基于EKF与UKF的利率期限结构模型估计及对比  

Estimations of Term Structure of Interest Rate Model Based on EKF and UKF Approaches

作　　者：杨宝臣[1] 苏云鹏[1] 李玲珍[1] 

机构地区：[1]天津大学管理学院,天津300072

出　　处：《系统管理学报》2009年第3期344-349,354,共7页Journal of Systems & Management

基　　金：国家自然科学基金资助项目(70471051;70771075);教育部博士点基金资助项目(200800560032);教育部新世纪优秀人才支持计划项目(NCET-08-0397)

摘　　要：在CKLS广义模型框架下,引入基于扩展卡尔曼滤波(EKF)和无损卡尔曼滤波(UKF)的利率期限结构均衡模型的估计方法,并使用加拿大国债数据对EKF和UKF的模型估计效果进行了对比实证研究。结论表明,引入的基于UKF的模型估计方法相对于文献中普遍采用的基于EKF的估计方法的估计效果有明显改善,尤其存在强非线性和非正态分布的模型条件下,基于UKF的模型估计方法相对于基于EKF的估计方法有很大优势。进一步,基于UKF估计方法对Vasicek模型和CIR模型的数据拟合性进行了对比研究。结果表明,Vasicek模型和CIR模型均具有较好的数据拟合性,而Vasicek模型相对更好。In the CKLS 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）.Using fourteen years of daily Canadian zero-coupon bond price data,we make a survey and contrast between the estimation performances of the EKF-based and UKF-based algorithms.The empirical result comes to a conclusion that the UKFbased algorithm introduced in this paper offers a superior performance to the EKF-based one,which is used as a standard method to yield the likelihood function in literature.The superiority is further magnified when it comes to a strong nonlinear system with a non-Gaussian distribution.Furthermore,the fitness of Vasicek model and CIR model is compared with the data above using the UKF-based algorithm,which indicates that both the models perform well in capturing the dynamics of the interest rates,while Vasicek model does even better.

关 键 词：利率期限结构模型 参数估计 扩展卡尔曼滤波 无损卡尔曼滤波 遗传算法 

分 类 号：O212[理学—概率论与数理统计]