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Lumifer comments on When the uncertainty about the model is higher than the uncertainty in the model - LessWrong
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Comments (78)
You keep asserting that but provide no arguments and don't explain what do you mean by "better".
Huh? Black-Scholes doesn't tell you what the price of the option is because you don't know one of the inputs (volatility). Black-Scholes is effectively a mapping function between price and volatility.
I don't understand what do you mean. In situations where Black-Scholes does not apply (e.g. you have discontinuities, aka price gaps) people use different models. Volatility smile is not a "patch" on Black-Scholes, it's an empirically observed characteristic of prices in the market and Black-Scholes is perfectly fine with it (again, being a mapping between volatility and price).
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).