168 Frequently Asked Questions In Quantitative Finance
REGARCH Range-based Exponential GARCH. This mod-
els the low to high range of asset prices over a ‘day.’
IGARCH Integrated GARCH. This is a type of GARCH
model with further constraints on the parameters.
FIGARCH Fractionally Integrated GARCH. This model
uses the fractional differencing lag operator applied
to the variance. This adds an extra parameter to the
GARCH model, and is such that it includes GARCH and
IGARCH as extremes. This model has the long memory,
slow decay of volatility as seen in practice.
FIEGARCH Fractionally Integrated Exponential GARCH.
This models the logarithm of variance and again has
the long memory, slow decay of volatility as seen in
practice.
TGARCH Threshold GARCH. This is similar to GARCH
but includes an extra term that kicks in when the shock
is negative. This gives a realistic asymmetry to the
volatility model.
PARCH Power ARCH. In this model the variance is
raised to a power other than zero (logarithm), one
(AGARCH) or two. This model can have the long mem-
ory, slow decay of volatility seen in practice.
CGARCH Component GARCH. This models variance
as the sum of two or more ‘components.’ In a two-
component model, for example, one component is used
to capture short-term and another the long-term effects
of shocks. This model therefore has the long memory,
slow decay of volatility seen in practice.
