Polynomial term structure models

TL;DR

This paper classifies and characterizes polynomial term structure models for interest rates, providing explicit parameter sets and extending to multi-factor and time-inhomogeneous cases, enhancing tractability in bond pricing.

Contribution

It offers a comprehensive classification of single-factor polynomial models and characterizes feasible parameters, extending the framework to more complex models.

Findings

Complete classification of time-homogeneous single-factor models

Explicit parameter characterization for bounded factor processes

Extensions to multi-factor and time-inhomogeneous models

Abstract

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.