中国铜期货市场波动率估计与风险度量——基于广义已实现测度的Realized HAR GARCH模型

The Volatility Estimation and VaR Measurement of China’s Copper Future Market:Based on Realized HAR GARCH Model Incorporating Generalized Realized Measures

为探究中国铜期货市场价格波动的变化规律并以此预测其风险值,以沪铜期货高频价格数据为样本,综合考虑其收益率波动的聚集性、偏峰厚尾性与长记忆性,将广义已实现测度引入偏t分布假设下的Realized GARCH模型与拓展的Realized HAR GARCH模型中,并通过样本内拟合与样本外滚动预测,结合似然函数、VaR后验测试与损失函数MCS检验法综合比较了采用不同已实现测度的Realized GARCH以及Realized HAR GARCH模型在沪铜期货收益波动率估计和VaR预测上的效果。实证结果显示:对于沪铜期货市场而言,无论是波动率估计还是风险预测,广义已实现测度的引入显著地提升了Realized GARCH与Realized HAR GARCH模型的拟合效果与预测能力,其中基于日内损失RMAD与RES测度下的Realized HAR GARCH模型分别拥有最优的估计与预测表现。

As China’s copper futures market continues to expand, accurate estimation of the volatility of copper futures prices is of particular interest to academics.In this paper, using the high-frequency data samples of copper futures in Shanghai Futures Exchange, the Realized GARCH model and the Realized HAR GARCH model involving different types of realized measures are established under the skew-t distribution to forecast the volatility of returns and the daily VaR.Besides using the conventional realized measures as our benchmarks, the generalized realized measures are introduced into the models. Then, through the in-sample fitting and out-of-sample rolling prediction, likelihood function, VaR posterior tests, and loss function MCS test are applied to compare the results of the models on volatility estimation and evaluate the forecasting effects of the VaR.The empirical results show that: 1) With the maximum likelihood value as the criterion, the introduction of the generalized realized measures can provide more effective fitting effects for both models, and the RMAD measure has the best improvement effect. Moreover, the Realized HAR GARCH models outperform Realized GARCH models under all realized measures in estimation performances;2) In terms of VaR forecasting, almost all models pass the posterior tests, which shows that the Realized GARCH-types models are very effective tools for copper futures risk prediction. However, after considering the loss function, the MCS tests show that the Realized HAR GARCH models using the generalized realized risk measures provide substantial improvements in out-of-sample VaR prediction. And integrating all test results, the optimal model in copper futures VaR predicting is the Realized HAR GARCH-RES model.Our findings provide new ideas and methods for the application in volatility modeling and risk forecasting and will have implications for investors and policymakers in the practice of risk management in financial markets.