# Regularities in stock markets

## TL;DR

This paper identifies universal statistical regularities in stock market indices across six major economies, revealing exponential growth, Gaussian fluctuations, and self-similarity in daily and monthly stock behaviors.

## Contribution

It provides a comprehensive analysis of stock market regularities across multiple countries, highlighting universal patterns in growth and fluctuations.

## Key findings

- Exponential mean growth in stock values and trade volume.
- Gaussian distribution of daily fluctuations with convergence.
- Self-similarity in monthly average growth and decline in volatility.

## Abstract

From the stock markets of six countries with high GDP, we study the stock indices, S&P 500 (NYSE, USA), SSE Composite (SSE, China), Nikkei (TSE, Japan), DAX (FSE, Germany), FTSE 100 (LSE, Britain) and NIFTY (NSE, India). The daily mean growth of the stock values is exponential. The daily price fluctuations about the mean growth are Gaussian, but with a non-zero asymptotic convergence. The growth of the monthly average of stock values is statistically self-similar to their daily growth. The monthly fluctuations of the price follow a Wiener process, with a decline of the volatility. The mean growth of the daily volume of trade is exponential. These observations are globally applicable and underline regularities across global stock markets.