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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.

Suggested Citation

  • 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, Business School - Economics, University of Glasgow.
  • Handle: RePEc:gla:glaewp:2005_2
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    File URL: http://www.gla.ac.uk/media/media_22193_en.pdf
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    1. repec:bla:jfnres:v:22:y:1999:i:1:p:107-130 is not listed on IDEAS
    2. 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 335-338, July.
    3. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    4. Duan, Jin-Chuan & Simonato, Jean-Guy, 1999. "Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter," Review of Quantitative Finance and Accounting, Springer, vol. 13(2), pages 111-135, September.
    5. 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.
    6. 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.
    7. 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 107-130, Spring.
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    Cited by:

    1. Long H. Vo, 2014. "Application of Kalman Filter on modelling interest rates," Journal of Management Sciences, Geist Science, Iqra University, Faculty of Business Administration, vol. 1(1), pages 1-15, March.

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