Exponential-polynomial families and the term structure of interest rates

Abstract

Exponential-polynomial families like the Nelson-Siegel or Svensson family are widely used to estimate the current forward rate curve. We investigate whether these methods go well with intertemporal modelling. We characterize the consistent Itô processes which have the property to provide an arbitrage-free interest rate model when representing the parameters of some bounded exponential-polynomial type function. This includes diffusion processes in particular. We show that there is a strong limitation on their choice. Bounded exponential-polynomial families are best not used for modelling the term structure of interest rates.