Nonlinear Kalman Filtering in Affine Term Structure Models

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 filtering 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 filter is much more accurate than its extended counterpart in filtering the states and forecasting swap rates and caps. 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 coupon bonds and the estimation of quadratic term structure models.

Number of Pages in PDF File: 48

Keywords: Kalman filtering, nonlinearity, term structure models, swaps, caps

JEL Classification: J12

working papers series