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Simple and extended Kalman filters: an application to term structures of commodity prices


  • Delphine Lautier
  • Alain Galli


This article presents and compares two different Kalman filters. These methods provide a very interesting way to cope with the presence of non-observable variables, which is a frequent problem in finance. They are also very fast even in the presence of a large information volume. The first filter presented, which corresponds to the simplest version of a Kalman filter, can be used solely in the case of linear models. The second filter - the extended one - is a generalization of the first one, and it enables one to deal with non-linear models. However, it also introduces an approximation in the analysis, whose possible influence must be appreciated. The principles of the method and its advantages are first presented. It is then explained why it is interesting in the case of term structure models of commodity prices. Choosing a well-known term structure model, practical implementation problems are discussed and tested. Finally, in order to appreciate the impact of the approximation introduced for non-linear models, the two filters are compared.

Suggested Citation

  • Delphine Lautier & Alain Galli, 2004. "Simple and extended Kalman filters: an application to term structures of commodity prices," Applied Financial Economics, Taylor & Francis Journals, vol. 14(13), pages 963-973.
  • Handle: RePEc:taf:apfiec:v:14:y:2004:i:13:p:963-973
    DOI: 10.1080/0960310042000233629

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    References listed on IDEAS

    1. Babbs, Simon H. & Nowman, K. Ben, 1999. "Kalman Filtering of Generalized Vasicek Term Structure Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(01), pages 115-130, March.
    2. repec:dau:papers:123456789/871 is not listed on IDEAS
    3. Gibson, Rajna & Schwartz, Eduardo S, 1990. " Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-976, July.
    4. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
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    Cited by:

    1. Lubnau, Thorben & Todorova, Neda, 2015. "Trading on mean-reversion in energy futures markets," Energy Economics, Elsevier, vol. 51(C), pages 312-319.
    2. Islyaev, Suren & Date, Paresh, 2015. "Electricity futures price models: Calibration and forecasting," European Journal of Operational Research, Elsevier, vol. 247(1), pages 144-154.
    3. Lubnau, Thorben, 2014. "Spread trading strategies in the crude oil futures market," Discussion Papers 353, European University Viadrina Frankfurt (Oder), Department of Business Administration and Economics.

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