Self-Controlled Phase Transitions During Market Crashes and Price Corrections

We study the behavior of ensemble measures of financial markets during crash periods to see if they exhibit the behavior typical for second-order phase transitions. We find that during market crashes the order parameter (defined as the ensemble-average correlation) sharply increases and fluctuations (defined as ensemble volatility) exhibit a spike. In addition, the hysteresis effect is observed for correlations and drawdown (market drop) and a similar effect exists for trading volume and drawdown. These facts point that during crashes the markets not only resemble but undergo a second-order phase transition. Market phases can be identified on a volatility vs drawdown diagram as regions with high and low order parameter. While market dynamics has a self-coordinated nature, the two inputs on phase diagram are measurable directly from the markets.