Stock market dynamics: Before and after stock market crashes

This paper presents a brief analysis on the distribution of magnitude of major stock market shocks. Based on the Gutenberg–Richter law in geophysics, we model the dynamics of market index returns prior and after major crashes in search of statistical regularities. For a large number of market crashes, our analysis suggests that the distribution of market volatility before and after the stock market crash is described well by the Gutenberg–Richter law, which reflects the scale-invariance and self-similarity of the underlying dynamics by a robust power-law relation. In addition, the rate of the decay of the aftershock sequence is well described by another power law, which is known as the Omori law. Power law relaxation seems to be a common behavior observed in complex systems such as the financial markets.