Analysis of a finite volume element method for a degenerate parabolic equation in the zero-coupon bond pricing

Abstract

We construct and analyze a stable exponentially fitted numerical scheme for a degenerate parabolic equation in the zero-coupon bond pricing. Introducing weighted Sobolev spaces, we present the Garding coercivity and the weak maximum principle for the differential solution. The differential problem is discretized by a fitted finite volume element method resolving the degeneration. We derive coercivity of the discrete bilinear form as we also show that the fully discrete system matrix is essentially of positive type which implies the maximum principle for the implicit time stepping. Numerical experiments validate the theoretical results.