  In this article, we explore a class of tractable interest rate models that
have the property that the price of a zero-coupon bond can be expressed as a
polynomial of a state diffusion process. Our results include a classification
of all such time-homogeneous single-factor models in the spirit of Filipovic's
maximal degree theorem for exponential polynomial models, as well as an
explicit characterisation of the set of feasible parameters in the case when
the factor process is bounded. Extensions to time-inhomogeneous and
multi-factor polynomial models are also considered.
