I would like to add a few points to the relative importance of historical and
implied distribtions

(1) it is the future - not the past - historical distribution that matters
======================================================
of course the price of an option depends on the distribution of the returns;
even more, it depends on the returns itself and in which order they appear, ie
the entire path. unfortunately none of these things is known. making certain
hypothesis allows us to extrapolate future scenarios from past observations, but
this is always subjective.

being rational physicists, all of us will probably disagree with 'momentum
investors' who essentially assume that a stock will go up tomorrow because it
will go up today. even worse is probably the wizardry of chartists with all
these resistance lines, channels and oscillators. however - projecting past
distributions into the future is more or less doing the same thing, just a bit
more sophisticated (and maybe for that actually more 'true')

I however agree that if we would know the future distribution of returns  we
would have an amazing tools to price options - but so would we if we could
predict the final spot



(2) market makers use implied vol, short term traders use implied and
historical, long term trader use ????
========================================================================================
let us do some bourbaki and define terms before use: an 'option market maker' is
someone who is trading options but who is not taking a vega position, ie as soon
as he is given a  position he is going to square it.  for this trader all that
matters is the current implied distribution, and the historical distribution of
the underlying market is completely irrelevant.

a short term trader (gamma trader) is a trader who can buy and sell derivative
securities with a very short tem horizon in a frequency that allows him to have
a significant number of maturing trades during his evaluation period. an example
is a forex trader where very short maturities (even over night !) are common.
assuming a certain stationarity of the returns a trader can actually play the
higher moments, for example by selling the butterfly (wings against money, a
play on the fourth moment - see Nassim Taleb's book for more details) and if his
assumption about the relation between implied and historical distribution is
right, he will actually make money in the long run.

a long term trader (vega trader) is a trader trading products whose maturity is
much longer than his evaluation period. he does not really care about historical
distributions but rather about the markets perception of future distribtion
INCLUDING RISK PREMIUMS because at one point he will have to sell his position
(or marking it to market, which in  this context is more or less the same thing)


======================================
to conclude I think the past historical distribution is a proxy benchmark,
similar to the past performance of a stock. knowing nothing else it makes sense
to assume that future distribution will look similar, and obvious discrepencies
between implied and historical distributions can give rise to trading decisions
similar to the rich / cheap analyis in bonds. the question which distribution
matters, depends on the actual question studied, but  I would assume it safe to
say that both distributions together are important for most problems.

s














-----------------------------------------------------------------------------
This message is confidential; its contents do not constitute a 
commitment by Paribas except where provided for in a written agreement 
between you and Paribas. Any unauthorised disclosure, use or 
dissemination, either whole or partial, is prohibited. If you are not 
the intended recipient of the message, please notify the sender 
immediately. 

Ce message est confidentiel ; son contenu ne représente en aucun cas un 
engagement de la part de Paribas sous réserve de tout accord conclu par 
écrit entre vous et Paribas. Toute publication, utilisation ou 
diffusion, même partielle, doit être autorisée préalablement. Si vous 
n'êtes pas destinataire de ce message, merci d'en avertir immédiatement 
l'expéditeur.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%