Exponential-polynomial families and the term structure of interest rates

Exponential-polynomial families like the Nelson-Siegel or Svenson family ar e widely used to estimate the current forward rate curve. We investigate wh ether these methods go well with intertemporal modelling. We characterize t he consistent It (o) over cap, 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 mode lling the term structure of interest rates.