Warning this is for quants only. If you understand the problems of leptokurtosis in options pricing or the nature of gamma risk read on.....

I have recently been reading the Black Swan, which any serious quant will have finished a long time ago. Thinking about black swans etc. the inherent failures of Black Scholes variants to work as a good pricing mechanism got me to thinking.....

If one converts a vol point on a curve into a probability or likely hood event, then one can also construct a time likelihood etc. easily, ie. this is a in 10 trillion year event (See Goldman Sachs alpha fund et al for details.) The post fact analyst and pundit always can say that common sense made it obvious such and such was a falsehood.

I think a more interesting way to step out of the fallacy of pricing extreme events or price variants is to step outside of the price box altogether and to posit a regime type question. ie. how long has this phenomenon existed. Then using the work of Gott, one could arrive at the probability of it not existing. Here is an example instead of pricing AAA CDO's based on a finite time series of a few years and then assessing the shift outside of say 2 stdev's. My suggestion would be to use Gott's theorem pose the question how long has this instrument been priced below/above X. Then convert the time back into a probability to use in pricing the instrument.

Now this approach has flaws in that, the answer will vary on the way the question is framed. I would posit however that the naive approach of only using previous price is also only a singular frame of reference to assign value.

The major thesis is to not diminish VaR, and BS theory but rather to add an infinite number of ways to assess the framework of price and value and to free valuation from the context only of price and potentially put valuations into a wider framework of analysis.

Any comments...?