Articlegreen2000

Exponential-Polynomial Families and the Term Structure of Interest Rates

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Stochastic processes and financial applications Financial Markets and Investment Strategies Economic theories and models

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...

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References

1999Continuous Martingales and Brownian Motion 1992Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation 1987Parsimonious Modeling of Yield Curves 1991Continuous Martingales and Brownian Motion 1987Limit Theorems for Stochastic Processes 1997Martingale Methods in Financial Modelling 1994Estimating and Interpreting Foreward Interest Rates: Sweden 1992-1994 1999Interest Rate Dynamics and Consistent Forward Rate Curves

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2013Yield Curve Modeling and Forecasting 2001Are Interest Rate Derivatives Spanned by the Term Structure of Interest Rates?2002Design and Estimation of Quadratic Term Structure Models 2004On the Geometry of Interest Rate Models 2013A Theoretical Foundation for the Nelson-Siegel Class of Yield Curve Models 2000Invariant manifolds for weak solutions to stochastic equations

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