Black-Scholes isn't

Thursday, 24th September 2009

According to a paper co-authored by Nassim Nicholas Taleb, Black and Scholes (along with Merton) are wrongly credit with originating the widely used option pricing formula, and their version of the formula is inferior to its predecessors in many ways.

The first surprise is that some aspects of options have been well understood for a long time. Put-call parity has probably been used since at least 1600, and possible longer. This is not, on reflection, surprising as derivative markets have existed for centuries.

Louis Bachelier and Edward O. Thorp's produced predecessors to the Black-Scholes formula that were better in many ways, including being valid even if probability distributions of the price of underlying securities are scale free (fractal). This fits in very well with Taleb's dislike of using the normal distribution!

So, we really should be calling using the Bachelier-Thorp distribution, as both produced formulae that are actually closer to what traders use in practice.

On another subject, Taleb seems to be spending a lot of time trying to explain to people that the credit crunch was not a Black-Swan because it was predictable.