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… vol at each strike as a function of spot-vol covar (skewness) and vol-of-vol (convexity) depending on vanna/volga exposure at each strike.
This Peter Carr paper has some good details — https://poseidon01.ssrn.com/delivery.php?ID=887104096000094090107030026116070007059014046014006078009096019067075112006014090110126001100120033059005011077005074018001112016049064053067093018118113071001068088028055096108004065029105096024077124066116008093029119020107071097122088068006123022&EXT=pdf&INDEX=TRUE …
yeah i would strongly advise using the constrained model in this paper over a larger one, as a larger one will fit the data better but will sometimes assign loopy economic values to the vanna / volga pricing
I implemented it to do risk on options a while back. I found (a) important to weight liquid strikes more heavily to avoid crazy fits (b) can get a good fit with just three params (atm vol, skew, convexity) except for short dated, where more terms were needed to fit the wings.
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