Probabilities, or frequencies that are calculated via Black-Scholes, Binominal Tree or even the more esoteric methodology of GARCH, all essentially utilise a Gaussian distribution of stock prices in their volatility calculations.This as the old saw notes, generally works well, until it doesn’t. <<Read>>
Essentially, probabilities are calculated by one or another model using a sample past data. This is a problem. As we know, in real life, stock market distributions do not really adhere to distribution assumptions of the various models - Black Scholes, Binomial Tree et al. There are models that are allegedly better, but not in common use. More particularly, the data sample used, or even volatility projections implied by option price may bear no relation to future volatility as it is realized. Also, statistical probabilities change as events unfold.
Two days can change the statistical landscape the trader has used to place a trade altogether.
The whole problem with using a model is... well, it's just a model...
...and models fail.
So when option traders make assumptions about probabilities and take risks based on them, it is really treading on thin ice. It's a guess. It may be an educated guess, but a guess nonetheless.
Ergo, option traders should question how probable the probability is.
"It'll never happen", happens with enough frequency to weed out model arrogance.
Survivors of 8 sigma events are those wise enough to mistrust "probabilities" and religiously cover their ass.