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

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  • Eric Ghysels
  • Serena Ng

Abstract

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.

Suggested Citation

  • Eric Ghysels & Serena Ng, 1997. "A Semi-Parametric Factor Model of Interest Rates and Tests of the Affine Term Structure," CIRANO Working Papers 97s-33, CIRANO.
  • Handle: RePEc:cir:cirwor:97s-33
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    Cited by:

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    2. Guidolin, Massimo & Thornton, Daniel L., 2018. "Predictions of short-term rates and the expectations hypothesis," International Journal of Forecasting, Elsevier, vol. 34(4), pages 636-664.
    3. D H Kim, 2005. "Nonlinearity in the Term Structure," Centre for Growth and Business Cycle Research Discussion Paper Series 51, Economics, The University of Manchester.
    4. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
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    6. Teresa Corzo Santamaría & Javier Gómez Biscarri, 2005. "Nonparametric estimation of convergence of interest rates: Effects on bond pricing," Spanish Economic Review, Springer;Spanish Economic Association, vol. 7(3), pages 167-190, September.
    7. Bams, Dennis & Schotman, Peter C., 2003. "Direct estimation of the risk neutral factor dynamics of Gaussian term structure models," Journal of Econometrics, Elsevier, vol. 117(1), pages 179-206, November.
    8. Dong Heon Kim, 2004. "Nonlinearity in the Term Structure," Econometric Society 2004 Far Eastern Meetings 440, Econometric Society.
    9. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    10. Zongwu Cai & Jiazi Chen & Linlin Niu, 2021. "A Semiparametric Model for Bond Pricing with Life Cycle Fundamental," Working Papers 2021-01-06, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    11. D H Kim, 2004. "Nonlinearity in the Term Structure," Economics Discussion Paper Series 0401, Economics, The University of Manchester.
    12. Hoi Wong & Tsz Wong, 2007. "Reduced-form Models with Regime Switching: An Empirical Analysis for Corporate Bonds," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(3), pages 229-253, September.
    13. Zongwu Cai & Jiazi Chen & Linlin Liu, 2021. "Estimating Impact of Age Distribution on Bond Pricing: A Semiparametric Functional Data Analysis Approach," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202102, University of Kansas, Department of Economics, revised Jan 2021.
    14. Chen, Xirong & Li, Degui & Li, Qi & Li, Zheng, 2019. "Nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates," Journal of Econometrics, Elsevier, vol. 212(2), pages 433-450.

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    More about this item

    Keywords

    Term structure; zero-coupon bonds; average derivative estimator; factor models; Structureà terme des taux; obligationsà coupon zéro; estimateur de la dérivée moyenne; modèlesà facteurs;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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