Buffett seized on this failing of Black-Scholes in a letter to Berkshire shareholders three years ago.
Frederick cautions that Black-Scholes underestimates the probability of big moves, like that freakish crash on Oct. 19, 1987.
And it was the Black-Scholes equation that opened up the world of derivatives.
But for Ian Stewart, the story of Black-Scholes - and of Long-Term Capital Management - is a kind of morality tale.
They were not marking to market, were not evaluating potential losses on a rolling basis and therefore were not using Black-Scholes.
But is it really fair to blame Black-Scholes for what followed it?
"The Black-Scholes technology has very specific rules and requirements, " says Scholes.
The quite popular Black-Scholes calculator figures the value of warrants using current price, strike price, time until expiry, interest rate risk and share volatility as variables.
You see, the credit crunch had almost nothing at all to do with those derivatives, the options and futures, that we value using the Black-Scholes equation.
The Black-Scholes equation, brainchild of economists Fischer Black and Myron Scholes, provided a rational way to price a financial contract when it still had time to run.
Tail risk makes put options worth more than Black-Scholes predicts.
Black-Scholes changed the culture of Wall Street, from a place where people traded based on common sense, experience and intuition, to a place where the computer said yes or no.
There is reasonable concern that current methods of option pricing, both the Black-Scholes and binomial models, are not appropriate for determining the cost of the nontransferable, long-term options that companies issue to employees.
The idea that significant arbitrage opportunities are unlikely to exist (and certainly do not persist) is precisely the mechanism behind the Black-Scholes option-pricing model that Mr. Derman admires as a financial model behaving pretty well.
At Goldman he rose to the level of Managing Director and co-invented the tool for pricing options on Treasury bonds with Goldman colleagues Bill Toy and the late Fischer Black, of Black-Scholes formula fame.
FORBES: A Review of Emanuel Derman's New Book: Models.Behaving.Badly.
The Chicago native earned a finance doctorate at the University of Chicago in the early 1970s, when he worked with advisors like Nobel Prize winner Merton Miller and Fischer Black and Myron Scholes, coauthors of the Black-Scholes options pricing model.
They understood and calculated volatility, perhaps not so precisely as the Black-Scholes model that later garnered a Nobel Prize in economics, but good enough to get by and not misprice quotes on the puts and calls they made markets in.
Fischer Black, co-originator of the options-pricing model for which Messrs Merton and Scholes were recognised, died a year too soon to join his collaborators on the podium.
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