兰州大学机构库 >数学与统计学院
随机利率模型的应用实证分析
Alternative TitleEmpirical Analytic Applications of Stochastic Interest Rate Models
黄伟明
Thesis Advisor严定琪
2016-05-14
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword随机过程 Merton Carlo 最小二乘 二叉树
Abstract随着我国利率市场化进程的不断推进,以及固定收益证券理财市场的持续扩大,使得对动态利率期限结构的研究具有重大的现实意义。 本文通过随机过程理论引入随机利率模型。针对Ho-Lee、BDT两种典型的无套利随机利率模型,通过将固定付息债券转化成零息债券而得到市场价格数据,从而分别构建固定波动率参数和时变波动率参数假设条件下的利率及其价格二叉树模型,在Excel建模过程中采用单变量求解法和规划求解法求解非线性方程组,并且使用Merton Carlo模拟验证利率期限结构末端利率水平的分布特征。采用隔夜Shibor数据对Vasicek、CIR两均衡随机利率模型进行参数估计时,综合使用了WLS方法、对偶变量技术条件下的Merton Carlo模拟方法和条件方差公式。针对Vasicek模型预测的偏差,使用了ARIMA模型对数据进行重新拟合,并且做出了偏差的经济学解释。在放开对CIR模型固定波动率参数假设的前提下,引入了GARCH(1,1)模型结合极大似然估计法来估计时变波动率参数。通过使用模型对不同期限的Shibor数据进行拟合来验证利率期限结构的曲线形状。本文综合使用Excel、Eviews、Spss软件和Python语言来选取市场数据、估计模型参数、分析拟合结果。强调可操作性和实用性并举,通过模型描绘出动态利率的运动轨迹。
Other AbstractWith the development of the process of marketization of interest rates, and the continued expansion of fixed-income securities in the investment market, so as to have great practical significance to study the dynamic term structure of interest rates. This paper through the theory of stochastic processes to instruct stochastic interest rate models. For Ho-Lee, BDT two typical no-arbitrage stochastic interest rate model, and obtain market price data by converted fixed coupon bonds into zero-coupon bonds, which were constructed interest rate and price binomial model when volatility parameters fixed and variable parameters volatility in assumption, take single goal seeking and solver in Excel to solver nonlinear equations, and use Merton Carlo simulation and verification distribution of the end term structure of interest rates . When using the overnight Shibor data to estimate Vasicek, CIR two equilibrium stochastic interest rate model parameter under a combination WLS method, Merton Carlo simulation method for a coupling variable technical conditions and the conditional variance formula.For Vasicek model prediction error, we use the ARIMA model for data re-fitting and made of economics interpretation to deviations. Under the premise of the CIR model release fixed volatility parameter assumptions, take GARCH (1,1) model combines maximum likelihood estimation method to estimate the variable volatility parameter . By using different period Shibor date to fit the model to verify that the curve shape of the term structure of interest rates. This paper use Excel, Eviews, Spss software and Python languages to select market data, estimate model parameters, analysis the fitting results. It emphasizes operability and practicality simultaneously, through a dynamic model depicts the trajectory of interest rates.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224661
Collection数学与统计学院
Recommended Citation
GB/T 7714
黄伟明. 随机利率模型的应用实证分析[D]. 兰州. 兰州大学,2016.
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