短期利率模型的参数估计及偏差校正

发布时间：2018-07-05 10:54

本文选题：短期利率 + 参数估计　；参考：《西南财经大学》2014年硕士论文

【摘要】：利率是金融市场中的核心变量。近年来,随着中国利率市场化进程的不断加快,利率研究的理论和实用价值日益凸显,本文以短期利率作为研究对象,探讨了单因素短期利率模型参数估计的方法,提出一种基于广义自助法的偏差修正方法。最后以三个月拆借期限的Shibor为样本进行实证分析。对于参数估计,本文对比分析了欧拉似然法和模拟似然法(SMLE),这两种方法都属于伪似然估计方法,其中,模拟似然法(SMLE)是欧拉似然法和蒙托卡罗方法的结合,具有更好的统计性质,但是计算复杂,欧拉似然方法则更简单和易于计算。当样本量不够大时,两种估计方法都存在较大的偏差。因此,我们提出一种新的基于广义Bootstrap的偏差修正方法。其基本思想是对似然函数赋予随机权重,构造加权似然函数,得到基于加权似然函数的新的参数估计值,以此估计出参数估计的偏差,最后进行偏差校正。通过随机模拟实验,我们发现这种方法在一定程度上能够降低欧拉似然估计的偏差。此外,本文对Shibor利率进行实证研究,估计出了8个常见短期利率模型的参数值,并进行了偏差校正。最后运用CIR模型对零息债券定价,分析利率期限结构,得出价格变动曲线和收益率变动曲线。
[Abstract]:Interest rate is the core variable in the financial market. In recent years, with the accelerating process of interest rate marketization in China, the theoretical and practical value of interest rate research has become increasingly prominent. This paper takes short-term interest rate as the object of study, and discusses the method of parameter estimation of single-factor short-term interest rate model. A deviation correction method based on generalized self-help method is proposed. Finally, the three-month loan term of Shibor as a sample for empirical analysis. For parameter estimation, Euler likelihood method (Euler likelihood method) and simulated likelihood method (SMLE), both of which belong to pseudo likelihood estimation method, are compared and analyzed in this paper. Among them, simulated likelihood method (SMLE) is a combination of Euler likelihood method and Monto Carlo method. It has better statistical properties, but the calculation is complicated, and the Euler likelihood method is simpler and easier to calculate. When the sample size is not large enough, there is a big deviation between the two estimation methods. Therefore, we propose a new bias correction method based on generalized bootstrap. The basic idea is to give random weight to likelihood function, construct weighted likelihood function, obtain new parameter estimation value based on weighted likelihood function, estimate the deviation of parameter estimation, and correct the deviation finally. We find that this method can reduce the deviation of Euler likelihood estimation to some extent. In addition, this paper makes an empirical study on Shibor interest rate, estimates the parameter values of eight common short-term interest rate models, and corrects the deviation. Finally, the CIR model is used to price zero interest bond, and the term structure of interest rate is analyzed, and the price change curve and yield change curve are obtained.
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F832.1

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