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英文文献：Nonlinear Kalman Filtering in Affine Term Structure Models-仿射期限结构模型中的非线性卡尔曼滤波
英文文献作者：Peter Christoffersen,Christian Dorion,Kris Jacobs,Lotfi Karoui
英文文献摘要：
When the relationship between security prices and state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear fi?ltering is computationally demanding. We conduct an extensive investigation of this linearization and analyze the potential of the unscented Kalman ?filter to properly capture nonlinearities. To illustrate the advantages of the unscented Kalman ?filter, we analyze the cross section of swap rates, which are relatively simple non-linear instruments, and cap prices, which are highly nonlinear in the states. An extensive Monte Carlo experiment demonstrates that the unscented Kalman fi?lter is much more accurate than its extended counterpart in fi?ltering the states and forecasting swap rates and caps. Our fi?ndings suggest that the unscented Kalman fi?lter may prove to be a good approach for a number of other problems in fi?xed income pricing with nonlinear relationships between the state vector and the observations, such as the estimation of term structure models using coupon bonds and the estimation of quadratic term structure models.
在动态期限结构模型中，当证券价格与状态变量之间存在非线性关系时，现有的研究通常将这种关系线性化，因为非线性fi?过滤是需要计算的。我们对这种线性化进行了广泛的调查，并分析了无痕迹卡尔曼滤波器的潜力，以适当地捕捉非线性。为了说明无迹卡尔曼滤波的优点，我们分析掉期利率的横截面，这是相对简单的非线性工具，上限价格，这是高度非线性的状态。一个广泛的蒙特卡洛实验表明，无气味的卡尔曼菲?lter比fi?中的扩展版本更准确。并预测掉期利率和上限。我们的fi吗?有证据表明，无气味的卡尔曼·菲?lter可能被证明是解决fi中其他一些问题的好方法。状态向量与观测值之间存在非线性关系的混合收益定价，如使用息票债券的期限结构模型的估计和二次期限结构模型的估计。
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