#09-07
Nonlinear Filtering in Affine Term Structure Models: Evidence from the Term Structure of Swap Rates
Peter Christoffrsen, Kris Jacobs, Lotfi Karoui and Karim Mimouni, December 2008
Abstract: When the relationship between observed fixed-income securities and the latent state
variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear filtering is computationally demanding. We
propose the use of the unscented Kalman filter to allow for nonlinearities. To illustrate
its advantages, we analyze the cross section of swap yields, which are relatively simple non-linear instruments. An extensive Monte Carlo experiment demonstrates that
the unscented Kalman filter generates much smaller swap rate prediction errors and
also smaller errors in parameter estimates. Estimation using an extensive sample of
swap data indicates large differences between the state variables obtained using the
unscented Kalman filter and the more conventional extended Kalman filter. Our findings suggest that the unscented Kalman filter may prove to be a good approach for a
number of other problems in fixed income pricing with nonlinear relationships between
the state vector and the observations, such as the estimation of term structure models
using interest rate derivatives or coupon bonds, and the estimation of quadratic term
structure models.
Keywords: Kalman filtering; nonlinearity; term structure models; swaps.
JEL classifications: G12
