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A Semi-Parametric Factor Model of Interest Rates and Tests of the Affine Term Structure

  • Eric Ghysels
  • Serena Ng

Many continuous time term structure of interest rate models assume a factor structure where the drift and volatility functions are affine functions of the state variable process. These models involve very specific parametric choices of factors and functional specifications of the drift and volatility. Morevoer, under the affine term structure restrictions not all factors necessarily affect interest rates at all maturities simultaneously. This class of so called affine models covers a wide variety of existing empirical as well as theoretical models in the literature. In this paper we take a very agnostic approach to the specification of these diffusion functions and test implications of the affine term structure restrictions. We do not test a specific model among the class of affine models per se. Instead, the affine term structure restrictions we test are based on the derivatives of the responses of interest rates to the factors. We also test how many and which factors affect a particular rate. These tests are conducted within a framework which models interest rates as functions of fundamental factors, and the responses of interest rates to these factors are estimated with non-parametric methods. We consider two sets of factors, one based on key macroeconomic variables, and one based on interest rate spreads. In general, despite their common use we find that the empirical evidence does not support the restrictions imposed by affine models. Besides testing the affine structure restrictions we also uncover a set of fundamental factors which appear remarkably robust in explaining interest rate dynamics at the long and short maturities we consider. Nous étudions les modèles de strucutreà terme des taux d'intérêt. Nous nous penchons plus particulièrement sur une classe de modèles avec structure affinée. Cette classe contient une grande partie des modèles théoriques et pratiques recensés dans la littérature. Nous proposons des tests pour les restrictions imposées par la structure affinée. En utilisant des méthodes semi-paramétriques, nous arrivonsà dériver ces tests sous hypothèses très faibles sur la forme fonctionnelle du processus des facteurs et la forme des relations affinées. Nous introduisons l'estimateur de la dérivée moyenne qui est adaptéà un contexte de séries temporelles. Les résultats empiriques indiquent que les restrictions de la structure affinée sont fortement rejetées par les données.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 97s-33.

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Length: 40 pages
Date of creation: 01 Oct 1997
Date of revision:
Handle: RePEc:cir:cirwor:97s-33
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  1. Yacine Ait-Sahalia, 1995. "Nonparametric Pricing of Interest Rate Derivative Securities," NBER Working Papers 5345, National Bureau of Economic Research, Inc.
  2. Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation for Research in Economics, Yale University.
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  8. Courtadon, Georges, 1982. "The Pricing of Options on Default-Free Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(01), pages 75-100, March.
  9. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
  10. Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc.
  11. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  12. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
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  14. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
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  16. Stanton, Richard, 1997. " A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
  17. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
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