The Research On Volatility Modeling Of China’s Stock Market In The Perspective Of Multifractal

With the development of nonlinear science, multifractal is widely used in the research on the complexity of financial market’s time series since it can careful analyse different amplitude fluctuation under different scale, which is not only a further exploration to the complexity of financial markets in the traditional sense, but also the provision of a new method and tool for digging deeper the inherent law of financial markets. Therefore, depicting and researching the fluctuation behavior of financial price by the use of multifractal which is the intrinsic characteristics of the financial markets is attracting more and more attention.On the basis of the previous literature researches, this paper chooses the Shanghai composite index as the research object, and research on the volatility modeling of China’s stock market in the perspective of multifractal, the main work and conclusions are listed as follows:Firstly, the paper uses the method of multifractal spectrum to confirm multifractal characteristics, and reveals that Aa in a certain extent can measure the volatility of share price and yield by analysing the correlation between the multifractal spectrum parameters and the index fluctuation as well as the yield fluctuation, in addition, the paper further tests the correspondence of Aa and volatility in the share price under the condition of disturbing sequence to weaken the multifractal strength, which preliminarily confirms the feasibility and effectiveness of Aa used on volatility measurement, providing the empirical support for the next phase to use the extracted multifractal indicators in quantifying volatility risk.Secondly, under the premise of making sure that the spectrum parameters have effectiveness on the fluctuation measurement in the above article, aiming at the shortcomings of the correction factor, the paper adjusts the multifractal volatility measure, and establishes ARFIMA models and HAR models reflecting the multifractal characteristics. The empirical studies confirm that the stock market of China has significantly long memory, leverage effect and heterogeneous volatility. The empirical results from out-of-sample forecasts show that the models based on multifractal volatility are more effective forecasting models than the GARCH family models and that the adjusted multifractal volatility measure provides more effective volatility estimation. It also shows that HAR-L-lnMFVt model has better forecast effect than that of ARFIMA-L-lnMFVt model, laying the foundation for the below modeling optimization of the adjusted multifractal volatility and its applications in risk measurement.Thirdly, with reference to the quadratic variation theory, the paper strips the jump variance sequence from the adjusted multifractal volatility, and then on the basis of choosing the effective volatility model in the above article, the paper establishes HAR-lnMFVt-CJ and HAR-L-lnMFVt-CJ models considering the factor of jump for fitting and forecast as well as ES measurement analysis. The empirical results show that no matter whether the jump component is significant or not, it is to a certain extent having an effect on optimizing the models’goodness of fit. Moreover, the significant effect of jump component on multifractal volatility fitting and forecast rises gradually with the increase of time. In addition, HAR-L-lnMFVt-CJ model is optimal no matter used for the fitting, forecast or the ES measurement, which from the other side further confirms the effectiveness of the adjusted multifractal volatility and its feasibility in risk management application.The research is sponsored by National Natural Science Foundation of China: Research on Jump Behavior of Financial Assets Based on Realized Measurement Methods (NO.71171056).