Research On Model Estimation Of Term Structure Of Interest Rates By Kalman Filters

The theories and models on term structure of interest rates are one of the most challenging works in finance research and an important fundamental branch in financial engineering field. And the model estimation of term structure of interest rates is the foundation and key link for the theoretical and empirical research on interest rates. The family of Kalman filters is part of the classical theory of optimal filtering. They have got advantages such as real time corresponding, speed computing, precise estimating, steady running and easy operating, which makes them widely used in various fields such as signal processing, communication, control and so on. In light of the excellent estimation effects these filters have obtained in the fields above, this dissertation, by reviewing the evolving process of both theories on modeling term structure of interest rates and algorithms of the family of Kalman filters, pursues a systemic application of the family of Kalman filters to the model estimation of term structure of interest rates, which supplies an estimation method and application foundation for the theoretical and empirical research on modeling the term structure of interest rates.The dissertation firstly divided the models into two families: equilibrium models and no-arbitrage models and makes a detailed discussion on models in each family about their origin, construction and model characters. Then, the dissertation systematically introduce the theories and algorithms of the family of Kalman filters, including Kalman filter (KF), extended Kalman filter (EKF) and unscented Kalman filter (UKF), as well as their applications to the model estimation of the term structure of interest rates.Finally, the dissertation carries out parameter estimation of Vasicek model, in Matlab 7.0, using EKF and UKF respectively. And then a discussion is given on the two filters in the aspects of characters, applicability scopes and superiority, by contrasting their estimation results in estimation effects, computing speed and so on.As one of its research achievements, the dissertation is financed by the National Natural Science Fund project'Research on Approach to Dynamically Pricing and Hedging of Interest Rate Risk of Fixed Income Securities'(No. 70471051).