Sheri Markose and Amadeo Alentorn  have finally got their paper in press
“The Generalized Extreme Value (GEV)Distribution, Implied Tail Index and Option Pricing 
Journal of Derivatives. Spring edition, Volume 18, No 3, 2011.

Stephen Figlewski (JOD Editor) and a referee said that the paper was very ‘illuminating’  about the behaviour of  fat tailed (GEV Frechet ) distributions for asset returns under extreme market conditions.  Markose & Alentorn obtain a close form solution for the GEV option price.
They say:
“We find that the traded option price implied GEV model for the Risk Neutral Density (RND)yields results that
strongly  challenge traditionally held views on tail behaviour of asset returns based on Gaussian distributions
which predicate  simultaneous existence of thin tails in both directions during all market conditions. The GEV
distribution for asset   prices  which is governed by the tail shape parameter is found to switch tail shape with
underlying market conditions. Further, a non-zero value for the tail shape parameter results in significant
skewness in the probability mass of the GEV density function during extreme market conditions which implies
large one directional movements and truncation in the     probability mass in the other direction. During extreme market drawdowns, a positive value for the tail shape parameter of the GEV RND function for losses implies extreme price drops with the large probability mass on the right and a finite tail in the other direction implying an upper bound on possible gains. To date, proposed option pricing models intended to deal with both the fat tail and the skew in asset returns have failed to highlight the above characteristic features of fat tailed distributions.”

All  Matlab codes for the GEV option pricing model, GEV RND implied statistics such as volatility, Extreme Economic VaR  etc.   will soon be available  at https://www.acefinmod.com/index.html  .       .