164 Frequently Asked Questions In Quantitative Finance
What is GARCH?
Short Answer
GARCH stands for Generalized Auto Regressive Con-
ditional Heteroscedasticity. This is an econometric
model used for modelling and forecasting time-depen-
dent variance, and hence volatility, of stock price re-
turns. It represents current variance in terms of past
variance(s).
Example
The simplest member of the GARCH family is GARCH(1, 1)
in which the variance,vnof stock returns at time stepn
is modelled by
vn=(1−α−β)w 0 +βvn− 1 +αvn− 1 B^2 n− 1 ,
wherew 0 is the long-term variance,αandβare posi-
tive parameters, withα+β<1, andBnare independent
Brownian motions, that is, random numbers drawn from
a normal distribution. The latest variance,vn, can there-
fore be thought of as a weighted average of the most
recent variance, the latest square of returns, and the
long-term average.
Long Answer
What? GARCH is one member of a large family of econo-
metric models used to model time-varying variance.
They are popular in quantitative finance because they
can be used for measuring and forecasting volatility.
It is clear from simple equity or index data that volatil-
ity is not constant. If it were then estimating it would be
very simple. After all, in finance we have what some-
times seems like limitless quantities of data. Since
volatility varies with time we would like at the very least
to know what it isright now. And, more ambitiously, we
