Tractable forms for the Bond Pricing Equation

Abstract

So far, a small number of analytically tractable single-factor models have been devised for the well-known Bond Pricing Equation (BPE). In this paper, new tractable models are formulated in a systematic manner. First, the BPE is transformed to a standard canonical form in which only one coefficient function appears. In some interesting cases, this single coefficient function is identically zero, leaving nothing more to solve than the classical heat equation. In many cases, the canonical form allows a general solution by standard mathematical techniques such as separation of variables and Laplace transforms. In other cases, the general solution of the BPE is reduced to a single inverse Laplace Transform.