Study On The Multifractal Measurement Of Financial Market Risk

Financial market, as well as many other natural phenomena, is full of uncertainties and changes. However, man’s curiosity and exploration in the basic promotion laws behind them have never stopped. As an important component of national economic system, financial market exerts great impact upon social development of a country. The frequent outbreaks of financial crisis and abnormal price fluctuations in the market in recent decades are observed with wider ranges and deeper influence, and have brought the investors and regulators new challenges.More than a century ago, Bachelier from France introduced random walking into the pricing modeling of financial market. Since then, the continuous development of the exploration in financial theories has experienced mainly three stages:Old Finance, Modern Finance and New Finance. The Old Finance refers to studies of the financial market before the1960s, when the methods were primarily focused on the accounting information of individual companies, and there were no rigorous theoretical systems. The1960s came with the rapid rise of Modern Finance and has witnessed its fully occupation of financial research frontline. This type of research methodology is based on a series of strict assumptions, which includes participants’rationality, random waling price and independently and identically distributed yields. Based on these seemingly reasonable assumptions, many classic models and theories are applied widely both in academic researches and real practices. Fama summaried modern financial researches and introduced the "Efficient Market Hypothesis"(EMH), which has become the theoretical base of a full set of modern financial research framework, including corporate finance, assets pricing, investment decisions, and the like.With the development of market innovation and empirical research, many Anomalies of financial market that could not be explained within the Modern Finance framework are discovered. These anomalies in violation of the EMH are not the unique characteristics of particular market, but are generally found in markets of different regions and different levels of development, which raises the awareness and discussion of the operating laws of financial market and brings about the era of "New Finance".Behavioral Finance and Econophysics are two important representatives, both of which reject the hypothesis of rational investors and try to build a new theoretical foundation of financial research. With the knowledge of psychology and sociology, Behavioral Finance mainly investigates the connections between the psychological changes of investors and market prices fluctuations. Econphysics, however, adopts physical theories such as Nonlinear Dynamic, Statistic Physics and Complex System, to capture the movements of financial markets.Fractal theory is a relatively prominent method in Econophysics. It defines the complex graphics and phenomena that widely exist in nature and society. Fractal, especially Multifractal, is able to reveal much information while exploring things at different magnitudes, and has become a powerful tool to study complex movements, which, in financial market, are often displayed as fluctuations of prices and returns. With the help of Multifractal measures, new perspectives and methods could be obtained to study the financial complexity.Based on the research methods of Fractal Market Theory, this paper explores and analyzes the fractal and multifractal movement of price and returns with representative multifractal measure tools. And risk measurements are thus established according to the multifractal analysis. The main structure of research contents are organized as follows:1) Introduction. The overview of the background, the purpose and significance of the topic are put forward, as well as the contents and structure of this paper.2) Theoretical basis and research review. Theories in Modern Finance and financial risk management are introduced, along with the challenges from practical market. The birth and development of Econophysics are summarized. A brief report of relative research from home and abroad is presented.3) The distribution characteristics of the financial market. Descriptive statistics and normality tests of Shanghai Composite Index are introduced. 4) Multifractal characteristics of financial market. With the methods of Rescaled Range analysis, the persistence of financial market is empirically studied. The multifractal characteristics are empirically researched by employing Structure Partition Function.5) Multifractal measure and risk management. Two important indicators in Multifractal measurement are investigated with the methodology of Box-counting. New risk measurements based on Multifractal analysis are represented.6) Conclusion, inspiration and outlook. Conclusions of the research in this paper are given. Recommendations and outlook on the future direction and methods of this research are put forward.The innovations of this paper are:instead of focusing only on the Unifracal shape of financial market, both Unifractal and Multifractal characteristics of the market are empirically studied. Various methods of risk measurement based on Multifractal theory are put together to be comparatively analyzed.The research of this paper is mainly restricted by the availability of the timely high-frequent data, as well as author’s limited knowledge of basic Econopysics theories which includes physics, mathematics geometry and so on. This paper also lacks empirical test of the effectiveness of risk measurement proposed within the analysis, which would be the next phase of the research.