unfortunately, mathematical analysis of skew is extremely hard to do.  the 
question is why does skew exist and does the market do a proper job of 
correcting for violations of the black scholes model.  in my mind, there are 
three big reasons for skew.  one is that the assumption of stochastic 
volatility as a function of price level gets violated.  commodities tend to 
have long range trading ranges that exist due to the economics of supply and 
elasticity of the demand curve.  nat gas tends to be relatively stable when 
we are in that historical pricing environment.  however, moving to a 
different pricing regime tends to bring volatility.  an options trader wants 
to be long vol outside the trading range, believing that a breakout of the 
range leads to volatility while trying to find new equilibrium.  supports a 
vol smile theory.  in addition, in some commodities realized vol is a 
function of price level.  nat gas historically is more volatile at $5 than at 
$4 and more volatile at $4 than $3.  thus there has been a tendency for all 
calls to have positive skew and all puts except weenies to have negative 
skew.  the market certainly trades this way as vol has a tendency to come off 
in a declining market and increase in a rising market.  to test, regress 15 
day realized vol versus price level and see if there is any correlation.  
second reason is heptocurtosis, fatter tails than lognormal distribution 
predicts.  supports vol smile theory.  easy to test how your market compares 
by plotting historical one day lognormal returns versus expected 
distribution.  
third, is just supply and demand.  in a market where spec players are 
bearish, put skew tends to get bid as vol players require more insurance 
premium to add incremetal risk to the book.  if you have a neutral view 
towards market, or believe that market will come off but in an orderly 
fashion, enron can take advantage of our risk limits by selling more 
expensive insurance.  crude market tends to have strong put skew and weak 
call skew as customer business in options is nearly all one way: producer 
fences.  if you believe vol is stochastic in the region of prices where the 
fence strikes are, can be profitable to take other side of trade.  
if you want to discuss further give me a call 4-6 pm houston time.  hope this 
helps,
john




Sharad Agnihotri
04/04/2001 12:44 PM
To: Mike Maggi/Corp/Enron@Enron, John Arnold/HOU/ECT@ECT
cc:  
Subject: Gas Implied Volatility Smile

John, Mike

I work for the London Research team and am looking at 
some option pricing problems for the UK gas desk.
Dave Redmond the options trader told me that you had done 
some fundamental research regarding 
the gas implied volatility smiles and may be able to help.

I would be grateful if you tell me 
what you have done or suggest 
someone else that I could ask.

Regards
Sharad Agnihtori