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The existence of "Fat Tails" actually makes options impossible to
actually price using a conventional options model. The only method to
utilize(which is what the more knowledgeable trading firms use)is an
actual montecarlo simulation. A binomial will will kinda sorta work,
but not really. What you would observe, if the contra party was doing a
montecarlo simulation, would be an "unusually" high volatility. This is
most likely the reason for the much of the unusual vol. readings we live
with. One would have to assume that over time the marketplace would
evolve and that the hedging methodology of the trading floors would
adapt, which I believe we are observing
The overall concern would be that overtime actual volatility would be
far below implied. For the last few years implied has been below
actual....an envirornment that exists when option buyers make money, as
they have for the last few years(I'm generalizing here). Buyers make
money when actual exceeds implied and sellers make money when implied
exceeds actual.
Fat tails may also occur when the dealer community creates skew so as to
facilitae their need to struture hedges. When they7 need to create
backspreads(the current hedge of choice)otm options would be marked up
in attempt to create natural sellers. These natural sellers would
eliminate the gamma risk of the dealer community. This weekends Barrons
has an article(I've had it quoted to me..I'll read it asap)talking
about the huge risk to the community with the sale of Insurance which is
the merely delta hedged. The reality of the post 1987 envirornment is
that hedging has become a lot more than mere delta hedging.
Another consideration is that(this is my favorite and actually a
combination of sorta everything)is that each individual option and it's
implied represents a unique price distribution(again this is where the
rocket science currently rests). In fact a consensus distribution may
exist which represents the current implied. Another important
consideration(and this far from a complete analysis)i9s that implied,
right now, is has been a better forecast of future actual than ever
before. This has been true for some time, but I don't observe it
everyday...I wish I had the time and resources to really examine this
issue, because if it holds it would be an huge money making opportunity,
I think.
Recognize too that vol is a consensus reflecting both pure
math(variation of price)and a whole bunch of other stuff generally
relating to liquidity and illiquidity(collars, uptick rules, etc). In
ordinary markets most of the vol is the pure math....in unusual
markets(like this one)the other stuff will weigh heavily in the vol
calculation and in fact change the culture of marketmaker hedging.
Whew, my fingers hurt. Having said that the hole topic of vol is really
more of an art than a science. As such it is subject to lots of
massaging and valuation. Other than a few pieces of work done by the
top trading and research firms...VERY FEW people have a really good
handle on it. Even most market makers will tell you they let the
marketplace "set" the vol.
I'm in Minneapolis and it was 4 below zero last nite. I actually miss
Chicago.
Happy Thanksgiving!!
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