Being able to forcast extreme volatility is a central issue in financial riskmanagement. We present a large volatility predicting method based on thedistribution of recurrence intervals between volatilities exceeding a certainthreshold $Q$ for a fixed expected recurrence time $\tau_Q$. We find that therecurrence intervals are well approximated by the $q$-exponential distributionfor all stocks and all $\tau_Q$ values. Thus a analytical formula fordetermining the hazard probability $W(\Delta t |t)$ that a volatility above $Q$will occur within a short interval $\Delta t$ if the last volatility exceeding$Q$ happened $t$ periods ago can be directly derived from the $q$-exponentialdistribution, which is found to be in good agreement with the empirical hazardprobability from real stock data. Using these results, we adopt adecision-making algorithm for triggering the alarm of the occurrence of thenext volatility above $Q$ based on the hazard probability. Using a "receiveroperator characteristic" (ROC) analysis, we find that this predicting methodefficiently forecasts the occurrance of large volatility events in real stockdata. Our analysis may help us better understand reoccurring large volatilitiesand more accurately quantify financial risks in stock markets.
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