基于QRNN+GARCH族MA方法的多期VaR和CVaR度量研究

Measuring Multi-Period VaR and CVaR Based on QRNN+GARCH Family MA Method

收益序列通常具有聚集性、非对称性和非线性等复杂的典型特征,综合考虑这些特征对收益序列进行建模非常重要。本文基于GARCH族模型平均(MA)方法,引入非线性分位数回归模型对收益序列进行刻画,构建了固定形式的非线性分位数回归(QR+GARCH族MA)方法和非固定形式的非线性分位数回归(QRNN+GARCH族MA)方法测度多期VaR和CVaR风险。构建的新方法不仅能够捕获收益序列的复杂特征、减少信息损失,也无需对多期收益序列分布特征做具体假定,直接对多期收益进行建模就能一次实现不同持有期的风险测度,有效地提高了多期风险测度精度和效率。本文选取8个中国试点城市的碳排放交易价格作为研究对象,使用似然比检验与平均相对误差来评估新方法在多期VaR风险测度的效果;并且构建平均分位误差指标来评估新方法多期CVaR风险度量效果。实证结果表明:在多期VaR和CVaR风险测度中,QRNN+GARCH族MA方法表现出更高的准确性和稳健性。

The return series usually has complex typical characteristics such as aggregation,asymmetry and nonlinearity.It is very important to consider these characteristics comprehensively to model the return series.In this paper,a nonlinear quantile regression model is introduced to characterize the return sequence based on the model averaging(MA)method for a GARCH family,including a fixedform nonlinear quantile regression(QR+GARCH family MA)method and a non-fixed form nonlinear quantile regression(QRNN+GARCH family MA)method are constructed to measure the multi-period VaR and CVaR risk.The new methods,which can effectively improve the accuracy and efficiency of the multi-period risk measurement,can not only capture the complex characteristics of the return series and reduce the information loss,but also realize the risk measurement of different holding periods at one time by modeling the multi-period return directly without making specific assumptions about the distribution characteristics of the multi-period return series.The carbon emission trading prices of eight pilot cities in China are taken as the research object.Likelihood ratio test results and average relative error sizes are used to evaluate the effects of new methods in multi-period VaR risk measurement.Moreover,the average quantile error index is constructed to evaluate the effects of new methods in multi-period CVaR risk measurement.The results show that the QRNN+GARCH family MA method is more accurate and robust in the risk measurement of multi-period VaR and CVaR.