Nonlinear Kalman Filtering in Affine Term Structure Models

• 成果类型: Article
• 署名作者: Christoffersen, Peter; Dorion, Christian; Jacobs, Kris; Karoui, Lotfi
• 署名单位: University of Toronto; Copenhagen Business School; CREATES; Universite de Montreal; HEC Montreal; University of Houston System; University of Houston
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2013.1870
• 发表日期: 2014
• 页码: 2248-2268
• 关键词: Kalman filtering; nonlinearity; term structure models; Swaps; caps; particle filtering

摘要

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.