Abstract
Based on concepts and methods from statistical physics, we investigate extreme-volatility dynamics in the crude oil markets, using the high-frequency data from 2006 to 2010 and the daily data from 1986 to 2016. The dynamic relaxation of extreme volatilities is described by a power law, whose exponents usually depend on the magnitude of extreme volatilities. In particular, the relaxation before and after extreme volatilities is time-reversal symmetric at the high-frequency time scale, but time-reversal asymmetric at the daily time scale. This time-reversal asymmetry is mainly induced by exogenous events. However, the dynamic relaxation after exogenous events exhibits the same characteristics as that after endogenous events. An interacting herding model both with and without exogenous driving forces could qualitatively describe the extreme-volatility dynamics.
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