基于非对称双成份CARR模型的波动率预测

Volatility Forecasting Based on Asymmetric Two-Component CARR Model

研究表明,基于日内(高低价)数据构建的价格极差测度相比日度收益率包含更多关于真实波动率的信息,同时,波动率具有聚集性、非对称性和长记忆性等丰富、复杂的典型特征,综合考虑这些特征对波动率进行建模与预测非常重要。本文在对价格极差建模的CARR模型的基础上,对其进行扩展,构建了双成份CARR(CCARR)模型来对波动率进行预测。该模型假设价格极差的条件均值由两个成份组成,即长期成份与短期成份.该模型能够捕获波动率长记忆性,且容易进一步扩展为非对称CCARR(ACCARR)模型来捕获杠杆效应(波动率非对称性)。(A)CCARR模型具有较高的建模灵活性,且易于实现。采用上证综合指数、香港恒生指数、日本Nikkei225指数、法国CAC40指数和德国DAX指数数据进行实证分析,以价格极差与已实现波动率(RV)作为比较基准,四种预测评价指标及Mincer-Zarnowitz检验结果表明:杠杆效应与双成份极差(波动率)都对样本外波动率预测具有重要影响,且杠杆效应相比双成份极差对于样本外波动率预测的影响更大;考虑了杠杆效应的双成份ACCARR模型具有最好的样本外波动率预测效果,其次是ACARR模型,CARR模型表现最差。

It has been known that the intra-day(high-low)price range contains more information regrading to true volatility than do the daily returns.Meanwhile,volatility exhibits clustering,asymmetry and long-memory property,it is important to capture these empirical features to model and forecast volatility.In this paper,we extend the CARR model of intra-day price range and propose the two-component CARR(CCARR)model to forecast volatility.The proposed model assumes that the conditional mean of range consists of two components,a long-run component and a short-run component.The model can capture long-memory volatility and can be extended easily as asymmetric CCARR(ACCARR)model to further account for leverage effect(volatility asymmetry).The(A)CCARR model is flexible and easy to implement.An empirical study on the Shanghai Stock Exchange Composite Index of China,Hang Seng Index of Hong Kong,Nikkei 225 Index of Japan,CAC 40 Index of France and DAX Index of Germany shows that both the leverage effect and two-component range(volatility)have important impacts on out-of-sample volatility forecasting,and the leverage effect has a more significant impact than the two-component range.As a consequence,the ACCARR model performs best in out-of-sample volatility forecasting,followed by the ACARR model,and the CARR model performs worst.