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Stuart_Armstrong comments on When the uncertainty about the model is higher than the uncertainty in the model - Less Wrong
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The two examples in the post here are not sufficient?
From the Wikipedia article on the subject "This anomaly implies deficiencies in the standard Black-Scholes option pricing model which assumes constant volatility..."
The two examples being the 20-sigma move and the volatility smile?
In the first example, I don't see how applying an ad hoc multiplier to a standard deviation either is "better" or makes any sense at all. In the second example, I don't think the volatility smile is an ad hoc adjustment to Black-Scholes.
The Black-Scholes model, like any other model, has assumptions. As is common, in real life some of these assumptions get broken. That's fine because that happens to all models.
I have the impression that you think Black-Scholes tells you what the price of the option should be. That is not correct. Black-Scholes, as I said, is just a mapping function between price and implied volatility that holds by arbitrage (again, within the assumptions of the Black-Scholes model).