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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 ...


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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 ...



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