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Estimating and Testing Exponential Affine Term Structure Models by Kalman Filter

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Jin-Chuan Duan
Jean-Guy Simonato

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Abstract

This paper proposes a unified state-space formulation for parameter estimation of exponential-affine term structure models. This class of models, charaterized by Duffie and Kan (1993), contains models such as Vasicek (1977), Cox, Ingersoll and Ross (1985) and Chen and Scott (1992), among others. The proposed method uses an approximate linear Kalman filter which only requires specifying the conditional mean and variance of the system in an approximate sense. The method allows for measurement errors in the observed yields to maturitiy, and can simultaneously deal with many yields on bonds with different maturities. A Monte Carlo study indicates thet the proposed method is a reliable procedure for moderate sample sizes. An empirical analysis of three existing exponential-affine term structure models is carried out using monthly U.S. Treasury yield data with four different maturities. Our test results indicate a strong rejection of all three models.

Cette recherche propose une approche unificatrice pour l'estimation des paramètres de modèles de structure de taux d'intérêt de la classe exponentielle-affine. Cette famille de modèles, caractérisée par Duffie et Kan (1993), contient entre autres les modèles de Vasicek (1977), Cox, Ingersoll et Ross (1985) et Chen et Scott (1992). La méthode proposée utilise un filtre de Kalman approximatif qui requiert la spécification de l'espérance et de la variance conditionnelle du système. La méthode utilise simultanément plusieurs séries de rendements et permet l'ajout d'erreurs de mesure pour chaque serie. Une étude de simulation indique que la méthode proposée est fiable pour des échantillons de taille modérée. Une étude empirique utilisant trois modèles différents de la classe exponentielle-affine est présentée.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 95s-44.

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Date of creation: 01 Oct 1995
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Handle: RePEc:cir:cirwor:95s-44

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Keywords: Term Structure; Kalman Filter; Exponential Affine; State Space Model; Quasi Maximum Likelihood; Lagrange Multiplier Test; Structure à Terme; Filtre de Kalman; Exponentielle-affine; Modèle State-Space; Quasi-maximum de vraisemblance; Test du Multiplicateur de Lagrange;

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  8. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 573-92. [Downloadable!] (restricted)
  9. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. de Jong, Frank, 1999. "Time-series and Cross-section Information in Affine Term Structure Models," CEPR Discussion Papers 2065, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  2. Fendel, Ralf, 2004. "Towards a Joint Characterization of Monetary Policy and the Dynamics of the Term Structure of Interest Rates," Discussion Paper Series 1: Economic Studies 2004,24, Deutsche Bundesbank, Research Centre. [Downloadable!]
  3. Rana Chatterjee, 2004. "Application Of The Kalman Filter For Estimating Continuous Time Term Structure Models: Evidence From The Uk And Germany," Computing in Economics and Finance 2004 346, Society for Computational Economics. [Downloadable!]
  4. Marco Lyrio & Hans Dewachter & Konstantijn Maes, 2006. "A joint model for the term structure of interest rates and the macroeconomy," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 439-462. [Downloadable!]
    Other versions:
  5. Sergio Pastorello & Valentin Patilea & Éric Renault, 2003. "Iterative and Recursive Estimation in Structural Non-Adaptive Models," CIRANO Working Papers 2003s-08, CIRANO. [Downloadable!]
  6. Esben Hoeg & Per Frederiksen, 2006. "The Fractional OU Process: Term Structure Theory and Application," Computing in Economics and Finance 2006 194, Society for Computational Economics. [Downloadable!]
  7. Power, Gabriel J. & Turvey, Calum G., 2008. "On Term Structure Models of Commodity Futures Prices and the Kaldor-Working Hypothesis," 2008 Conference, April 21-22, 2008, St. Louis, Missouri 37608, NCCC-134 Conference on Applied Commodity Price Analysis, Forecasting, and Market Risk Management. [Downloadable!]
  8. Massoud Heidari & Liuren Wu, 2002. "Term Structure of Interest Rates, Yield Curve Residuals, and the Consistent Pricing of Interest Rates and Interest Rate Derivatives," Finance 0207010, EconWPA, revised 05 Sep 2002. [Downloadable!]
  9. Somnath Chatterjee, 2005. "Application Of The Kalman Filter For Estimating Continuous Time Term Structure Models: The Case Of Uk And Germany," Working Papers 2005_2, Department of Economics, University of Glasgow. [Downloadable!]
  10. Simon Babbs & K. Nowman, 1998. "Econometric Analysis of a Continuous Time Multi-Factor Generalized Vasicek Term Structure Model: International Evidence," Asia-Pacific Financial Markets, Springer, vol. 5(2), pages 159-183, May. [Downloadable!] (restricted)
  11. Gonzalo Cortazar & Eduardo S. Schwartz & Lorenzo F. Naranjo, 2007. "Term-structure estimation in markets with infrequent trading," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 12(4), pages 353-369. [Downloadable!]
  12. Gonzalo Cortazar & Eduardo Schwartz & Lorezo Naranjo, 2003. "Term Structure Estimation in Low-Frequency Transaction Markets: A Kalman Filter Approach with Incomplete Panel-Data," University of California at Los Angeles, Anderson Graduate School of Management 1109, Anderson Graduate School of Management, UCLA. [Downloadable!]
  13. Anders B. Trolle & Eduardo S. Schwartz, 2006. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," NBER Working Papers 12744, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  14. Li Chen & Damir Filipovic, 2003. "A Simple Model for Credit Migration and Spread Curves," Finance 0305003, EconWPA. [Downloadable!]
  15. Gregory R. Duffee, 1996. "Estimating the price of default risk," Finance and Economics Discussion Series 96-29, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  16. Høg, Espen P. & Frederiksen, Per H., 2006. "The Fractional Ornstein-Uhlenbeck Process: Term Structure Theory and Application," Finance Research Group Working Papers F-2006-01, University of Aarhus, Aarhus School of Business, Department of Business Studies. [Downloadable!]
  17. Pierre Collin-Dufresne & Christopher S. Jones & Robert S. Goldstein, 2004. "Can Interest Rate Volatility be Extracted from the Cross Section of Bond Yields? An Investigation of Unspanned Stochastic Volatility," NBER Working Papers 10756, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  18. Ram Bhar & Carl Chiarella & Thuy-Duong To, 2004. "Estimating the Volatility Structure of an Arbitrage-Free Interest Rate Model Via the Futures Markets," Finance 0409003, EconWPA. [Downloadable!]
  19. Giovanni Caggiano & Leone Leonida, . "A note on the empirics of the neoclassical growth model," Working Papers 2006_2, Department of Economics, University of Glasgow. [Downloadable!]
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