I'm looking for a simple model I can use to calibrate equity implied volatility surface. There are several models published in the literature, and most of them seem far too sophisticated for my purposes. I'm just looking for something I can use out of the box given the raw implied vols (computed using Black-Scholes) for a set of option chains.

I imagine I'd first have to smooth out the curve using some kind of interpolation scheme, and then apply the skew model. What's the standard industry practice for this procedure? I'm just looking for a first order approximation that's better than using flat skew, i.e. ATM vol for all strikes.

  • $\begingroup$ How many degrees of freedom do you want? A simple scalar parameter controlling skew is OK? $\endgroup$ – Daneel Olivaw Jun 17 '19 at 15:35
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    $\begingroup$ Based on your requirements I'd say Gatheral's SVI model suffices for the interpolation and extrapolation part. There are several versions of SVI around now, the original one is probably the simplest and good enough for what you're looking for. When you say model, do you mean that after the inter and extrapolation you want a simple model to calibrate and then price exotic options with? $\endgroup$ – ilovevolatility Jun 17 '19 at 15:35
  • $\begingroup$ SVI will allow you to interpolate the IV curve in an arbitrage-free way. Then you're also interested in a "local" vol model which allows you to control skew right? $\endgroup$ – Daneel Olivaw Jun 17 '19 at 15:37
  • $\begingroup$ @DaneelOlivaw Thanks, yes, I realized that the OP probably wants more than just inter/extrap and I edited my post accordingly. $\endgroup$ – ilovevolatility Jun 17 '19 at 15:40
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    $\begingroup$ Well, SVI is a very sophisticated toy model, and based on your answer it should give you what you want. First calibrate the 5 parameters to an ATM option + 2 otm calls + 2 otm puts. Then change the level parameter value in the SVI model (which basically results in parallel shift). You can change the other params as well to play around with possible shapes of the smile. $\endgroup$ – ilovevolatility Jun 17 '19 at 16:08

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