利率期限结构静态拟合模型及其应用研究

发布时间：2019-06-03 04:40

【摘要】：利率期限结构拟合是金融数学中非常重要的研究课题,它主要是应用数学方法拟合利率曲线。研究利率期限结构对于资产定价、金融产品设计、风险管理等具有重要理论意义和实用价值。本文分析了利率期限结构静态模型和动态模型的建模原理及模型的适用性。并从静态拟合的角度,研究了惩罚样条函数利率期限结构模型和Nelson-Siegel扩展模型,进行了相应的参数估计与算法设计,并将其应用于拟合企业债信用价差。主要工作及创新点如下： 1、论文建立了惩罚样条函数利率期限结构模型。模型中通过逐点删除方法确定样条节点,应用广义交叉验证法(GCV)确定惩罚因子,并通过遗传算法获得惩罚因子的最优值,最后应用上海证券交易所国债数据进行实证分析。结果表明惩罚样条模型能够提高曲线拟合的平滑度,但可能降低曲线的拟合精度。 2、从理论上系统地分析了利率期限结构Nelson-Siegel族模型中的NS模型、SV模型、NSM模型、FF模型及SF模型,采用遗传算法获得各个模型的即期利率,最后应用上海证券交易所国债数据进行了实证分析和比较。结果表明FF模型与SF模型的拟合精度与灵活性均优于其他模型,能够反映我国国债的利率期限结构。 3、结合利率期限结构静态拟合模型与Jarrow简化信用价差模型建立了单个企业债券的信用价差拟合模型。该方法以企业债的市场价格为输入变量,适合于研究实际观测到的信用价差。
[Abstract]:Term structure fitting of interest rate is a very important research topic in financial mathematics, it mainly applies mathematical method to fit interest rate curve. It is of great theoretical significance and practical value to study the term structure of interest rate for asset pricing, financial product design, risk management and so on. In this paper, the modeling principle and applicability of static model and dynamic model of interest rate term structure are analyzed. From the point of view of static fitting, the term structure model of penalty spline function interest rate and Nelson-Siegel extension model are studied, and the corresponding parameter estimation and algorithm design are carried out, and they are applied to fit the credit price difference of corporate debt. The main work and innovations are as follows: 1. The term structure model of penalty spline function interest rate is established in this paper. In the model, the splines are determined by point-by-point deletion method, the penalty factors are determined by the generalized cross-verification method (GCV), and the optimal value of the penalty factors is obtained by genetic algorithm. Finally, the empirical analysis is carried out by using the national debt data of Shanghai Stock Exchange. The results show that the penalty spline model can improve the smoothness of curve fitting, but may reduce the fitting accuracy of curve. 2. The NS model, SV model, NSM model, FF model and SF model in the Nelson- Siegel family model of interest rate term structure are systematically analyzed theoretically, and the spot interest rates of each model are obtained by genetic algorithm. Finally, the empirical analysis and comparison are carried out by using the national debt data of Shanghai Stock Exchange. The results show that the fitting accuracy and flexibility of FF model and SF model are better than those of other models, and can reflect the term structure of interest rate of national debt in China. 3. Combined with the static fitting model of interest rate maturity structure and Jarrow simplified credit spread model, the credit spread fitting model of single enterprise bond is established. This method takes the market price of enterprise debt as the input variable, which is suitable for the study of the observed credit price difference.
【学位授予单位】：北京化工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F820;F832.51

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