Universal Behavior of Extreme Price Movements in Stock Markets

TL;DR

This paper demonstrates that stock price movements, especially extreme changes, can be better modeled by incorporating slow fluctuations in volatility, revealing a universal pattern across different stocks and markets.

Contribution

It introduces a modified stochastic model with fluctuating volatility that explains the frequency of extreme price movements and their universal behavior across stocks.

Findings

Extreme price movements are better explained by a model with fluctuating volatility.

Price fluctuations across stocks follow a universal curve.

The model aligns with observed high frequency of crashes and large swings.

Abstract

Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using a large collection of data from three different stock markets, we present evidence that a modification to the random model -- adding a slow, but significant, fluctuation to the standard deviation of the process -- accurately explains the probability of different-sized price changes, including the relative high frequency of extreme movements. Furthermore, we show that this process is similar across stocks so that their price fluctuations can be characterized by a single curve. Because the behavior of price fluctuations is rooted in the characteristics of volatility, we expect our results to bring increased interest to stochastic volatility models, and especially to those that can produce the properties of volatility reported here.