Early warning of large volatilities based on recurrence interval analysis in Chinese stock markets

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 τQ$ \tau _Q $. We find that the recurrence intervals with large τQ$ \tau _Q $ are well approximated by the stretched exponential distribution for all stocks. Thus, an analytical formula for determining the hazard probability W(Δt|t)$ W(\Delta t |t) $ that a volatility above Q will occur within a short interval Δt$ \Delta t $ 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.