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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

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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Bibliographic Info

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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  1. Hamilton, James D., 1988. "Rational-expectations econometric analysis of changes in regime : An investigation of the term structure of interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 385-423.
  2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  3. Jin-Chuan Duan, 1994. "Maximum Likelihood Estimation Using Price Data Of The Derivative Contract," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 155-167.
  4. 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.
  5. Longstaff, Francis A & Schwartz, Eduardo S, 1992. " Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-82, September.
  6. Pennacchi, George G, 1991. "Identifying the Dynamics of Real Interest Rates and Inflation: Evidence Using Survey Data," Review of Financial Studies, Society for Financial Studies, vol. 4(1), pages 53-86.
  7. Titman, Sheridan D & Torous, Walter N, 1989. " Valuing Commercial Mortgages: An Empirical Investigation of the Contingent-Claims Approach to Pricing Risky Debt," Journal of Finance, American Finance Association, vol. 44(2), pages 345-73, June.
  8. Richard, Scott F., 1978. "An arbitrage model of the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 33-57, March.
  9. Marsh, Terry A & Rosenfeld, Eric R, 1983. " Stochastic Processes for Interest Rates and Equilibrium Bond Prices," Journal of Finance, American Finance Association, vol. 38(2), pages 635-46, May.
  10. Brown, Stephen J & Dybvig, Philip H, 1986. " The Empirical Implications of the Cox, Ingersoll, Ross Theory of the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 41(3), pages 617-30, July.
  11. Jin-Chuan, Duan & Moreau, Arthur F. & Sealey, C. W., 1995. "Deposit insurance and bank interest rate risk: Pricing and regulatory implications," Journal of Banking & Finance, Elsevier, vol. 19(6), pages 1091-1108, September.
  12. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  13. Domowitz, Ian & White, Halbert, 1982. "Misspecified models with dependent observations," Journal of Econometrics, Elsevier, vol. 20(1), pages 35-58, October.
  14. Hall, Anthony D & Anderson, Heather M & Granger, Clive W J, 1992. "A Cointegration Analysis of Treasury Bill Yields," The Review of Economics and Statistics, MIT Press, vol. 74(1), pages 116-26, February.
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