The Study On Volatility Of Futures Based On Logistic Distribution GARCH Models

Modern financial activities is a capital trading system which mainly includes futures market, stock market and foreign exchange market. Systemic risk is unavoidable in the stock market, but in the futures market systemic risk could be effectively avoided.Futures market provides hedging for spot dealer. At the same time futures market could create profits for investors. Therefore, accurate analysis of fluctuations in the futures market is the fundamental of the healthy development of China’s future market, and the analysis also is one of the core problems in finance research.Firstly, this paper introduce the relevant theories for the calculation method of the financial assets return and the distribution characteristics theory, then discussed the differences between simple returns and log returns rate; next we mainly introduce the characteristics and expressions of GARCH models, which included the ARCH model,GARCH model, GARCH-M model, non-symmetric GARCH and IGARCH model.Application of maximum likelihood estimation method investigates the parameters of ARCH model, GARCH model and EGARCH model.Secondly, this paper discusses the properties of the Logistic distribution. We analyze the difference of the original data that is based on the SHFE futures copper of1159 days transaction date, then we get the logarithm yield rate. Through analysis sample data of logarithmic returns rate trend figure and column-like Figure,we found that returns rate has Volatility clustering and limited interval distribution features;Through Normality tests and QQ figure test, we can see Logistic distribution is better than normal distribution to intend collection SHFE period copper of day closing logarithmic returns rate of actual distribution. Through GARCH models test, we found that SHFE returns rate has Spikes heavy tails, leverage effect", and the asymmetryfeatures.Finally, this paper compared the difference of the assumed normal distribution,GED distribution and Logistic distribution, using the GARCH(1,1) model,EGARCH(1,1) model and TGARCH(1,1) model analysis simulation empirically of the logarithm of SHFE copper futures. Through analysis parameter of estimated volume and4 errors statistics volume(MSE, MAE, RMSE, MAPE), we get that Logistic distribution three species model of intends collection effect is better than GED distribution and distribution of intends collection effect, and Logistic distribution GARCH(1,1) in forecast capacity SHFE is better than distribution GARCH(1,1). In the identical species distribution, EGARCH(1,1) model and TGARCH(1,1) model are more accurate than the GARCH(1,1) model.