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There is this school of thought, that the market has a volatility
without bound. They get their theory from the stable distributions,
of which the central limit theorem is a special case. There is this
thing called the alpha parameter. If it is '2', the max, then you
have a stable distro with a finite variance, and the thing reduces to
the central limit theorem. If alpha is less, then you have something
with infinite variance. If alpha is less than one, then even the mean
is infinite (if I remember correctly).
Also, another school of thought, uses the correlogram to determine
something called the fractional order of integration. If this order
is less than 0.5, then the response to shocks becomes infinte and the
system is inherently unstable.
These schoolds are the guys calling for higher margin as the market
basically is much more volatile - in their opinion - than what we
think and is too dangerous for the average person to participate in,
so we need high margins. If any of these holds (alpha<2 or d<=0.50),
there is no way in which it (volatility) can be transformed away.
Anyhow, I think ATR works because it deals with extremes. Yet another
school uses EVT (extreme value theory) to measure tails and fit
distros to the tails. Every nondegenerate distro lies in the maximum
domain of attraction of an EVT distro (if I remember correctly) which
means in practise you can model the tail of almost any distro using an
EVT distro.
The way in which you fit an EVT distro is to first filter out all the
extreme values, say the largest and smallest values per week. So you
reduce the time series from say 50 values (5 per week) to 10 values
(one per week). Now you fit an EVT distro to this and use it to
predict say the next day extreme. ATR uses the high and low of the
day, so I guess it relates quite a bit to EVT. But you would not use
ATR when pricing options e.g. Here you'll start with good ol' stdev,
maybe weight it as in an example in a previous post, maybe expand it
to a GARCH model as in another example or something like that.
Regards
MG Ferreira
TsaTsa EOD Programmer and trading model builder
http://www.ferra4models.com
http://fun.ferra4models.com
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