四因子CIR利率期限结构模型及实证研究

发布时间：2018-05-04 17:58

本文选题：利率期限结构 + 卡尔曼滤波　；参考：《安徽财经大学》2013年硕士论文

【摘要】：近年来,随着我国金融市场的不断发展和完善以及利率市场化改革的持续深入,我国国债的期限结构日趋合理,国债交易规模不断增大。这方面要求我们对利率期限结构进行更加深入的研究,为投资者进行投资决策和国家制定货币政策提供依据,另一方面丰富的国债交易数据也为我们对利率期限结构进行进一步的研究提供了数据基础。本文首先对几种经典的静态利率期限结构模型进行了介绍,并分析了各模型在拟合收益率曲线时的优缺点。在对比各模型的拟合效果后,笔者认为N-S模型较为适宜用来估计我国利率期限结构,因此,本文选择使用N-S模型来对上交所国债所隐含的利率期限结构进行估计。从文中的实际估计结果来看,N-S模型对上交所国债所隐含的利率曲线结构拟合效果出色,这同时也说明了我国国债市场相对有效,且投资者较为理性。基于N-S模型估计出的每一日的利率期限结构,通过计算可以获得当日的任意到期期限国债的到期收益率,根据本文研究需要,本文求出了到期期限分别为1、2、3、4、5、7、10年的即期收益率。在对不同到期期限的即期收益率序列进行相关性检验后发现,所有相关系数均不为1,这说明单个因子不足以刻画瞬时利率的动态特性,瞬时利率的动态特性需要由多个因子来刻画,从而说明了建立多因子模型的必要性。随后,本文对不同到期期限的即期利率序列进行了主成分分析,主成分分分析结果显示,前四个因子的解释能力较高,总解释能力达到99.941%,因此本文认为使用四个因子来刻画瞬时利率的动态特性较为合适。鉴于单因子模型与事实不太相符,于是本文在单因子CIR模型的基础上对其进行了扩展,将因子个数从一个增加到四个,从而建立了四因子CIR模型。在四因子CIR模型的估计方面,本文首先使用回归法估计出各参数的初始值,进而使用卡尔曼滤波方法来求得模型参数的最优估计。随后,本文选择误差均分方跟作为评价模型拟合优度的指标并计算得出了各期限利率序列的误差均方根,计算结果表明,四因子模型对样本的拟合效果优良。
[Abstract]:In recent years, with the continuous development and perfection of our financial market and the continuous deepening of the reform of market-oriented interest rate, the term structure of national debt is becoming more and more reasonable, and the scale of national debt trading is increasing. In this regard, we are required to conduct a more in-depth study of the term structure of interest rates to provide a basis for investors to make investment decisions and countries to formulate monetary policies. On the other hand, the abundant data of bond trading also provide the data basis for our further study on the term structure of interest rate. In this paper, several classical term structure models of static interest rate are introduced, and the advantages and disadvantages of these models in fitting the yield curve are analyzed. After comparing the fitting results of each model, the author thinks that N-S model is more suitable to estimate the term structure of interest rate in China. Therefore, this paper chooses N-S model to estimate the term structure of interest rate implied by Shanghai Stock Exchange. From the actual estimation results in this paper, we can see that the N-S model fits well the interest rate curve structure implied by Shanghai Stock Exchange, which also shows that the bond market in China is relatively effective and the investors are more rational. Based on the N-S model, the term structure of interest rate per day can be calculated to obtain the maturity yield of the bond with arbitrary maturity on the same day. According to the need of this study, this paper calculates the spot yield of 10 years, and the maturity period is 1 / 2 / 3 / 4 / 4 / 5 / 7 and 10 years respectively. It is found that all the correlation coefficients are not 1, which indicates that a single factor is not enough to describe the dynamic characteristics of instantaneous interest rate. The dynamic characteristics of the instantaneous interest rate need to be characterized by multiple factors, so it is necessary to establish a multi-factor model. Then, the paper makes principal component analysis on the sequence of spot interest rates with different maturities. The results of principal component analysis show that the first four factors have higher explanatory ability. The total explanatory ability is 99.941, so it is more appropriate to use four factors to describe the dynamic characteristics of instantaneous interest rate. In view of the fact that the single factor model is not quite consistent with the facts, this paper extends the single factor CIR model, and increases the number of factors from one to four, thus establishing a four-factor CIR model. In the estimation of four-factor CIR model, the initial value of each parameter is estimated by regression method, and then the optimal estimation of model parameters is obtained by using Kalman filter method. Then, this paper selects the error mean square followed as the index to evaluate the goodness of fit of the model and calculates the root of the error mean square of the interest rate sequence of each term. The results show that the four-factor model has a good fitting effect on the sample.
【学位授予单位】：安徽财经大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.51;F224

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