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There are several reasons, maybe the most important and also quite intuitive one: Implied volatility more or less assumes that the stock price is driven by Brownian motion and thus moves in a continuous fashion. What we observe is that stocks can jump (usually downwards, sometimes upwards) which needs to be modelled using something like a jump process ...


The volatility smile is the result of market forces knowing form experience that out of the money option pay out more often that what would be expected by a normal (Gaussian) distribution. For years Quants speculated why the market drove the out of the money options higher that the price of the Black-Scholes model. The best theory speculates that the ...


it's difficult to say that they are not popular. Some people definitely use them for live pricing. I'd say the real question is "why are they not popular in the academic literature"? One answer would simply be that most the questions that arise in their use are ones of fiddliness which do not make good papers.

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