Inverse Cubic Law for the Probability Distribution of Stock Price Variations

TL;DR

This paper analyzes a large dataset of stock trades to reveal that stock price changes follow an inverse cubic power-law distribution, with an exponent around 3, indicating heavy tails beyond the Levy regime.

Contribution

It provides the first large-scale empirical evidence that stock price variations follow an inverse cubic law, extending understanding of financial market fluctuations.

Findings

Stock price changes follow an inverse cubic power-law distribution.

The distribution's tail exponent is approximately 3.

The dataset includes over 40 million data points from US stock markets.

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.