In this article, we explore a class of tractable interest rate models that have the property that the prices of zero-coupon bonds can be expressed as polynomials of a state diffusion process. These models are, in a sense, generalisations of exponential polynomial models. Our main result is a classification of such models in the spirit of Filipovic's maximal degree theorem for exponential polynomial models  .
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 .
R
prices of
price of a
R
bonds
bond
R
polynomials
a polynomial
R
These models are, in a sense, generalisations of exponential polynomial models. Our main result is
Our results include
R
such
all such time-homogeneous single-factor
A
, 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