Early warning of large volatilities based on recurrence interval analysis in Chinese stock markets
提出一种基于波动率复发间隔分布的大波动预测方法，利用拉伸指数分布推导危险概率，并通过ROC分析验证该方法能有效预警中国股市的大波动事件。
Forecasting extreme volatility is a central issue in financial risk management. We present a large volatility predicting method based on the distribution of recurrence intervals between successive volatilities exceeding a certain threshold Q, which has a one-to-one correspondence with the expected recurrence time . We find that the recurrence intervals with large are well approximated by the stretched exponential distribution for all stocks. Thus, an analytical formula for determining the hazard probability that a volatility above Q will occur within a short interval if the last volatility exceeding Q happened t periods ago can be directly derived from the stretched exponential distribution, which is found to be in good agreement with the empirical hazard probability from real stock data. Using these results, we adopt a decision-making algorithm for triggering the alarm of the occurrence of the next volatility above Q based on the hazard probability. Using the ‘receiver operator characteristic’ analysis, we find that this prediction method efficiently forecasts the occurrence of large volatility events in real stock data. Our analysis may help us better understand reoccurring large volatilities and quantify more accurately financial risks in stock markets.