Firstly, we use the Multi-Scale LPPLS Confidence Indicator approach to detectboth positive and negative bubbles at short-, medium- and long-term horizons forthe stock markets of the G7 and the BRICS countries. We were able to detect majorcrashes and rallies in the 12 stock markets over the...

For five stock market crashes, we compare price declines with predictions from market microstructure invariance. During the 1987 crash and the 2008 sales by Société Générale, prices fell by magnitudes similar to predictions from invariance. Larger-than-predicted temporary price declines...