Volatility clustering

Volatility Clustering is a phenomenon in time series of asset prices. In contrast to the often-assumed log-normal distribution of asset price returns, it is often observed that periods of high price volatility follow periods of low volatility and vice versa. For example, stock returns prior to an earnings announcement or other anticipated news item are frequently observed to have higher variance than those seen in the weeks following the release.

Observations of this type in financial time series have led to the use of GARCH models in financial forecasting and derivatives pricing. This is a more precise formulation of the intuition that asset volatility tends to revert to some mean rather than remaining constant or moving in monotonic fashion over time.

Volatility clustering: as noted by Mandelbrot, “large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes.” A quantitative manifestation of this fact is that, while returns themselves are uncorrelated, absolute returns |rt| or their squares display a positive, significant and slowly decaying autocorrelation function: corr(|rt|, |rt+τ |) > 0 for τ ranging from a few minutes to a several weeks.