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Application Of The Kalman Filter For Estimating Continuous Time Term Structure Models: The Case Of Uk And Germany

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  • Somnath Chatterjee

Abstract

The purpose of this paper is to see how the term structure of interest rates has evolved in the sterling and euro treasury bond markets over the period 1999-2003. German bonds have been used as a proxy for euro-denominated bonds. A state-space representation for the single-factor Cox, Ingersoll and Ross (1985) model is employed to analyse the intertemporal dynamics of the term structure. Quasi-maximum likelihood estimates of the model parameters are obtained by using the Kalman filter to calculate the likelihood function. Results of the empirical analysis show that while the unobserved instantaneous interest rate exhibits mean reverting behaviour in both the UK and Germany, the mean reversion of the interest rate process has been relatively slower in the UK. The volatility component, which shocks the process at each step in time is also higher in the UK as compared to Germany.

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Paper provided by Business School - Economics, University of Glasgow in its series Working Papers with number 2005_2.

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Date of creation: Jan 2005
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Handle: RePEc:gla:glaewp:2005_2

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  1. Steeley, James M, 1997. "A Two-Factor Model of the U.K. Yield Curve," The Manchester School of Economic & Social Studies, University of Manchester, vol. 65(0), pages 32-58, Supplemen.
  2. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 297-316, July.
  3. Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Estimating and Testing Exponential Affine Term Structure Models by Kalman Filter," CIRANO Working Papers 95s-44, CIRANO.
  4. Geyer, Alois L J & Pichler, Stefan, 1999. "A State-Space Approach to Estimate and Test Multifactor Cox-Ingersoll-Ross Models of the Term Structure," Journal of Financial Research, Southern Finance Association & Southwestern Finance Association, vol. 22(1), pages 107-30, Spring.
  5. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  6. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 335-38, July.
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