基于高斯粒子滤波法的CIR利率期限结构估计

摘要

To improve the state estimation accuracy for CIR term structure model of interest rates, the discrete nonlinear filtering formulation of CIR model is established and then the Gaussian particle filter (GPF) is adopted to generate the approximate optimal state estimation. Compared with the popular extended Kalman filter (EKF), GPF employs Gaussian distribution based on importance sampling algorithm to approximate the posterior probability while avoiding the error resulting from linearly approximating the function itself. The two nonlinear estimation methodologies are implemented and compared on simulated data. Results are presented to demonstrate the more accurate ability of GPF based CIR filtering model to describe the dynamics of the term structure of interest rates.%为了提高CIR利率期限结构模型中的状态估计精度,建立了该问题的离散非线性滤波模型,采用高斯粒子滤波法进行状态近似最优估计.相对于文献中普遍采用的扩展卡尔曼滤波方法,高斯粒子滤波法避免了线性近似带来的误差,利用基于重要性采样得到的高斯分布来近似状态变量的后验分布,具有更强的状态估计能力.仿真实验比较了高斯粒子滤波和扩展卡尔曼滤波两种非线性估计法,结果表明,基于高斯粒子滤波的CIR滤波模型更准确地描述了利率期限结构的动态变化特征.