Power Law Distributions for Stock Prices in Financial Markets

TL;DR

This paper investigates the statistical distributions of stock prices and returns across four markets, finding power law behavior in prices and exponential-like distributions in returns, contributing to understanding market dynamics.

Contribution

It provides empirical evidence of power law distributions in stock prices and exponential forms in normalized returns across multiple markets.

Findings

Stock prices follow Zipf's law or power law distributions.

Normalized returns exhibit an exponential-like distribution.

Results are consistent with previous numerical studies.

Abstract

We study the rank distribution, the cumulative probability, and the probability density of returns of stock prices of listed firms traded in four stock markets. We find that the rank distribution and the cumulative probability of stock prices traded in are consistent approximately with the Zipf's law or a power law. It is also obtained that the probability density of normalized returns for listed stocks almost has the form of the exponential function. Our results are compared with those of other numerical calculations.