基于无损卡尔曼滤波的HJM模型及实证研究  

Model calibration of HJM models based on UKF with application

作　　者：杨宝臣[1] 苏云鹏[1] 

机构地区：[1]天津大学管理学院,天津300072

出　　处：《管理科学学报》2010年第4期67-75,共9页Journal of Management Sciences in China

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：在多因子HJM框架下,将一类具有特定波动率结构设定的非马尔可夫远期利率模型转化为马尔可夫模型,并将其表示成状态空间模型形式.进一步,引入基于无损卡尔曼滤波的极大似然估计法对HJM模型进行估计,解决了模型非线性和潜在状态变量的问题.实证研究中,基于上海银行间同业拆放利率(SHIBOR)期限结构的实际动态特性,对HJM模型的波动率结构进行相应的设定,并引入随机市场风险价格,构建了SHIBOR期限结构的三因子HJM模型.结果表明,三因子HJM模型可以很好的刻画SHIBOR期限结构的动态特性和波动率结构,水平因子和斜率因子是驱动SHIBOR利率系统的主要因素.In a multifactor HJM framework, this paper transforms a class of non-Markovian forward rate models with a specific volatility specification into the Markovian representation, which is further cast into a state-space model. Then a maximum likelihood estimator based on the unscented Kalman filter is introduced into the estimation of the term structure models, thus getting the problems of nonlinearity and the existence of latent variables resolved. For the empirical study, a three-factor HJM model is established for the Shanghai Interbank Offered Rate （SHIBOR） market by introducing stochastic market price of risk and a volatility specification appropriate for the market. It is found that the dynamics and volatility structure of SHIBOR are both well captured by the model, and the level and slope factors explain the majority of the variation of the yield curve .

关 键 词：HJM模型 无损卡尔曼滤波 极大似然估计 上海银行间同业拆放利率 

分 类 号：F830.91[经济管理—金融学]