The Estimation of the Heath-Jarrow-Morton Model by Use of Kalman Filtering Techniques

  • Ramaprasad Bhar
  • Carl Chiarella
Part of the Advances in Computational Economics book series (AICE, volume 6)

Abstract

A fairly flexible functional form for the forward rate volatility is applied to the Heath—Jarrow—Morton model of the term structure of interest rates to reduce the system dynamics to Markovian form. The resulting stochastic dynamic system is cast into a form suitable for estimation by use of nonlinear filtering methodology. The technique is applied to 90 day bank bill and 3 year treasury bond data in the Australian market.

Keywords

Term Structure Forward Rate Bond Price Markovian System Volatility Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berndt, E.K., B.H. Hall, R.E. Hall, and Hausman, J.A., 1974, ‘Estimation and inference in non-linear structural models’, Annals of Economic and Social Measurement 3, 653–665.Google Scholar
  2. Bhar, R. and C. Chiarella, 1996, ‘Transformation of Heath-Jarrow-Morton models to Markovian systems’, The European Journal of Finance (forthcoming).Google Scholar
  3. Bhar, R. and C. Chiarella, 1995, ‘The estimation of the Heath-Jarrow-Morton model by use of Kalman filtering techniques’, Working Paper No. 54, University of Technology, Sydney.Google Scholar
  4. Bhar, R. and B.F. Hunt, 1993, ‘Predicting the short-term forward interest rate structure using a Parsimonious model’, Review of Futures Markets 12 (3), 577–590.Google Scholar
  5. Carverhill, A., 1994, ‘When is the short rate Markovian’, Journal of Mathematical Finance 4, 305–312.CrossRefGoogle Scholar
  6. Efron, B., 1987, ‘Better bootstrap confidence intervals’, J. American Statistical Assoc. 82, 171–200.CrossRefGoogle Scholar
  7. Falb, P.L., 1967, ‘Infinite-dimensional filtering: The Kalman-Bucy filter in Hilbert space’, Information and Control 11, 102–137.CrossRefGoogle Scholar
  8. Harvey, A.C., 1989, Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge: Cambridge University Press.Google Scholar
  9. Heath, D., R. Jarrow, and A. Morton, 1990, ‘Contingent claim valuation with a random evolution of interest rates’, Review of Futures Markets 9 (1), 54–82.Google Scholar
  10. Heath, D., R. Jarrow, and A. Morton, 1992a, ‘Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation’, Econometrica 60 (1), 77–105.CrossRefGoogle Scholar
  11. Heath, D., R. Jarrow, and A. Morton, 1992b, ‘Easier done than said’, RISK 5 (9), 77–80.Google Scholar
  12. Hunt, B.F., 1994, ‘Testing alternative methods of modelling yields on coupon paying bonds’, Paper presented at the First Annual Coneference, Asia-Pacific Finance Association, Sydney, September 28, 1994.Google Scholar
  13. Kloeden, P.E. and E. Platen, 1992, Numerical Solution of Stochastic Differential Equations, Berlin: Springer-Verlag.Google Scholar
  14. Lo, A.W., 1988, ‘Maximum likelihood estimation of generalised Ito processes with discretely sampled data’, Econometric Theory 4, 231–247.CrossRefGoogle Scholar
  15. Maddala, G.S., C.R. Rao, and H.D. Vinod, 1993, Handbook of Statistics, Vol. 11, Amsterdam: Elsevier.Google Scholar
  16. Ozaki, T., 1992, ‘Identification of nonlinearities and non-Gaussianities in time series’, in D. Brillinger et al. (Eds), New Directions in Time Series Analysis, Part 1, Berlin: Springer-Verlag.Google Scholar
  17. Ritchken, P. and L. Sankarasubramanian, 1995, ‘Volatility structures of forward rates and the dynamics of the term structure’, Journal of Mathematical Finance 5, 55–72.CrossRefGoogle Scholar
  18. Stoffer, D.S. and K.D. Wall, 1991, ‘Bootstrapping state-space models: Gaussian maximum likelihood estimation and the Kalman filter’, Journal of American Statistical Association 86, 1024–1033.CrossRefGoogle Scholar
  19. Tanizaki, H., 1993, Nonlinear Filters: Estimation and Applications, Berlin: Springer-Verlag.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Ramaprasad Bhar
  • Carl Chiarella

There are no affiliations available

Personalised recommendations