Research On Micro Fluctuations Of Chinese Stock Markets Based On Fractal Feature

From Markowitz' Portfolio Theory to Sharp'Capital Asset Pricing Model,then to Black – Scholes' Option Pricing Model,these classic models are based in Efficient Market Hypothesis(EMH).The real capital market is not as efficient as EMH described,and empirical researches show that: asset price volatility has memory;asset price is not normally distributed and shows leptokurtosis;market price information is not being fully reflected and the same market information may have different meanings for different investors;not all the market investors are rational thus market price would rather be non-linear.The Black Monday of global stock market,October 19,1987,financial tsunami triggered by subprime mortgage crisis in 2007,flash collapse of US stock market in 2010,thousand shares reached daily limitup and limitdown durning June to August in 2015,twice blown phenomenon of A share durning 2016 January 4th and 6th,show that the frequency of abnormal fluctuations in global capital markets,particularly in A share challenge hypothesis of effective market equilibrium model greatly.As Efficient Market Hypothesis lacks of assumptions and characterization of non-equilibrium market,it is necessary to explore the value of other doctrines.Since Mandelbrot(1967)found long memory and other features of asset price volatility,and proposed the concept of fractal,the fractal theory has evolved into one of the most popular tools for asset price fluctuation analysis.Peters(1991)constructed Fractal Market Hypothesis(FMH)based on the fractal theory to make up the defect of the EMH.FMH could explain the formation mechanism of liquidity in the market from an investor point of view of non-homogeneity,stability and further characterization of market price fluctuations.Fractal Market Hypothesis holds that the local randomness of markets and the overall uncertainty coexist and diversified investment logics may form fractal structure to ensure the market has sufficient stability.While the market once lost fractal structure and multi-investment logics,market crash may occur.Financial market microstructure has been the focus in the field of financial research.Traditional empirical study is based on daily or weekly frequency data.These frequency data lost a large number of market information,and the research results are not complete.As computer storage capacity and computing power grow speedly,more accurately high-frequency data which record the original features of the high-frequency market become easier to obtain and process,thus it's capable to research high-frequency financial market microstructure.Since the 1970 s,scholars learn that the duration of intra-day trading(duration is the time interval between two successive intra-day trading)has been ignored before,could be a new research content in the high-frequency micro-data and then carry out the inherent characteristics of volatility model and forecasting model,as well as the correlation between the duration and the price or volume.Duration reflects liquidity of assets in some perspective is able to bring new ideas to model pricing and forecasting pattern.As the duration of high frequency data posses both feature traditional of low frequency data,such as leptokurtosis,volatility clustering,fractal characteristics,and some features that low frequency data does not have,such as irregular intervals,negative sequence correlation and mass number.Engle and Rusell(1998)proposed Autoregressive Conditional Duration(ACD)model,and ACD has become the mainstream method for researching duration.As ACD model fails to consider the fractal characteristics of durations,it is necessary to establish a model that has fractal properties.Taking into account that duration could be a new indicator that reflects liquidity and investors' enthusiasm,this paper will continue to model duration into the return volatility model for improving the characterizing effects of fractal characteristics and pridicting effects,and further propose a high-frequency financial risk management tools.Additionally,this article will also explore the sources of fractal characteristics from the structure of investors and trading logic to provide a realistic basis and understanding of preceding theoretical analysis and empirical analysis.This article tested fractal characters of A-share market,from the traditional low frequency(index,individual stocks)to a high frequency return and high frequency duration based on three angles.This paper find that the logic of investor decision determines the fractal characteristics of yields from the transaction duration,highlighting the duration model from a fractal point of view,the value of information of duration into the return volatility computing,the necessity of risk management tools to build based on high frequency intraday duration.The paper then confirme Markov Switching Multifractal duration model(MSMD)could characterize fractal characteristics and long memory.MSMD model establish a multi-level Markov Update process to fit the different duration fluctuation fluctuation levels.This paper propose MSMD-GARCH model,which can well describe relationship of yield and duration and find that the structure of investors and trading patterns impact the stock price and trading liquidity,thus the formation of fractal characteristics of securities.The empirical data show that MSMD-GARCH is significantly better than ACD-GARCH forecasting return based on forecast error.As MSMD-GARCH owns good predictive ability,MSMD-GARCH-VaR is proposed for micro-finance risk management solutions.Empirical findings show that the out of sample breakthrough rate of MSMD-GARCH-VaR ranges from 4-17% which is relatively low and is significantly lower than GARCH-Va R,thus MSMD-GARCH-VaR could be a better high-frequency intraday risk management tools for its robustness and effectiveness.Finally,this paper explores the sources of fractal by improved fractal market hypothesis to get a realistic basis for the understanding and application of fractals.