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You would simply calculate the prices of various strike options using your parameters, then calculate the black scholes implied vol of each option. Did I miss the point of your question ?


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Normally not, or even if - that would get you into trouble, since you'd have to drop the i.i.d assumption of residuals and then you could basically use almost no estimator anymore, for any moment. Even if and you could decompose into something like $f(t) + X_t + Y_t$, where $Y_t$ i.i.d, $X_t$ some dependent stochastic process and $f$ a deterministic ...



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