波动预测建模与尾部风险测量方法

Methodology of Volatility Forecasting Modelling and Tail Risk Measurement

作为中国资本市场的对冲工具,股指期货在2015年经历了一轮极端牛熊市。在股指异常波动阴影下,研究股指期货尾部风险的测量方法,对风险管理与资产配置具有理论意义和实践意义。传统风险测量方法通常利用低频波动率构建尾部风险VaR和ES估计量,但高频波动率比低频波动率蕴含更多信息且计算效率更高,利用高频波动率建立高效的尾部风险测量方法成为研究趋势。基于条件极值理论和新型高频波动率,构建RV-EVT框架的股指期货尾部风险测量方法。阐述已实现波动率衍生的跳跃、好坏波动和符号跳跃理论;为提高波动率估计精度,利用已实现核修正CPR跳跃检验、好坏波动和符号跳跃;考虑跳跃、好坏波动和符号跳跃建立4组对数形式的HAR类波动预测模型。在极值理论框架中嵌入HAR类模型预测波动率,构建两步法的RV-EVT尾部风险测量方法 ;根据样本外滚动预测评估股指期货尾部风险测量水平,采用无条件覆盖和自枚举检验对VaR和ES进行回测分析。研究结果表明,波动率的样本外滚动预测显示,HAR波动预测框架下好坏波动分解优于连续跳跃波动分解,好坏波动衍生出的正负符号跳跃具有极为突出的波动预测能力;回测分析检验结果显著,尾部超出数接近理论预期,表明RV-EVT尾部风险测量方法有效; HAR-RV-RS和HAR-RV-SJd模型的尾部风险测量表现最佳; ES模型比VaR模型具有更优的尾部风险测量水平,特别是在高风险状态下ES模型能弥补VaR模型失控的缺陷;通过量化交易资金管理研究,揭示尾部风险测量方法的应用价值。建立了高频波动率与风险管理的桥梁,为金融资产尾部风险度量提供了有效方法,对资产配置和风险控制具有借鉴意义。

As an important hedge tool for China’s capital market,stock index futures went through a round of abnormal bull and bear market in 2015. Under the shadow of abnormal stock index,investigating the tail risk measurement of stock index futures is of theoretical and practical significance to risk management and asset allocation. Traditional risk measurements usually use lowfrequency volatility to compute tail risk VaR and ES estimators. However,high frequency volatility contains more information than low frequency volatility. So,it is a hot topic to use high frequency volatility to establish an efficient method for tail risk measurement.Based on the conditional extreme value theory and the new notions of high-frequency volatility,a tail risk measurement method named the RV-EVT framework is constructed for stock index futures. First of all,the jump,good-bad volatility and signed jump theory derived from high-frequency volatility are expounded. In order to improve the accuracy of volatility estimation,the CPR jump test,good-bad volatility and signed jump are revised using realized kernel estimator. Based on jump,good-bad volatility and signed jump,4 logarithmic HAR-type models are established. In the framework of extreme value theory,embedding those HAR-type models for volatility prediction,the two step of RV-EVT tail risk measurement method is constructed. The RVEVT tail risk measurement of stock index futures is evaluated based on the out-of-sample rolling prediction,and the conditional coverage test and bootstrap method are used for VaR and ES backtesting.The main conclusions of this paper are as follows: Under the framework of HAR-type modeling,the decomposition of goodbad volatility is superior to that of continuous-jump variance,and the( positive and negative) signed jump derived from good-bad volatility exhibits prominent volatility forecasting ability. Backtesting results show that the RV-EVT tail risk measurement method is rational and effective. Under the framework of RV-EVT risk measure,the performances of HAR-RV-RS and HAR-RV-SJd models are the best. The result of the tail risk estimating on the daily and weekly shows that ES has a better performance than VaR. Money management method is proposed based on tail risk measurement for quantitative trading strategy,which shows great economic value.The bridge of high frequency volatility and risk management is established in this paper,which provides an effective method for the tail risk measurement of financial assets,which is of important reference to asset allocation and risk control.