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What is the best way to model implied volatility surface in filtered historical simulation (other than keeping it constant)? Is it appropriate to apply GARCH-like model to every point on the surface? Any reduction techniques? Any suggestions will be appreciated.

Thanks.

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    $\begingroup$ A possible way: simulate paths with FHS until expiry date $T$, then return an array of underlying prices from such paths. You can fit a parametric density to this array, like a 2-Lognormal mixture, by means of the EM algorithm. Once you have the Lognormal mixture 5 parameters, you can get the option prices for that maturity using something like this. From option prices, invert B&S and get the implied volatility, as usual. Repeat for different values of $T$ to get a surface. $\endgroup$ – Lisa Ann May 16 at 13:52
  • $\begingroup$ @LisaAnn, how to map implied volatilities onto volatility smile ("moneyness") in this method? Will it be the same result if I simply integrate GARCH volatilities along each path up to maturity to get an estimation of the implied volatility? Thanks. $\endgroup$ – marain May 17 at 19:36

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