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Market prices tend to exhibit periods of high and low
volatility. This sort of behavior is called
volatility clustering. It can
be modeled with various
heteroskedastic
stochastic
processes used in finance and economics, including ARCH,
GARCH and
stochastic
volatility models.
Heteroskedasticity, recall,
is the property of time-varying (conditional or unconditional)
variance in a stochastic
process. Volatility clustering is the property that there are periods of
high and low (conditional or unconditional) variance. The
volatility "clusters." This is
illustrated in Exhibit 1. Its top graph is a realization of a
heteroskedastic stochastic process without volatility clustering. Its
volatility may fluctuate, but it is independent from one time to the next.
The second graph is a heterokedastic stochastic process with volatility
clustering.
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Two time series are illustrated. The first
does not exhibit volatility clustering. The second one does. |
It is important to distinguish between observed market
behavior and the stochastic processes we use to model that behavior.
People often speak of markets as being heteroskedastic, but this is a
mathematical, not financial, notion. For example, the time series in the
top chart of Exhibit 1 could be modeled with a heteroskedastic
stochastic process without volatility clustering, or it could just as
accurately be modeled with a
homoskedastic (constant volatility)
leptokurtic (fat tailed) stochastic process. If you ponder this, you
will understand that, although heteroskedasticity and volatility
clustering are distinct mathematical notions, the only reason to model
with heteroskedastic stochastic process is to accommodate volatility
clustering (or some similar interdependency between variances at
different points in time). The latter is impossible without the former.
The former is irrelevant without the latter.
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