Black-Scholes: The maths formula linked to the financial crash (BBC)

[Lucky Luciano]

5. Everyone in finance knows Black Scholes is flawed,

Last edited Sat Apr 28, 2012, 06:21 PM - Edit history (2)

but it is a good benchmark to start from. It is not like there is this one statistician on Wall Street who was discovering its flaws. The flaws were known from the start.

It assumes securities have a log normal distribution of returns and that the price path is continuous with constant log normal volatility. This is probably a good assumption during most trading hours, but only a few minutes of this assumption being incorrect misprices the option.

People have tried a lot of models where Black Scholes was a starting point to something more complicated like local volatility models, stochastic volatility, stochastic vol with jump diffusion, local stochastic vol. They are all flawed and make assumptions like any model, but improve the original Black Scholes model.

The hardest thing for wall street models to get right is correlation. Correlation is very hard to hedge and anticipate when things go to shit. Like, " how many subprime borrowers should default in this CDO if we know that x number have defaulted in the past.". The correlation of defaults was tough to model. Not enough hard data that was similar in the history of the US with such lax lending standards to properly estimate.

I could go on and on, but...