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Nonlinear Kalman Filtering in Affine Term Structure Models

Author

Listed:
  • Peter Christoffersen

    (Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada; Copenhagen Business School, 2000 Frederiksberg, Denmark; and CREATES, 8210 Aarhus V, Denmark)

  • Christian Dorion

    (HEC Montreal, Montreal, Quebec H3T 2A7, Canada)

  • Kris Jacobs

    (C. T. Bauer College of Business, University of Houston, Houston, Texas 77204)

  • Lotfi Karoui

    (Goldman, Sachs & Company, New York, New York 10282)

Abstract

The extended Kalman filter, which linearizes the relationship between security prices and state variables, is widely used in fixed-income applications. We investigate whether the unscented Kalman filter should be used to capture nonlinearities and compare the performance of the Kalman filter with that of the particle filter. We analyze the cross section of swap rates, which are mildly nonlinear in the states, and cap prices, which are highly nonlinear. When caps are used to filter the states, the unscented Kalman filter significantly outperforms its extended counterpart. The unscented Kalman filter also performs well when compared with the much more computationally intensive particle filter. These findings suggest that the unscented Kalman filter may be a good approach for a variety of problems in fixed-income pricing. This paper was accepted by Wei Xiong, finance .

Suggested Citation

  • Peter Christoffersen & Christian Dorion & Kris Jacobs & Lotfi Karoui, 2014. "Nonlinear Kalman Filtering in Affine Term Structure Models," Management Science, INFORMS, vol. 60(9), pages 2248-2268, September.
    • Handle: RePEc:inm:ormnsc:v:60:y:2014:i:9:p:2248-2268
    DOI: 10.1287/mnsc.2013.1870
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    More about this item

    Keywords

    Kalman filtering; nonlinearity; term structure models; swaps; caps; particle filtering;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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