Nonlinear Kalman Filtering in Affine Term Structure Models
研究了在仿射期限结构模型中，无迹卡尔曼滤波相比扩展卡尔曼滤波和粒子滤波在捕捉非线性关系上的表现，发现前者在利率互换和上限期权定价中更优，对固定收益定价问题有参考价值。
The extended Kalman filter, which linearizes the relationship between security prices and state variables, is widely used in fixed-income applications. We investigate whether the unscented Kalman filter should be used to capture nonlinearities and compare the performance of the Kalman filter with that of the particle filter. We analyze the cross section of swap rates, which are mildly nonlinear in the states, and cap prices, which are highly nonlinear. When caps are used to filter the states, the unscented Kalman filter significantly outperforms its extended counterpart. The unscented Kalman filter also performs well when compared with the much more computationally intensive particle filter. These findings suggest that the unscented Kalman filter may be a good approach for a variety of problems in fixed-income pricing. This paper was accepted by Wei Xiong, finance.