Study On Market Characteristics Of China’s Stock Index Futures Based On Fractal Market Theory

This paper uses the main contracts and the weighting contracts to study China’s stock index futures market. Based on the nonlinear dynamical system theory—Fractal Market Theory, the paper tests the effectiveness of the market, revealing its fractal structural characteristics and analyze the dual-long-memory of the return series, as well as its volatility. Besides that, the paper also presents the various factors which impact the fractal structure of the China’s market.Firstly, the paper uses the single fractal analysis method ’R/S analysis method’ and’ V/S analysis method’ to compute the Hurst exponent, finding that the market is hardly efficient and does not comply with the Weak Efficient Market definition in the Efficient Market Theory.However, the market has an apparent fractal characteristics, along with long memory features, which means the current market price and information will have a continuing impact on the future and this will last longer. After that,this paper conducts the efficient testing and sensitivity testing for the R/S and V/S method and determine to use the R/S method to calculate the Hurst exponent of the market (HR/S),using as a measurement to the long memory of the return series.Secondly, the paper establishes the ARFIMA-FIGARCH models and ARFIMA-HYGARCH models to study the dual-long-memory of the stock index futures market. When selecting the residuals distribution, the author compares the results and the goodness of the four distributions(normal、GED、t distribution and skt distribution), finding that the t and skt distribution are more closer to the real residuals distribution. In order to choose the best models, this paper produces the VaR backtesting to compare the accuracy in predicting VaR of each model. According to the results, we find that there is no significant difference in risk prediction capability between FIGARCH and HYGARCH models. Within the same model, FIGARCH model has the same performance under t distribution and skt distribution;on the contrary, HYGARCH model has a better performance under skt distribution than t-distribution. After all, this paper finally choose the skt-ARFIMA-HYGARCH model and use the long memory parameter in variance equation(dHYGARCH-skt)as a measurement of volatility’s long-memory. Therefore, the ultimate Measurable Indicators of the overall market fractal characteristics, also known as long-memory, has already established, that is [HR/S, dHYGARCH-skt].Finally, the paper analyzes the impact factors of the fractal in China stock index futures market and groups the factors into general factors and special factors. In the end of the paper, from the whole conclusions the author gives some reasonable policy recommendations.