Volatility distribution in the S&P500 Stock Index

TL;DR

This paper analyzes the volatility of the S&P500 index from 1984 to 1996, revealing it follows a log-normal distribution and exhibits long-range power-law correlations with a high Hurst exponent.

Contribution

It demonstrates that S&P500 volatility can be modeled by a log-normal distribution and exhibits persistent long-range correlations, providing insights into market dynamics.

Findings

Volatility follows a log-normal distribution.

Volatility exhibits power-law correlations with Hurst exponent ~0.9.

Long-range dependence in market volatility is confirmed.

Abstract

We study the volatility of the S&P500 stock index from 1984 to 1996 and find that the volatility distribution can be very well described by a log-normal function. Further, using detrended fluctuation analysis we show that the volatility is power-law correlated with Hurst exponent $\alpha\cong0.9$.