Estimation of Equilibrium Term Structure Models: EKF and UKF Based Approaches

• 1、College of Management and Economics, Tianjin University, Tianjin 300072

Abstract：In a general framework, this paper introduces approaches of estimation for equilibrium models of term structure of interest rates based on the extended Kalman filter (hereafter EKF) and unscented Kalman filter (hereafter UKF). This paper treats the estimation of the equilibrium models as a nonlinear filtering problem, and adopts EKF and the UKF respectively to estimate the model via the maximum likelihood method. Using fourteen years of daily Canadian zero-coupon bond price data, we apply the estimator to Vasicek and Cox-Ingersoll-Ross models based on EKF and UKF respectively. It is found that the EKF-based algorithm offers generally the same performance with the UKF-based one in model estimation when the system is linear or weak linear and the Gaussian distribution assumption is satisfied. But when it comes to the strong nonlinear system with a non-Gaussian distribution, the UKF-based algorithm does a better job than the EKF-based one in model estimation. However the UKF-based algorithm is about 50% slower than the EKF-based one in actual computation, though it is regarded in literature that they both have the same order of computational complexity.

keywords： financial engineering Term structure of interest rates Model estimation Extended Kalman filter Unscented Kalman filter Maximum likelihood estimator

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