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 inter-temporal modelling. We characterize the consistent Ito 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 in particular di#usion processes. We show that there is a strong limitation on their choice. Bounded exponential-polynomial families should rather not be used for modelling the term structure of interest rates. Keywords: consistent Ito process, di#usion process, exponential-polynomial family, forward rate curve, interest rate model, inverse problem 1. Introduction The current term structure of interest rates contains all the necessary information for pricing bonds, swaps and forward rate agreements of all maturities. It is used furthermore by the central banks...

Citations

597	Continuous Martingales and Brownian Motion. A - Revuz, Yor - 1999
400	Bond pricing and the term structure of interest rates: A new methodolgy for contingent claim valuation.” Econometrica 60 - Heath, Jarrow, et al. - 1992
329	Parsimonious Modeling of Yield Curves - Nelson, Siegel - 1987
79	Estimating and interpreting forward interest rates - Svensson - 1994
62	Martingale Methods in Financial Modelling - Musiela, Rutkowski - 2005
39	Interest rate dynamics and consistent forward rate curves - Björk, Christensen - 1999
26	Limit theorems for stochastic processes. Grundlehren der mathematischen Wissenschaften - Jacod, Schiryaev - 1987
3	Zero-Coupon Yield Curves - BIS - 1999
1	A general characterization of a#ne term structure models, Working paper - Filipovic - 1999