Research at the Massachusetts Institute of Technology suggests that there is evidence the frequency of stock market crashes follows an inverse cubic power law. This and other studies such as Prof. Didier Sornette's work suggest that stock market crashes are a sign of self-organized criticality in financial markets. In 1963, Mandelbrot proposed that instead of following a strict random walk, stock price variations executed a Lévy flight. A Lévy flight is a random walk that is occasionally disrupted by large movements. In 1995, Rosario Mantegna and Gene Stanley analyzed a million records of the S&P 500 market index, calculating the returns over a five-year period. Researchers continue to study this theory, particularly using computer simulation of crowd behaviour, and the applicability of models to reproduce crash-like phenomena.
What Time Do Stock Markets Open?
The mathematical description of stock market movements has been a subject of intense interest. The conventional assumption has been that stock markets behave according to a random log-normal distribution. Among others, mathematician Benoît Mandelbrot suggested as early as 1963 that the statistics prove this assumption incorrect. Mandelbrot observed that large movements in prices (i.e. crashes) are much more common than would be predicted from a log-normal distribution. Mandelbrot and others suggested that the nature of market moves is generally much better explained using non-linear analysis and concepts of chaos theory. This has been expressed in non-mathematical terms by George Soros in his discussions of what he calls reflexivity of markets and their non-linear movement. George Soros said in late October 1987, 'Mr. Robert Prechter's reversal proved to be the crack that started the avalanche'.
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On September 16, 2008, failures of massive financial institutions in the United States, due primarily to exposure to packaged subprime loans and credit default swaps issued to insure these loans and their issuers, rapidly devolved into a global crisis. This resulted in a number of bank failures in Europe and sharp reductions in the value of stocks and commodities worldwide. The failure of banks in Iceland resulted in a devaluation of the Icelandic króna and threatened the government with bankruptcy. Iceland obtained an emergency loan from the International Monetary Fund in November. In the United States, 15 banks failed in 2008, while several others were rescued through government intervention or acquisitions by other banks. On October 11, 2008, the head of the International Monetary Fund (IMF) warned that the world financial system was teetering on the "brink of systemic meltdown".