Volatility clustering
Encyclopedia
In finance
, volatility clustering refers to the observation, as noted by Mandelbrot
(1963), that "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 several weeks.
Observations of this type in financial time series have led to the use of GARCH models in financial forecasting and derivatives
pricing. The ARCH
(Engle
, 1982) and GARCH (Bollerslev
, 1986) models aim to more accurately describe the phenomenon of volatility clustering and related effects such as kurtosis
. The main idea behind these two widely-used models is that volatility is dependent upon past realizations of the asset process and related volatility process. 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.
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
, volatility clustering refers to the observation, as noted by Mandelbrot
Benoît Mandelbrot
Benoît B. Mandelbrot was a French American mathematician. Born in Poland, he moved to France with his family when he was a child...
(1963), that "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 several weeks.
Observations of this type in financial time series have led to the use of GARCH models in financial forecasting and derivatives
Derivative (finance)
A derivative instrument is a contract between two parties that specifies conditions—in particular, dates and the resulting values of the underlying variables—under which payments, or payoffs, are to be made between the parties.Under U.S...
pricing. The ARCH
Arch
An arch is a structure that spans a space and supports a load. Arches appeared as early as the 2nd millennium BC in Mesopotamian brick architecture and their systematic use started with the Ancient Romans who were the first to apply the technique to a wide range of structures.-Technical aspects:The...
(Engle
Robert F. Engle
Robert Fry Engle III is an American economist and the winner of the 2003 Nobel Memorial Prize in Economic Sciences, sharing the award with Clive Granger, "for methods of analyzing economic time series with time-varying volatility ".-Biography:Engle was born in Syracuse, New York and went on to...
, 1982) and GARCH (Bollerslev
Tim Bollerslev
Tim Peter Bollerslev is a Danish economist, currently the Juanita and Clifton Kreps Professor of Economics at Duke University. A fellow of the Econometric Society, Bollerslev is known for his ideas for measuring and forecasting financial market volatility and for the GARCH model...
, 1986) models aim to more accurately describe the phenomenon of volatility clustering and related effects such as kurtosis
Kurtosis
In probability theory and statistics, kurtosis is any measure of the "peakedness" of the probability distribution of a real-valued random variable...
. The main idea behind these two widely-used models is that volatility is dependent upon past realizations of the asset process and related volatility process. This is a more precise formulation of the intuition that asset volatility
Volatility (finance)
In finance, volatility is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices...
tends to revert to some mean rather than remaining constant or moving in monotonic fashion over time.