In
finance
Finance refers to monetary resources and to the study and Academic discipline, discipline of money, currency, assets and Liability (financial accounting), liabilities. As a subject of study, is a field of Business administration, Business Admin ...
, volatility clustering refers to the observation, first 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
or their squares display a positive, significant and slowly decaying autocorrelation function: corr(, r, , , r , ) > 0 for τ ranging from a few minutes to several weeks. This empirical property has been documented in the 90's by
Granger and Ding (1993) and Ding and
Granger (1996) among others; see also. Some studies point further to long-range dependence in volatility time series, see Ding, Granger and
Engle (1993) and Barndorff-Nielsen and Shephard.
[
]
Observations of this type in financial time series go against simple random walk models and have led to the use of
GARCH models and mean-reverting
stochastic volatility
In statistics, stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed. They are used in the field of mathematical finance to evaluate derivative securities, such as options. The name ...
models in financial forecasting and
derivatives pricing. The
ARCH
An arch is a curved vertical structure spanning an open space underneath it. Arches may support the load above them, or they may perform a purely decorative role. As a decorative element, the arch dates back to the 4th millennium BC, but stru ...
(
Engle, 1982) and GARCH (
Bollerslev, 1986) models aim to more accurately describe the phenomenon of volatility clustering and related effects such as
kurtosis
In probability theory and statistics, kurtosis (from , ''kyrtos'' or ''kurtos'', meaning "curved, arching") refers to the degree of “tailedness” in the probability distribution of a real-valued random variable. Similar to skewness, kurtos ...
. The main idea behind these two 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
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of ord ...
fashion over time.
See also
*
GARCH
*
Stochastic volatility
In statistics, stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed. They are used in the field of mathematical finance to evaluate derivative securities, such as options. The name ...
References
Derivatives (finance)
Technical analysis
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