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Hi Bilo,
thanks for your reply. I had to smile a little when I read this because I
have been working along similar lines some years ago. My approach was
weighted more towards trying to ferret out transition probabilities to model
information content through Markov processes. Your work seems to place a
stronger emphasis on cyclical components, though.
Best regards,
Michael Suesserott
-----Ursprüngliche Nachricht-----
Von: Bilo Selhi [mailto:biloselhi@xxxxxxxxxxx]
Gesendet: Wednesday, December 05, 2001 04:28
An: holygrail@xxxxxxxxxxxxx; systems-only@xxxxxxxxxxxxx; MikeSuesserott;
Omega List
Betreff: from roulette to price volatilitly and back...
>
> interesting. Would you care to elaborate a little how you quantify this
> second process?
well i guess i could write a few lines here.
suppose you want to predict volatility of price time series.
the stylized facts that you base your model on are:
- it's mean reverting
- it's gaussian in log or near gaussian or stable, whatever but stable.
- it's persistent, serially correlated, clustered
- it usually positively correlated to volume
- it scales in time, usually based on either square root of time law or exp
law.
that's all you have to go by and often there is very little explained as far
as
the fundamental nature of volatility or risk. why does volatility go up and
go
down and how you explain the persistence, mean reversion, scaling laws
and volume correlation??? if the model does not explain the above but just
takes those as facts then most likely the model won't perform since you will
miss something in there...
to explain it all you have to start with the fundamental nature of financial
markets.
the market is an information processing "machine" in which a true value of
the
underlying traded is found based on incoming information and profits and
losses
are allowed to be made as a payoff for performing information processing
function.
look at the market as a box on the input of which you have new information
and on the
output of which you have new value, more over there is feedback since new
value
itself is part of new information input.
types of info that you have on the input are:
- fundamental information, news, rumors, facts, you name it.
- technical ( feedback ) information, price action itself, bandwagon
expectations ie momentum ie trend, etc...
now, information comes in cycles, waves and there are two basic cycles
that correspond to up and down moves in price.
for simplicity: current info cycle and new contradicting or competing
cycle.
example, you have a major fed announcement that creates an information cycle
that pushes
prices higher, after initial factoring of that information a new counter
cycle develops
based on different interpretation of the same report, prices recede,
next a bandwagon expectation develops where everyone piles up
on that second reaction, since we all observe the price action every new
down tick
represents for us new information, next after the bandwagon pile up cycle
ends (
information factored ) yet another new information cycle develops where
people
get a clue that the move might be over and the intraday profit taking move
sets in that
itself is new information, and on and on and on...
so you can see the market outputs price value and creates new information
that begets new
information, etc...
once we know the basics we can link volatility to information or lack of
thereof.
information in general could be measured in 1.content, 2.units, 3. weights
there might be several units of information with different weight based on
different content that the market factors in at any given moment.
so information factoring is a cycle which has duration, magnitude and
defines direction
which is basically realized as price move. those info cycle overlap,
counteract,
resonate, etc...
sometimes there is little new information to take in for the market and the
market
kinda dies down, sometimes there is lots of new info to factor and the
market explodes and
once the info is factor it fades down...
look at the example of new information cycle, the market open.
the open presents an ideal example of the new information that piled up
from previous day, overnight and preopen and is ready to be factored in
straight from the open... trading interest increases, order sizes
increase...
as a result the common observation is that intraday volatility is the
highest
on the open, same goes about the volume of the transactions...
once the market process the info after a hour, hour and a half after the
open
the factoring is done the new value is found and volatility dies down
towards
lunch where typically there is little new information to process and up till
the close where information content again grows and those who did
not participate in morning factoring do so on the close...
thus volatility is directly proportional to the current new information
intake.
more information coming into the market, the higher the volatility goes
and information is factored and no new info coming in the volatility dies
down,
fades... the best way to visualize volatility increase and decrease cycle is
by
drawing a horizontal number eight figure. 8
half the eight ( one zig-zag, not the circle part ) is increase cycle and
the other half
is decrease. see gif
the point of symmetry in 8 which is in the middle corresponds to the
mean volatility. the rightmost point corresponds to highest outlier and the
leftmost to lowest volatility value...
immediately you can see that to predict volatility proper you not only need
to
know which part of 8 you are in, below or above the mean but
what cycle you are in, increase or decrease...
you can be below the mean but if you assume a decrease cycle ( no new
information, info fading ) where as it's increase cycle ( new information )
you will be wrong in your forecast.
math wise, you need to have two terms in your volatility model at least.
one to take care of the mean reversion and the other to take care of
the increase cycle. ( since log volatility is assumed to be normal there
is symmetry between the 4 parts of 8, ie below mean inc/dec and above mean
inc/dec )
take a look at the garch regression model ( i substituted sigma for V and
remove squared
for simplicity ):
Vn = c + a*Rn-1 + b*Vn-1
can you id if there are mean reversion terms and cycle terms and which ones
they are and
most importantly if they are proper?
well c + a*Rn-1 represents the mean reversion term and b*Vn-1 is the cycle
representation
attempt. in typical garch model mean returns is assumed to be 0 and c is
very close to
zero, right?
so c + a*Rn-1 is typically comes from c + a*(Rn-1 - m ) where m = mean
return an app.
zero... so this part trying to take care of the "reversion" or fading cycle.
next is b*Vn-1 which is an attempt to id the increase/decrease cycle, where
b is typically
large compared to a, representing the persistency factor. Vn-1 is in this
case is
volatility estimate and Rn-1 is the innovation.
if we analyze the model closer we can see that there is symmetry in
parameters for
volatility increase and decrease cycles, this is a "dumb" fading model
always
anticipating mean reversion... since a + b < 1
hence the assumption that garch only works well
predicting in the fading cycle... ie garch can't predict volatility increase
well but does
well on the volatility decay side... sure it is hard to predict new
information or predict
the end of the current info cycle and assume fading started... you kinda
understand what i
mean?
so, where i am going with this is that the true volatility model should:
- attempt to separate the volatility cycle in either increase or decrease
based on
whatever technique, ma, cycle id, momentum, etc... something that tells
the model
that you are most likely in volatility increase OR decrease cycle.
- then on top of that the model must id where you are relative to the mean
volatility,
are you under or are you over... this is important because if you are well
over
you are likely to revert back or reverting back already, Prob of reversion
is greater
at the extremes of the distribution... ( not in roulette case )
the best model would then be two ( four ) factor models that are enabled
whether you are
in the increase or decrease volatility cycle. then you can regress/estimate
two models
separately on mean reversion and increase/decrease... the volatility
distribution
must then be conditioned into two separate distributions: either under or
over mean
or increase / decrease for ease of parm estimation...
so you have two or four models with 3 parms each... you then enable the 1 or
2 (3,4)
model based on either increase in decrease cycle you are in...
( as you might infer the kink is in the cycle id technique )
each model has same number of terms, parms and estimated same way but
from different conditional probability density derived from joint volatility
density.
the general model should then be:
1. Vn = a1 + b1*Xn-1 + c1*Yn-1 + d1*et
2. Vn = a2 + b2*Xn-1 + c2*Yn-1 + d2*et
with 3 parms to estimate b,c,d ( a could be estimated as mean cond. distrib
of Vn)
Xn-1 - reversion explanatory var
Yn-1 - cycle explanatory var
et - noise
summary:
- garch is not so good and only catches half of the action, fading cycle.
- current computing power can do the above, i think it's doable.
- as the computing power improves the model complexity will increase, the
accuracy should increase too...
- some papers now confirm that two factor models ( they unknowingly point
to increase and decrease cycles ) are advantageous, ie garch (2,2) will do
better than 1,1 but not by a whole lot since the parms are estimated from
the same density and 2,2 model is not really structured as a two factor
model.
that's aside, i am currently finishing up on one factor model where
i just added the cycle term... since for my log range proxy the cycles are
symmetrical
i think i can do away with one factor model with 2 expl. vars one for cycle
one for reversion. for the cycle id proxy i took just the 1 bar volatility
proxy
momentum ( the simplest ), ie if on the last bar volatility went up i assume
it's an up
cycle...
simple but better cycle id techniques are guaranteed to improve the
accuracy.
it is possible to use kalman or arima or kernel regression or fft or
wavelets, or
mesa or any technique that will tell you whether current volatility is
measured as up or
down cycle.
so LTCM not having the cycle id term in there model:-) could not id the
volatility
increase cycle and as the crisis ws spreading all over the world they were
reverting
where they should be waiting for the reversion to start... it's like
catching
the bottom/top ( falling knife ) but catching the top in volatility and they
did not
catch it on time... blew horn as further increase in volatility took em out
of
trading business. dynamic hedging fell apart as the model predicted
reversion
where as the reality reflected the snowball. if they properly id-ed the
smallest
increase cycle they would have waited for
the top in volatility and then took the proper positions... funny that
catching
tops and bottoms is a typical newbie trader error ,we all know it right?
pretty neat story and there is math to learn from that for sure.
do not catch tops and bottoms instead wait for the move to get underway then
jump on it.
likewise do not anticipate new volatility cycle, wait for it to start first
then act in
continuation.
but i don't blame em, prediction is hard business...measurement is easier.
in roulette there is no volatility, no cycles, no reversion, just
probabilities,
expectations and runs.
bilo.
ps. the end result of that rocket science risk model is simply an adaptive
entry/exit technique for a trading system where risk on a given trade
is computed adaptively based on the above considerations. the complexity of
the model is on the level of garch... but structurally it is much better
than garch.
the dll might be available for a fee as this model is half the trading
system itself.
it's funny that the result sounds simple but the road to it so complex.
math pays. math's the key ( in systematic trading ).
see gif.
and finally no matter what the thread is you always end up dicussing what
YOU are
interested in. ain't it so?
>
> As regards the mean reversion of volatility, the good news is that for
some
> option strategies such as ratio backspreads you really don't have to worry
> much about its reliability because of the inherent loss limitation of
these
> positions. The great mistake of LTCM was to choose strategies whose *sole*
> prerequisite was mean reversion. They finally did learn that lesson, if at
a
> price.
>
> Michael Suesserott
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