the Zero-Coupon Bond Pricing

TL;DR

This paper develops a finite volume difference scheme to numerically solve a degenerate parabolic equation in zero-coupon bond pricing, ensuring monotonicity and non-negativity of solutions.

Contribution

It introduces a finite-volume discretization for degenerate parabolic equations in bond pricing, proving the system matrix is an M-matrix for stability.

Findings

The scheme is efficient near degeneracy points.

Discretization preserves non-negativity of bond prices.

Numerical results confirm the scheme's effectiveness.

Abstract

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.