Volatility clustering is the tendency of large changes in prices of financial assets to cluster together, which results in the persistence of these magnitudes of price changes. Another way to describe the phenomenon of volatility clustering is to quote famous scientist-mathematician Benoit Mandelbrot, and define it as the observation that "large changes tend to be followed by large changes...and small changes tend to be followed by small changes" when it comes to markets. This phenomenon is observed when there are extended periods of high market volatility or the relative rate at which the price of a financial asset change, followed by a period of "calm" or low volatility.

## The Behavior of Market Volatility

Time series of financial asset returns often demonstrates volatility clustering. In a time series of stock prices, for instance, it is observed that the variance of returns or log-prices is high for extended periods and then low for extended periods. As such, the variance of daily returns can be high one month (high volatility) and show low variance (low volatility) the next. This occurs to such a degree that it makes an iid model (independent and identically distributed model) of log-prices or asset returns unconvincing. It is this very property of time series of prices that is called volatility clustering.

What this means in practice and in the world of investing is that as markets respond to new information with large price movements (volatility), these high-volatility environments tend to endure for a while after that first shock. In other words, when a market suffers a volatile shock, more volatility should be expected. This phenomenon has been referred to as the *persistence of volatility shocks*, which gives rise to the concept of volatility clustering.

## Modeling Volatility Clustering

The phenomenon of volatility clustering has been of great interest to researchers of many backgrounds and has influenced the development of stochastic models in finance. But volatility clustering is usually approached by modeling the price process with an ARCH-type model. Today, there are several methods for quantifying and modeling this phenomenon, but the two most widely-used models are the autoregressive conditional heteroskedasticity (ARCH) and the generalized autoregressive conditional heteroskedasticity (GARCH) models.

While ARCH-type models and stochastic volatility models are used by researchers to offer some statistical systems that imitate volatility clustering, they still do not give any economic explanation for it.