The crude oil price bubbling and universal scaling dynamics of price volatility

The main goal of this paper is to reveal the effect of crude oil price bubbling on the price volatility dynamics. For this purpose, the time series of volatility at different horizons are mapped into a model of kinetic roughening of interface growing in a stochastic environment. In this way, we found that the volatility dynamics obeys the Family-Viscek dynamic scaling ansatz. Although during the period from January 2, 1986 to July 25, 2014 the volatility remains a slightly anti-persistent, the dynamic exponent is found to be quite different during different regimes of price evolution. Accordingly, we define the intrinsic time of price volatility and metric of volatility horizons. This allows us to construct the Langevin-type equation governing the volatility dynamics during bubble and non-bubble periods. The data analysis indicates that the bubbling does not affect the intrinsic time of volatility, but strongly affect the metric of volatility horizons. In this regard, numerical data suggest the existence of two universal metrics characterizing the volatility dynamics during the bubble and non-bubble regimes of crude oil price evolution, respectively. The results of this work help us to get a further insight into the dynamics of crude oil price volatility.