随机Ising金融系统的价格波动研究

发布时间：2018-05-18 07:32

本文选题：金融物理 + 随机Ising系统　；参考：《北京交通大学》2014年博士论文

【摘要】：全球化及互联网的发展使得金融市场的发展更加迅速,并渗入到人们日常生活工作的各个方面.从微观结构了解金融市场的形成机制及特征,对理解金融市场波动和管理金融风险有着很重要的作用.金融系统的复杂特性源于市场参与者之间的相互作用,研究这些参与者的行为对了解复杂系统的特性非常重要.因此,本文利用统计物理中的Ising动力学系统,建立投资者相互影响的金融市场模型来了解价格形成及影响机制,并定义了该模型对应的收益率时间序列.通过对所构建的金融模型进行计算机模拟,并对模拟的收益率序列进行统计分析,我们发现利用Ising系统建立的金融模型可以重现金融价格波动的重要特性,如尖峰厚尾性、收益率尾部的power-law特性、绝对收益率序列的长记忆性及收益率序列的多重分形等特性Ising动力学系统模型中个体参与者之间的相互作用给金融市场中动态变化和互惠关系给出了新的见解.这个跨学科建模的成功,意味着有自然界存在着的物理共同点并值得我们去探索.全文的组织结构如下：第一章中,介绍研究的背景和意义及本文的研究内容和创新点. 第二章中,着重介绍Ising系统的起源和发展,二维Ising系统的定义及特性,最后说明如何将随机Ising系统及其机制应用于构建金融市场价格模型. 第三章中,在二维随机Ising自旋模型的基础上建立金融市场的价格模型,将投资者每一天的受影响强度随机化.在边界分别为零边界、弱边界及强边界的情况下,建立了相应的金融模型.不同的边界代表着不同的投资环境.为了对比模拟的数据和实际金融市场的数据,我们分析了上证综合指数,深证成分指数和沪深300指数对应的收益率序列的统计特性,如波动聚集性、厚尾现象,绝对收益率尾部的power-law分布和分形现象.当边界全为正边界,即τ6的时候,深度参数y比零边界τ1和弱混合边界τ2,τ3要小,并且τ6的尾部指数变化范围比其它五种边界条件要小. 第四章中,我们用随机Ising模型研究金融收益率序列的波动性,并且把我们的研究结果和中国证券市场过去22年的实证结果进行比较,找出判别股市中大的和小的风险的临界点.从模型的微观角度,我们解释了波动率是如何变化的,这可以给金融市场的风险管理提供一定的建议. 第五章中,我们在Sierpinski格点地毯上使用Ising自旋模型建立金融模型.分形现象在自然界中普遍存在,分形格点的引入打破了每个投资者所受影响来源都是四个邻居的情况.为了研究此金融模型的波动特性,我们用Monte Carlo模拟和数值研究方法,以及统计分析和多重分形分析来研究金融时间序列.不同大小的Sierpinski格点地毯和Ising动态的受影响强度来得到不同的多重分形谱.我们还研究模拟价格序列、上证综合指数、深证成分指数、道琼斯工业平均指数、纳斯达克综合指数、SP500指数、恒生指数及日经225指数对应的收益率序列的统计特性,随时间变化的波动聚类现象和多重分形特性等.研究表明Sierpinski格点地毯上的金融模型可再现经验数据的重要特征. 第六章中,基于金融市场中投资者之间的相互作用及投资环境的影响,应用Ising动力学系统和平均场理论建立了符合股市特点的股市价格方程.借助于计算机软件Matlab,用Monte Carlo模拟方法,通过调整金融模型中的参数得到收益率序列.分析发现Ising动力系统构造的收益率同证券市场股票指数波动率—样具有尖峰厚尾等统计特征.对模拟收益率原序列及混洗后的序列进行多重分形分析,我们发现模拟收益率序列存在分布多重分形和相关性多重分形的结论. 第七章是对本论文的总结及工作的展望.
[Abstract]:The development of globalization and the Internet has made the development of the financial market more rapid and permeated all aspects of people's daily life. Understanding the formation mechanism and characteristics of the financial market from the micro structure is very important for understanding the volatility of the financial market and managing the financial risks. The complex characteristics of the financial system are derived from market participation. The interaction between the participants is very important to understand the characteristics of the complex systems. Therefore, this paper uses the Ising dynamic system in statistical physics to establish a financial market model with mutual influence by investors to understand the mechanism of price formation and influence, and to define the corresponding return time series of the model. On the basis of the computer simulation of the established financial model and the statistical analysis of the simulated return sequence, we find that the financial model established by the Ising system can reproduce the important characteristics of the volatility of the financial price, such as the peak thick tailing, the power-law characteristics of the return rate tail, the long memory and the order of return of the absolute return sequence. The interaction between individual participants in the Ising dynamic system model of multi fractal and other characteristics gives new insights into the dynamic and reciprocal relationships in the financial market. The success of this interdisciplinary modeling means that there are physical common points in nature and deserve our exploration. The structure of the full text is as follows:
In the first chapter, we introduce the background and significance of the study, as well as the research contents and innovations of this paper.
In the second chapter, we focus on the origin and development of the Ising system, the definition and characteristics of the two-dimensional Ising system, and finally explain how to apply the random Ising system and its mechanism to the construction of the price model of the financial market.
In the third chapter, the price model of the financial market is built on the basis of the two-dimensional random Ising spin model, and the investor's affected intensity is randomised every day. In the case of zero boundary, weak boundary and strong boundary, the corresponding financial model is established. The different boundary represents different investment environment. Data and real financial market data, we analyze the statistical properties of the Shanghai Composite Index, the deep evidence component index and the Shanghai and Shenzhen 300 index, such as volatility aggregation, thick tail phenomenon, the power-law distribution and fractal phenomenon at the tail of absolute return. When the boundary is all positive boundary, that is, Tau 6, the depth parameter is y to zero. The boundary tau 1 and the weak mixing boundary 2, tau 3 are small, and the tail index of tau 6 is smaller than the other five boundary conditions.
In the fourth chapter, we use the random Ising model to study the volatility of the financial return sequence, and compare our results with the empirical results of the Chinese stock market for the past 22 years to find out the critical point of identifying the large and small risks in the stock market. From the microscopic perspective of the model, we explain how the volatility is changing, which is possible. In order to provide some suggestions for risk management in financial market.
In the fifth chapter, we use the Ising spin model on the Sierpinski lattice carpet to establish a financial model. The fractal phenomenon is common in nature. The introduction of fractal lattice breaks the situation that each investor is affected by four neighbors. In order to study the volatility of the financial model, we use Monte Carlo to simulate and value the numerical value. Research methods, statistical analysis and multifractal analysis to study the financial time series. Different sizes of Sierpinski lattice carpet and the affected intensity of Ising dynamics are different multifractal spectra. We also study the simulated price series, the Shanghai Composite Index, the deep evidence component index, the Dow Jones industrial average index, the NASDAQ ensemble. The statistical properties of the index, the SP500 index, the Hang Seng Index and the 225 index of the Nikkei index, the fluctuation clustering and the multifractal characteristics with time change, show that the financial model on the Sierpinski lattice carpet can reproduce the important characteristics of the empirical data.
In the sixth chapter, based on the interaction between investors and the influence of the investment environment in the financial market, the stock market price equation is established by using the Ising dynamic system and the mean field theory. With the help of the computer software Matlab, the return sequence is obtained by adjusting the parameters in the financial model by using the Monte Carlo simulation method. The analysis found that the yield of the Ising power system and the stock index volatility - the stock index volatility has the statistical characteristics of peak and thick tail and so on. The multiple fractal analysis of the original sequence of simulated return and the sequence of mixed washing is carried out, and we find that there is a conclusion that there is a multi fractal distribution and a correlation multifractal in the simulated return sequence.
The seventh chapter is the summary of the thesis and the prospect of the work.
【学位授予单位】：北京交通大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：F830.91;F224

【参考文献】