The Research And Forecast On The Intraday Volatility Of The Stock Index Futures Based On GARCH Models

Volatility is one of the most important attributes of financial derivatives.It is an important basis for pricing,asset allocation,risk management and trading strategy formulation of financial derivatives,which has always been a hot topic in financial research.On one hand,duing to the continuous development of information technology,high frequency data which contain more market information can be obtained more easily,and the study of volatility has also been extended to higher frequency data research.On the other hand,the rise of high frequency trading also requires higher frequency volatility research to guide trading strategies,managing transaction risks,and optimizing the transaction process.However,most of the research on volatility is studing long interval samples of the volatility,such as five minutes or longer.In this context,this paper intends to study the characteristics of higher frequency volatility of the CSI300 stock index futures.The dynamic change process of the CSI300 stock index futures intraday volatility is dynamically depicted with the GARCH model,which is a mature model for the study of volatility,and than the stock index futures volatility can be forecasted based on the estimation model of optimal sampling frequency.Finally,the advantages and disadvantages of the forcast model are compared by the loss function.The research and forcast of volatility can provide support for investors’ investment decisions.It also provides reference for the policy-making and consummating the existing market regulation system by the regulatory authorities.The main contents of this paper are as follows:Firstly,by reviewing the previous research theory of volatility and combing the development process of the GARCH model theory,this paper constructs the theoretical framework for the study on the intraday volatility of stock index futures,which is used to reveal the dynamic change process of the intra day volatility of the CSI300 stock index futures.Secondly,the high frequency data of two pens per second for the CSI300 stock index futures of ten trading days are used as the research object.Based on the statistical description of ten sample data,this paper empirically tests the intraday high frequency return series of the CSI300 stock index futures by using ARMA model and GARCH model.The results show that the intraday high frequency volatility is characterized by volatility aggregation,long memory and strong persistence in the impact of market innovation.The model stability test and the sample forcast results show that the fitting model is stable and can reflect the internal fluctuation process of stock index futures.However,the forcast accuracy is not satisfactory on the forcast of the volatility of two such frequencies per second.Thirdly,in order to improve the forcast accuracy,the real GARCH model is chose to test the intraday high frequency return series by using the optimal sample.This model’s biggest advantage is that by combining the realized volatility with the GARCH model,which makes it possible to predict low frequency volatility by high frequency data.Through the fitting results of 12 samples of different sampling frequencies for 3 trading days,the results are found: there is a significant leverage effect in intraday volatility.The impulse function of different samples is very different,but the volatility impact function of the same sample interval is basically the same.In the four estimation models of sample1,volatility has a significant leverage effect on return rate,and positive return impact has greater impact on volatility than negative return;In the model estimation of sample2,the leverage effect is basically zero,and the impact of positive and negative returns on volatility is basically the same.In the sample6,there is also a leverage effect in the estimated sample model,but the negative return rate has a greater impact on the volatility.The forcast accuracy of the volatility of real GARCH model with different sampling frequencies is compared with the loss function,and the results are as follows: In Sample1,the forcast effect of 1s sample interval is significantly better than the other interval volatility forecasts,while other research samples with different sampling frequency volatility forecast effect is not very different.But in Sample2,the 2S interval rate forecast is better than the other interval sample;In Sample6,the forecast effect is better in the 15 s interval than other intervals.Finally,the forcast accuracy of three models of ARMA-GARCH,real GARCH and e GARCH by the loss function and the H-Z regression function is shown as follows:Taking the minimum loss function as the goal,the real GARCH model of Sample1 has the best forcast effect,while the e GARCH model of Sample2 and Sample6 has the best forcast effect.If we take the H-Z regression function as the goal,we find that the real GARCH model of Sample1 and Sample2 has the best forcast effect on the volatility of the CSI300 index futures,while the e GARCH forcast effect is the best in the sample Sample3.As a whole,the forcast effect of the volatility model reflecting the leverage is better than the forcast effect of the volatility model without leverage effect.The GARCH class model is one of the most commonly used models for volatility.In this paper,we take the CSI 300 stock index futures intraday high frequency data as research samples,and then use ARMA model,ARMA-GARCH model,real GARCH model and e GARCH model to study intraday characteristic of volatility and to forcast the intraday volatility.Finally,we also use the loss function and H-Z regression to evaluate the forcast accuracy of different GARCH models.The results have positive theoretical and practical value.Theoretically,this paper expands the field of volatility research,helps to enrich the theory of stock market futures market microstructure,and improves market regulation and market risk management theory.In practice,it provides the practical reference and theoretical basis for the supervision department to optimize the stock index futures market supervision system scientifically.It is helpful for high frequency trading investors to improve the level of risk management,and it also helps investors to understand the characteristics and rules of the volatility of stock index futures,and provides support for investors’ investment decisions.