Nonlinear Filtering in Affine Term Structure Models: Evidence from the Term Structure of Swap Rates

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 rates, which are relatively simple nonlinear 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 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.