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

Abstract

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.

Keywords:

• Extreme volatility
• Risk estimation
• Recurrence interval
• Large volatility forecasting
• Distribution
• Hazard probability

AMS Subject Classifications:

• G130
• G110

Acknowledgements

We are grateful for Yu-Lei Wan for preprocessing the data.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Z.-Q.J. and W.-X.Z. was supported by the National Natural Science Foundation of China [71131007 and 71532009], Shanghai ‘Chen Guang’ Project [2012CG34], Program for Changjiang Scholars and Innovative Research Team in University [IRT1028], China Scholarship Council [201406745014] and the Fundamental Research Funds for the Central Universities. A.C. acknowledges the support from Brazilian agencies FAPEAL [PPP20110902-011-0025-0069/60030-733/2011] and CNPq [PDE 20736012014-6]. H.E.S. was supported by NSF [Grants CMMI 1125290, PHY 1505000, and CHE-1213217] and by DOE Contract [DE-AC07-05Id14517].