You keep asserting that but provide no arguments and don’t explain what do you mean by “better”.
The two examples in the post here are not sufficient?
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).
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 in the post here are not sufficient?
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.
This anomaly implies deficiencies
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).
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).