多重分形视角下中国股市波动建模研究

发布时间：2018-02-26 10:16

本文关键词： 多重分形杠杆效应跳跃波动建模 ES　出处：《福州大学》2014年硕士论文　论文类型：学位论文

【摘要】：随着非线性科学的发展,多重分形因能细致分析不同标度下的不同幅度波动而被广泛应用于金融市场时间序列复杂性的研究,这不仅是对传统意义上金融市场复杂性的进一步探索,也为更深层次的挖掘金融市场的内在规律提供了又一新的方法与工具。因此,利用多重分形这一金融市场的固有特性刻画研究金融价格波动行为也越来越受到关注。在以往文献研究的基础上,本文以上证综合指数为研究对象,在多重分形视角下对中国股市的波动建模进行研究,主要工作和结论阐述如下：一、利用多重分形谱法确认多重分形特性,并通过多重分形谱参数与指数波动、收益率变动的关联性入手分析,发现△a可在一定程度上量度股价波动和收益率变动,此外,进一步在打乱序列削弱多重分形强度的情况下检验△a与股价波动的对应性,初步证实△a在波动度量上的可行性和有效性,为下一阶段利用所提取的多重分形指标量化波动风险提供实证支持；二、在前文确认谱参数△a对波动度量存在有效性的前提下,针对修正因子的不足,改进了多重分形波动率测度,并建立了反映多重分形波动特征的ARFIMA模型和HAR模型,实证研究证实：中国股市具有显著的长记忆性、杠杆效应和波动异质性,而样本外预测的实证结果表明：基于多重分形的波动模型是比GARCH类模型更有效的预测模型,而改进的多重分形波动率测度更能有效地估计波动率,并且HAR-L-lnMFVt模型预测效果优于ARFIMA-L-lnMFVtt模型,为下文的多重分形波动的建模优化和风险度量应用奠定基础；三、参照二次变差理论,对改进的多重分形波动率进行跳跃方差序列的剥离,并以前文有效波动模型的选择为基础,构建考虑跳跃因素的HAR-lnMFVt-CJ和HAR-L-lnMFVt-CJ模型进行拟合预测及ES度量分析,实证结果表明：无论跳跃成分显著与否,其都在一定程度上具有优化模型拟合优度的作用,并且随着期限的增加,跳跃成分对多重分形波动率拟合预测作用的显著性逐渐上升,此外,无论是在拟合、预测上,还是ES度量中,HAR-L-lnMFVt-CJ模型都最优,从另一侧面更坚定了改进的多重分形波动率的有效性及其在风险管理应用中的可行性。本论文是国家自然科学基金资助项目《基于已实现测量非参数方法的金融资产跳跃行为研究》(NO.71171056)的阶段性研究成果。
[Abstract]:With the development of nonlinear science, multifractal is widely used to study the complexity of time series in financial markets because of its ability to analyze the fluctuation of different amplitude under different scales. This is not only a further exploration of the complexity of the financial market in the traditional sense, but also provides a new method and tool for further exploring the inherent laws of the financial market. The use of multifractal, which is the inherent characteristic of financial market, to characterize the behavior of financial price volatility has attracted more and more attention. Based on the previous literature, this paper takes the Shanghai Composite Index as the research object. In this paper, the volatility modeling of Chinese stock market is studied from the perspective of multifractal. The main work and conclusions are as follows: firstly, multifractal spectrum method is used to confirm multifractal characteristics, and multifractal spectrum parameters and exponential fluctuations are used. Based on the analysis of the correlation of the variation of return rate, it is found that a can measure the fluctuation of stock price and yield to a certain extent. In addition, the correspondence between a and volatility of stock price is tested when the multifractal intensity is weakened by disordering sequence. The feasibility and effectiveness of a in volatility measurement are preliminarily confirmed, which provides empirical support for the next stage to quantify volatility risk by using the extracted multifractal index. On the premise of confirming the validity of spectral parameter a to the volatility measure, the multifractal volatility measure is improved, and the ARFIMA model and HAR model are established to reflect the multifractal volatility characteristics. The empirical results show that the Chinese stock market has significant long memory, leverage effect and volatility heterogeneity. The empirical results show that the volatility model based on multifractal is more effective than the GARCH model. The improved multifractal volatility measure can estimate volatility more effectively, and the prediction effect of HAR-L-lnMFVt model is better than that of ARFIMA-L-lnMFVtt model, which lays the foundation for modeling optimization and risk measurement application of multifractal volatility. Thirdly, referring to quadratic variation theory, The improved multifractal volatility is peeled off from the jump variance series, and based on the selection of the previous effective volatility model, the HAR-lnMFVt-CJ and HAR-L-lnMFVt-CJ models considering jump factors are constructed for fitting prediction and es metric analysis. The empirical results show that, no matter whether the jump component is significant or not, it has the function of optimizing model fit to a certain extent, and with the increase of term, the significance of jump component on multifractal volatility fitting prediction is gradually increased. In addition, HAR-L-lnMFVt-CJ model is optimal in fitting, forecasting and es measurement. The validity of the improved multifractal volatility and its feasibility in the application of risk management are strengthened from the other side. This paper is a project funded by the National Natural Science Foundation of China < Finance based on the realized measurement non-parametric method. Research on leaping behavior of assets. (no. 71171056).
【学位授予单位】：福州大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F832.51;F224

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