Inverse cubic law for the distribution of stock price variations
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The probability distribution of stock price changes is studied by analyzing a database (the Trades and Quotes Database) documenting every trade for all stocks in three major US stock markets, for the two year period January 1994 - December 1995. A sample of 40 million data points is extracted, which is substantially larger than studied hitherto. We find an asymptotic power-law behavior for the cumulative distribution with an exponent \(a \approx 3\), well outside the Lévy regime \((0 < \alpha < 2)\).