A statistical measure of financial crises magnitude

• We propose a new statistical measure of financial crises magnitude.
• The crash magnitude is computed by analogy with the earthquakes Richter scale.
• For the US market, we establish the magnitude and the hierarchy of financial crises.
• Statistical pattern of a financial crisis is described by Pareto and Wakeby distributions.
• We obtain a financial Gutenberg–Richter relation.

This paper postulates the concept of financial market energy and provides a statistical measure of the financial market crisis magnitude based on an analogy between earthquakes and market crises. The financial energy released by the market is expressed in terms of trading volume and stock market index returns. A financial “earthquake” occurs if the financial energy released by the market exceeds the estimated threshold of market energy called critical energy. Similar to the Richter scale which is used in seismology in order to measure the magnitude of an earthquake, we propose a financial Gutenberg–Richter relation in order to capture the crisis magnitude and we show that the statistical pattern of the financial market crash is given by two statistical regimes, namely Pareto and Wakeby distributions.