Abstract
What properties must a term structure model possess in order to have closed-form bond price solutions? Are there undiscovered models which offer simple bond price formula? Why do models that have closed-form bond price solutions also tend to have closed-form bond-option solutions? This paper attempts to answer these questions from an expectation approach. It is well known that the price of a derivative security can be expressed either as a solution to an expectation, or as a solution to a second order partial dierential equation. Except for normally distributed random processes, the expectation approach has been difficult to implement. In this paper we demonstrate that when the expectation is expressed as a path integral, and the law of iterated expectations is used, implementation becomes straightforward. This technique takes advantage of the fact that, in the continuous time limit, all innovations are normally distributed (excluding jump processes). Hence, for those models possessing simple closed-form solutions, implementation is quite easy, since only normally distributed processes need to be dealt with. Using this technique, the class of models which have closed form bond and bond-option solutions is identied. The approach also explains why closed-form solutions typically exist for both bond and bond-options, or neither. In addition, the approach allows one to evaluate bond-option prices when the model is infinite factor, where no PDE representation even exists.

Download the paper (Acrobat .pdf file) . Download Acrobat Reader.
Download the paper (Postscript .ps file) .