In this paper, 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 Filipović’s maximal degree theorem for exponential polynomial models, as well as an explicit characterization 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.

中文翻译：

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多项式期限结构模型

在本文中，我们探索了一类易于处理的利率模型，这些模型具有零息债券的价格可以表示为状态扩散过程的多项式的性质。我们的结果包括本着 Filipović 的指数多项式模型最大程度定理的精神对所有此类时间齐次单因子模型进行分类，以及在因子过程有界的情况下对一组可行参数的明确表征。还考虑了对时间非齐次和多因子多项式模型的扩展。