基于尺度混合方法随机波动模型的贝叶斯模拟及应用

发布时间：2018-01-10 13:23

本文关键词：基于尺度混合方法随机波动模型的贝叶斯模拟及应用　出处：《长春工业大学》2014年硕士论文　论文类型：学位论文

【摘要】：实际的金融或经济时间序列都存在着较普遍的波动性,因此波动性是金融市场所要研究的核心问题,并且通过对波动性的研究来预测时间序列的走向,波动性可以通过金融收益率的方差来测度。波动率中包含了市场变动和投资风险的信息。现实的金融市场里,资产收益率序列的波动性经常表现出“波动聚集”、波动率以连续的方式随时间变化、波动率不发散到无穷即波动率在固定的范围内变化、波动率对价格大幅上升和大幅下降的反应不同即“杠杆效应”的特点,资产收益率的分布也表现出“高峰厚尾”的特性。在第二章中研究了贝叶斯理论、MCMC算法及吉布斯抽样、介绍了本文所使用的软件基本内容和模型判断准则；在第三章分析了随机波动率(SV)模型的提出及发展,给出了常见的SV模型,详细推导了本文所用到的模型,研究了该模型的基本性质,并对模型进行了模拟分析；在第四章我们对上证综指和深圳成指进行了实证分析,首先对两市的收益率进行了预处理和描述性统计分析,发现两市的收益率都存在尖峰厚尾的性质。然后利用本文中的模型对两市分别进行研究,在两个股指中都找出了波动的异常值,这些异常值有些来自于收益,有些则来自于不可测的波动。
[Abstract]:The actual financial or economic time series have more general volatility, so volatility is the core issue to be studied in financial markets, and through the study of volatility to predict the trend of time series. Volatility can be measured by the variance of financial returns. Volatility contains information about market movements and investment risks. The volatility of asset return series often shows "volatility aggregation", volatility changes with time in a continuous way, volatility does not diverge to infinity, that is, volatility changes in a fixed range. The characteristics of "leverage effect" are different from the response of volatility to the sharp rise and fall of price. The distribution of asset return also shows the characteristic of "peak and thick tail". In the second chapter, Bayesian theory is studied. MCMC algorithm and Gibbs sampling, introduced the basic contents of the software used in this paper and model judgment criteria; In the third chapter, we analyze the development and development of the SVV model, give the common SV model, deduce the model used in this paper in detail, and study the basic properties of the model. The model is simulated and analyzed. In chapter 4th, we do empirical analysis on Shanghai Composite Index and Shenzhen Composite Index. Firstly, we do pre-processing and descriptive statistical analysis on the return rate of the two markets. It is found that the return rate of the two cities has the property of peak and thick tail. Then we use the model in this paper to study the two cities, and find out the abnormal value of volatility in the two stock indexes, some of which come from the return. Some come from unpredictable fluctuations.
【学位授予单位】：长春工业大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F832.51;O212.8

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