金融市场风险的多分形测度指标研究

发布时间：2018-05-06 02:25

本文选题：分形理论 + 多分形测度　；参考：《西南财经大学》2013年硕士论文

【摘要】：金融市场与自然界中的很多现象一样,瞬息万变,充满了不确定性,然而人们对事物运行规律的好奇心和探索从来没有停止,总是试图从繁乱复杂的现象中总结出简单而富有解释力的成因。由于金融市场往往关系到一个国家的经济发展程度和健康水平,保持它的平稳运行关系到国计民生甚至生活水平的基本保障,因此对金融市场的把握和预测显得尤为重要。特别是近几十年来,金融危机频频爆发,市场的大幅异常波动时有发生,波及范围越来越广,影响程度也随之加深,给投资者和监管机构的金融风险管理工作带来了新的挑战。自从法国人Bachelier将随机游走模型引入金融市场中资产价格的变化行为后,一个多世纪以来,对金融市场理论的探索不断发展,主要经历了三个阶段：“旧金融学”(Old Finance)阶段,“现代金融学”(Modern Finance)阶段以及“新金融学”(New Finance)阶段(魏宇,2004)。20世纪60年代以前的金融学研究称为“旧金融学”阶段,这一时期主要研究对象着重针对单个的市场参与者,利用其公司或机构的财务报表一类的会计信息进行分析,而没有对市场整体做出系统的研究,也缺乏严谨的理论体系。20世纪60年代后,“现代金融学”迅速崛起,很快就全面占领了金融市场研究的前线。这一类研究方法主要是基于一系列的假定,其中包括投资参与者理性、价格的随机游走、收益率服从独立同分布等等。通过这些看似合理简单的假设,将市场信息和市场资产的运动规律结合起来,产生了许多经典实用的模型和理论,至今仍为理论界和实务界所广泛运用。Fama将经典的现代金融学研究进行总结归纳,提出了“有效市场假说”(Efficient Market Hypothesis, EMH),众多以此为基础、研究范围涉及公司金融、资产定价以及投资决策的理论模型蓬勃发展,形成了一整套现代金融市场研究的体系框架。但随着市场创新发展的加速和实证研究的深入,人们发现了许多在经典金融市场理论条件下无法得到解释的金融市场“异象”(Anomalies)。这些违反有效市场假说的异常现象并不仅仅存在于某个特殊市场,而是普遍表现在各个不同地区、不同发展程度的市场中,因此动摇了EMH理论的成立基础。由此引发的对金融市场运行规律的重新认识和探讨,便开创了“新金融学”研究的时代。 “新金融学”的主要代表是行为金融学(Behavioral Finance)和经济物理学(Econophysics)。二者都摈弃了现代金融学中的投资者理性假说,试图从新的理论基础开始解释市场运行的规律。行为金融学主要考察投资者在市场中的心理变化与市场中资产价格走势的联系,包含了心理学、社会学等学科的知识。而经济物理学则把金融市场看作是一个非线性的复杂系统,结合物理学、几何学和经济金融学的知识,特别是物理学中的统计物理学(Statistic Physics)和复杂系统(Complex System)等理论方法来解释市场运动的特征及规律。经济物理学中比较突出的研究是利用分形(Fractal)理论来研究市场。分形定义的是自然界和社会中广泛存在、复杂无序而又具有某些规律的图形和现象。它能够探讨事物在多个测度空间上的自相似性,从局部的随机到整体的确定,是帮助认识许多复杂运动现象的有力工具。分形中的多分形(Multifractal)更是可以让我们在不同程度的测度范围内观察事物的多种变化特征,而这种方式正好符合金融风险管理中对资产价格(收益率)的波动特征进行细致全面剖析的要求。通过多分形的测度工具和分形市场理论对市场的重新认识,对市场运行规律的把握和解释便拥有了全新的视角和方法。本文基于分形市场理论的研究方法,对我国金融市场中的价格(收益率)分形运动特征进行了探讨和分析,形成了具有代表性的分形和多分形测度工具,并将之用于金融风险管理的实际指标构建中。文章的主体结构安排如下：第一章为绪论。主要概括介绍了选题背景,选题目的和意义,以及文章的内容与结构。第二章介绍理论基础及研究现状。梳理了本文涉及的有效市场假说理论,多分形的概念和分形市场理论以及风险管理相关理论。同时将国内外在这些方面的研究成果及本文的研究基础做了简要汇报。第三章介绍金融市场收益率的分布特征。主要针对以上证综指(SSCI)为代表的我国金融市场资产价格收益率做了描述性统计和正态检验。第四章介绍金融市场的多分形特征。主要用使用重标极差分析法(R/S方法)计算了H指数来验证我国市场收益率的持久性特征,然后使用结构化分割函数(Structure Partition Function)检验了多分形形态的存在性。第五章介绍金融市场的多分形测度研究和风险管理研究。用数盒子(Box-counting)的方法计算了多分形测度中的两个重要指标：奇异指数和多分形谱,并运用它们建立了新的风险测度指标,对其在金融风险管理中的作用和前景做了介绍。第六章为结论、启示和展望。总结论文研究结果以及得到的启示和不足,对以后的研究方向和方法提出建议和展望。本文的创新之处主要有：一是同时考察了市场收益率的分形和多分形特征,不同于以前多数文章只注意到了市场的单分形形态,本文通过实证验证检验了我国市场的确具有多分形的特征。其次是对多分形风险管理指标的综合创新,将奇异指数的宽度、多分形谱的宽度和奇异指数的标准差放在一起进行比较研究,考察了基于不同测度指标的风险管理办法。本文的不足之处主要是：文中所使用数据的及时可得性有一定的局限。这是由于股市高频数据库的数据比较难以获得,指数价格的高频数据更有一定的滞后。此外,文中对分形理论的基础证明并未展开详细阐述,只是做了基本介绍。由于分形理论设计的范围包括物理学、几何学、金融学等多个学科的融合,其方法的说明受到了作者知识的局限,因而略去了基础理论而直接将其运用到了金融市场的实证计算当中。最后,文章对于多分形测度指标在风险管理中的运用虽然进行了阐述,却未能对其在实际市场中的指导能力和有效性做实证方面的检验,这是文章较为遗憾的地方,也是作者下一步打算研究的主要方向。
[Abstract]:The financial market, like many phenomena in nature, is rapidly changing and full of uncertainty. However, the curiosity and exploration of the rules of the operation of things have never stopped, and they always try to sum up a simple and explanatory cause from the complicated and complicated phenomena. Because the financial market is often related to the economic development of a country. The level and health level, keeping its smooth operation related to the basic guarantee of the national economy, the livelihood of the people and even the standard of living, so it is particularly important to grasp and predict the financial market. In depth, it brings new challenges to financial risk management for investors and regulators.
Since French Bachelier introduced the random walk model to the change of asset price in the financial market, the exploration of financial market theory has been developing for more than a century. It has undergone three stages: the "Old Finance" stage, the "Modern Finance" stage and "the new finance" (N). The EW Finance) phase (Wei Yu, 2004) the financial studies before the 60s of the.20 century is called the "old finance" stage. This period mainly focuses on individual market participants, analyzing accounting information such as the financial statements of their companies or institutions, without systematic research on the market as a whole, and lack of a systematic study. A rigorous theoretical system, after the 60s.20 century, the rapid rise of "modern finance" has quickly occupied the front line of financial market research. This kind of research method is mainly based on a series of assumptions, including the rationality of the investment participants, the random walk of the price, the rate of return obeying the independent distribution, and so on. By combining the market information with the movement of market assets, many classical and practical models and theories are produced. So far, the classical modern finance research is summarized by.Fama, which is widely used by the theory and practice circles, and the "Efficient Market Hypothesis (EMH)" is put forward. On the basis of this, the theoretical models of the scope of research involving corporate finance, asset pricing and investment decision-making have flourished and formed a whole system framework for the research of modern financial markets.
However, with the rapid development of market innovation and the deepening of empirical research, many financial markets "Anomalies" which can not be explained under the classical financial market theory are found. These abnormal phenomena which violate the effective market hypothesis are not only in a particular market, but generally in different regions. In the market of different levels of development, the foundation of the EMH theory has been shaken up, and the re recognition and discussion of the rules of the operation of the financial market have initiated the era of "new finance".
The main representatives of "new finance" are behavioral finance (Behavioral Finance) and economic Physics (Econophysics). All two discarded the rational hypothesis of investor in modern finance and try to explain the law of market operation from the new theoretical basis. The behavioral finance owners should examine the psychological changes and market of investors in the market. The relationship between the price trend of the asset price includes the knowledge of psychology, sociology and other disciplines. Economic physics regards the financial market as a nonlinear complex system, combining the knowledge of physics, geometry and economics and finance, especially the Statistic Physics and the complex system (Complex System) in physics. Theoretical methods are used to explain the characteristics and laws of market movements.
The more prominent research in economic physics is to use the Fractal theory to study the market. The fractal definition is the graphics and phenomena that exist in nature and society, which are complex and unordered and have some laws. It can discuss the self similarity of things in multiple measure spaces, and it is helpful to determine from local random to whole. The multifractal (Multifractal) in fractal can also allow us to observe a variety of changes in the range of measurement in a different degree of measurement, and this way is exactly in line with the requirements of the detailed and comprehensive analysis of the volatility characteristics of the asset price (rate of return) in the financial risk management. The multifractal measure tool and the fractal market theory have a new perspective and method to understand the market and grasp and explain the operation rules of the market.
Based on the research method of fractal market theory, the fractal movement characteristics of price (rate of return) in China's financial market are discussed and analyzed, and a representative fractal and multi fractal measure tool is formed and used in the construction of the actual index of financial risk management. The main body structure of the article is as follows:
The first chapter is the introduction, which mainly introduces the background of the topic selection, the purpose and significance of the topic, and the content and structure of the article.
The second chapter introduces the theoretical basis and the research status. It combs the theory of effective market hypothesis, the concept of multifractal, the fractal market theory and the related theory of risk management, and briefly reports the research results at home and abroad and the foundation of this study.
The third chapter introduces the distribution characteristics of the rate of return in the financial market. This paper makes a descriptive statistics and a normal test on the rate of return on the asset price of our financial market, which is represented by the SSCI.
The fourth chapter introduces the multi fractal characteristics of the financial market. The H index is used to verify the persistence characteristics of the market returns in our country by using the R/S method (R/S method), and then the existence of the multifractal morphology is tested by using the structured partition function (Structure Partition Function).
The fifth chapter introduces the research of multifractal measurement and risk management in financial markets. By using Box-counting, the two important indexes in multifractal measure are calculated: singular index and multifractal spectrum, and a new index of risk measurement is established by using them, and the role and prospect in the financial risk management are introduced.
The sixth chapter is the conclusion, inspiration and prospect. It summarizes the research results and the enlightenment and shortage of the paper, and puts forward suggestions and prospects for future research directions and methods.
The main innovations of this paper are as follows: first, the fractal and multi fractal characteristics of market returns are examined at the same time. Unlike most of the previous articles, only the single fractal morphology of the market is paid attention to. In this paper, the characteristics of multi fractal in China's market are verified by empirical verification. Secondly, the comprehensive innovation of the multi fractal risk management index will be made, and the second is the comprehensive innovation of the multi fractal risk management index. The width of the singular exponent, the width of the multifractal spectrum and the standard deviation of the singular exponent are compared, and the risk management method based on the different measure indexes is investigated.
The shortcoming of this paper is that the timely availability of data used in this paper is limited. This is because the data comparison of the high frequency database in the stock market is difficult to obtain, and the high frequency data of the index price is lagging behind. In addition, the basic proof of the fractal theory is not expounded in detail, but the basic introduction is made. The scope of fractal theory design includes the integration of many disciplines such as physics, geometry, finance and other disciplines. The explanation of the method is limited by the author's knowledge, so the basic theory is omitted and applied directly to the empirical calculation of the financial market. Finally, the article is on the use of the multi fractal measure index in risk management. However, it has been expounded, but not the empirical test of its guidance ability and effectiveness in the actual market, which is a more regrettable place in the article, and the main direction of the author's next study.

【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;F224

【参考文献】