Inverse cubic law for the distribution of stock price variations

Abstract: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 $$(0 < \alpha < 2)$$ .