Inverse Cubic Law for the Probability Distribution of Stock Price Variations

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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 Jan 1994 -- Dec 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 alpha approximately 3, well outside the Levy regime 0< alpha <2.

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