“坏”跳跃、“好”跳跃与高频波动率预测

“Bad” Jumps,“Good” Jumps and High-frequency Volatility Forecasting

准确的波动率预测对资产组合配置和风险管理有非常重要的意义,在当今大数据时代,充分利用股市高频数据预测股票波动率成为可能。股市高频信息的一种应用是使用已实现方差和它的组成部分预测股票波动率。已实现方差可以拆分为已实现负半方差和已实现正半方差两个部分。由于已实现负半方差和已实现正半方差极限形式中包含的连续运动部分完全一致,所以它们的不同仅来源于它们跳跃部分的差异,但连续运动部分的存在是否会"稀释"股价跳跃对波动率所产生的影响,为此有必要进一步提取负跳跃和正跳跃。基于负跳跃变差和正跳跃变差,利用HAR模型研究两种不同方向的跳跃是否对波动率产生不对称影响,使用DM统计量和样本外R_(os)~2作为评判标准,考察这种区分跳跃方向的做法是否改进了对波动率的预测能力。研究结果表明,①负跳跃对应未来波动率上升,正跳跃对应未来波动率下降。作为风险规避者的投资者厌恶风险和不确定性,意味着投资者厌恶未来波动率上升而偏好未来波动率下降。因此,将股价的负跳跃称为"坏"跳跃,将股价的正跳跃称为"好"跳跃。②"好"跳跃导致未来波动率下降,而连续运动部分的上升导致未来波动率上升,两者效应的总和是已实现正半方差对未来波动率的影响不显著;"坏"跳跃和连续运动部分的上升都导致未来波动率上升,两者效应的总和是已实现负半方差对未来波动率产生显著的正影响。③利用"坏"跳跃和"好"跳跃不但能够更好地拟合样本内的未来波动率,而且还能够明显地改善波动率的样本外预测能力。研究结果支持日内收益率的正负符号信息在波动率预测领域有其价值,两种不同方向的跳跃对波动率产生不对称影响。在波动率预测实践中,利用"坏"跳跃和"好"跳跃能够改进对波动率的预测能力。

Accurate volatility forecasting is vital to asset allocation and financial risk management. With the advent of big data era,measuring and forecasting stock volatility with high-frequency stock data becomes possible.One way to utilize high-frequency stock data is to use realized variance and its components to predict stock volatility. We decompose the realized variance into two parts,namely the realized negative semi-variance and the realized positive semi-variance.In the limit form,the continuous motion in realized negative semi-variance and realized positive semi-variance are the same,and the only difference lies in the jump part. To isolate the pure effects of stock price jumps on volatility,we further extract the negative and positive jumps. We then apply HAR models to study the asymmetric effects of jumps in opposite directions on volatility.Based on DM statistic and out-of-sample Ros2,we further investigate negative and positive jump variations’ ability to improve volatility forecasting.The results show that: ①Negative jumps( 'bad'jumps) correlate positively with future volatility,whereas positive jumps( 'good'jumps) correlate negatively with future volatility. ②Since both'bad'jumps and the rise of continuous motion increase future volatility,higher negative semi-variance thus corresponds to higher future volatility. On the contrary,'good'jumps and the rise of continuous motion influence future volatility in an opposite way. The sum of these two competing effects therefore gives rise to an insignificant role of positive semi-variance in predicting future volatility. ③'Bad'and 'good'jump variations can greatly improve both in sample and out-of-sample volatility forecasting.Our research demonstrates how we can employ the sign information of intraday returns to more effectively predict volatility and assess asymmetries of jump variation’s impact over volatility. The use of'bad'and'good'jumps can significantly improve accuracy in practical volatility forecasting.