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Nonlinear Kalman Filtering in Affine Term Structure Models

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Author Info

  • Peter Christoffersen

    ()
    (University of Toronto - Rotman School of Management and CREATES)

  • Christian Dorion

    ()
    (HEC Montreal)

  • Kris Jacobs

    ()
    (University of Houston and Tilburg University)

  • Lotfi Karoui

    ()
    (Goldman, Sachs & Co.)

Abstract

When the relationship between security prices and state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear fi?ltering is computationally demanding. We conduct an extensive investigation of this linearization and analyze the potential of the unscented Kalman ?filter to properly capture nonlinearities. To illustrate the advantages of the unscented Kalman ?filter, we analyze the cross section of swap rates, which are relatively simple non-linear instruments, and cap prices, which are highly nonlinear in the states. An extensive Monte Carlo experiment demonstrates that the unscented Kalman fi?lter is much more accurate than its extended counterpart in fi?ltering the states and forecasting swap rates and caps. Our fi?ndings suggest that the unscented Kalman fi?lter may prove to be a good approach for a number of other problems in fi?xed income pricing with nonlinear relationships between the state vector and the observations, such as the estimation of term structure models using coupon bonds and the estimation of quadratic term structure models.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-49.

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Length: 48
Date of creation: 14 May 2012
Date of revision:
Handle: RePEc:aah:create:2012-49

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Kalman filtering; nonlinearity; term structure models; swaps; caps.;

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