利率期限结构研究-基于扩展的CIR模型
利率期限结构研究－基于扩展的CIR模型
Analysis of Term Structure－Base on Extended CIR Model
姓名：滕弋Teng Yi
学号：34020051300819
联系方式：135********
指导教师：郑鸣教授陈蓉副教授林海副教授
摘要
利率期限结构是指在某个时点上具有相同的风险和流动性，不同期限的利率所组成的一条利率曲线。它是资产定价、金融产品设计、保值和风险管理等方面的基础。利率期限结构研究可分为静态与动态研究两个方面。其中，静态研究是动态研究的基础，在实际应用方面，主要用到的是动态利率期限结构研究的成果。本文在运用Svensson模型进行静态研究的基础上，扩展双因子CIR模型来研究上海证券交易所的国债利率期限结构，探索适合于反映我国真实国债利率期限结构的模型与方法。本文的具体安排如下：
首先，我们阐述了中国正进行着利率市场化进程这一本文的研究背景，以及研究利率期限结构所具有的重要的理论意义和实践意义。接着，我们比较系统地回顾了国内外关于利率期限结构静态以及动态研究的发展过程，并着重评述了理论和实务中非常重要的CIR模型的相关研究。然后，我们研究了利率期限结构的理论基础，包括其形成过程的三种假设，静态估计中的Nelson-Siegel模型及Svensson扩展模型，动态模型中的双因子CIR模型及其扩展模型。在用状态空间形式表示这两个模型的基础上，阐述了卡尔曼滤波的估计方法。在实证研究部分，我们首先利用Svensson模型得出2007年5月8日的上交所国债利率期限结构，然后重复上述过程，在得到上交所国债利率时间序列数据后，运用双因子CIR模型及其扩展模型，根据卡尔曼滤波方法估计的参数，拟合出我国国债利率期限结构的时序数据，得出双因子CIR模型基本上可以反映我国上交所利率期限结构的变化，其扩展模型能够更好地拟合利率期限结构数据的结论。
ABSTRACT
The interest rate term structure is the curve formed by interest rates of the same risk and liquidity, but the different maturities at any point. It is the benchmark for asset pricing, financial product design, hedging, risk management and so on. The study of interest rate term structure can be separated into two parts: static state and dynamic state. The research of the dynamic state which has more application value is base on the result of the static state. In this dissertation, we use the Svensson model to study the static state of the interest rate term structure of the government bond in the Shanghai Security Exchange Market (SSE). Then we extend the two factor CIR model to explore for the method which suit to reflect the real interest rate term structure in China.
The main study work of this dissertation is the followings:
At first, we expatiate on the background of this dissertation: China is on the process of the interest rate liberalization. We discuss about the theory and application significance of the study on the interest rate term structure. Followed we review systematically the research process on the term structure, and emphasis on the famous CIR model which is very important. Then we discuss the theory about the term structure, including hypothesis of interest rate term structure formation, the Nelson-Siegel model and the Svensson model to estimate the interest rate term structure and the two factor CIR model and its extended form which used to analysis the dynamic term structure. Base on the state space representation of the two dynamic models, we expatiate how to use the Kalman Filter to estimate the parameters. In the following empirical test part, we construct a static interest rate term structure used the Svensson model base on the SSE’s trading data on 08/05/2007. Then repeat thus process, we constructs a yearly interest rate term structure from 01/09/2006 to 31/08/2007. Base on the parameters estimated by the Kalman Filter method, we use the two factor CIR model and its extend form to fit the time series data of the China government bond interest rate term structure. We find out the two factor CIR model can basically reflect the change of Chinese interest rate term structure, while its extend form is more suitable in application.