finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of fina ...

, 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

, r_,

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 Granger may refer to: People *Granger (name) *Hermione Granger, a fictional character in Harry Potter United States * Granger, Indiana * Granger, Iowa * Granger, Minnesota * Granger, Missouri * Granger, New York * Granger, Ohio * Granger, Texas ...

and Ding (1993) and Ding and

(1996) among others; see also. Some studies point further to long-range dependence in volatility time series, see Ding,

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 In econometrics, the autoregressive conditional heteroskedasticity (ARCH) model is a statistical model for time series data that describes the variance of the current error term or innovation as a function of the actual sizes of the previous time ...

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 The derivative of a function is the rate of change of the function's output relative to its input value. Derivative may also refer to: In mathematics and economics * Brzozowski derivative in the theory of formal languages * Formal derivative, an ...

pricing. The

ARCH An arch is a vertical curved structure that spans an elevated space and may or may not support the weight above it, or in case of a horizontal arch like an arch dam, the hydrostatic pressure against it. Arches may be synonymous with vaul ...

( Engle, 1982) and

( 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 el, κυρτός, ''kyrtos'' or ''kurtos'', meaning "curved, arching") is a measure of the "tailedness" of the probability distribution of a real-valued random variable. Like skewness, kurtosi ...

. 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 order ...

fashion over time.

References

Derivatives (finance) Technical analysis {{Econ-stub

See also

References