Abstract: Volatility is the core index to research the risk of financial assets, as well as one of the bases of the pricing of financial derivatives. Therefore, the research on volatility of financial assets, especially financial derivatives, has always been the focus and hot spot of academic research. Modeling to measure the volatility risk of financial products is also an important topic in the current financial research literatures. In previous studies, we used different volatility models to forecast the intra-day volatility of CSI 300 stock index futures samples, and different models have different performances. Therefore, how to compare the prediction level of different models on volatility is an important issue that we pay attention to at present. Under the premise of fixed sampling frequency, finding the optimal volatility prediction model for CSI 300 stock index futures will help investors grasp the trend of market changes and form appropriate financial assets through the combination and collocation of investment tools. In theory, it will further complement and improve the theoretical framework of price volatility prediction of financial derivatives.
In the series of volatility prediction methods, the GARCH family model is simple and extendable, so it is widely applied and extended in theory and practice. In the process of applying GARCH family model, loss function is often used to measure the accuracy of prediction model. In this paper, we use a variety of loss functions to evaluate the prediction accuracy of three GARCH models (General Autoregressive Conditional Heteroskedastic Model), and try to find the optimal intraday volatility prediction model for stock index futures to assist us in financial investment. Specifically, we use the previous research results, three CSI 300 stock index futures intra-day one-minute yield as the research object, the standard GARCH, eGARCH and RealGARCH models for empirical test, and a variety of loss functions to measure the prediction accuracy of the three volatility models from different perspectives.
First, from the fitting results of the volatility of the three research samples, the GARCH model, which can reflect the asymmetric fluctuations, has a more significant fitting coefficient for the samples, and its loss function is smaller, indicating that its fitting effect is better. This indicates that the intraday volatility of one-minute CSI 300 stock index futures has an obvious leverage effect, and the market fluctuations are different for positive and negative external shocks of the same size. Second, for the specific research object, the prediction accuracy of eGARCH and RealGARCH models is obviously better than that of standard GARCH model, and the prediction accuracy of RealGARCH models in Sample1 and Sample2 is better than that of eGARCH model. Third, the prediction accuracy of eGARCH model in Sample3 is higher. Therefore, when studying the intraday volatility of CSI 300 stock index futures, we should give priority to the volatility model that can reflect the asymmetric characteristics according to its sample characteristics to depict the de-volatility process and forecast the future volatility.
Problems for further research: eGARCH and RealGARCH models are mainly aimed at asymmetric problems, and nonlinear problems can be studied based on this model in the future.Econometric models such as GARCH do have advantages in capturing linear features of volatility, while current research shows that tools such as machine learning algorithms has begun to find application in volatility prediction because it is better at capturing non-linear features. Future research may consider combining GARCH model with machine learning algorithm to build a combined model to further improve the accuracy of prediction.
The reviewer has put forward good suggestions for the revision of this article. We would like to express my sincere thanks to the reviewer, but we shall take the responsibility for the article. At the same time, we would like to thank the Philosophy and Social Sciences Planning Foundation of Shenzhen, Guangdong Province, China for supporting this study.

Key words: high-frequency data, loss function, GARCH model, eGARCH model, RealGARCH model, prediction and evaluation

摘要： 本文的目的是通过利用多种损失函数评估三种GARCH模型的预测精度,找到最优的股指期货日内波动率研究预测模型。利用之前的研究结果,三个沪深300股指期货日内一分钟日内收益率被用作研究对象,对标准GARCH,eGARCH以及RealGARCH三个模型做了实证检验,并利用多种损失函数,从不同角度衡量三个波动率模型的预测精度。研究发现:Sample1样本的RealGARCH模型有最好的预测效果,而Sample2样本与Sample6样本的eGARCH模型有最好的预测精度。因此,在对沪深300股指期货日内波动率研究时,应根据其样本特征,优先选择具有能够反映非对称特征的波动率模型来刻画波动过程,对未来波动率做预测。

关键词: 高频数据, 损失函数, GARCH模型, eGARCH模型, RealGARCH模型, 预测评价