It seems to me that there's a deep relationship between the sticky strike vs sticky delta assumptions (in vol surface modelling) and Bayesian updating. A smile implies a probability distribution. So when spot moves, does your pdf stay the same (sticky strike) ...
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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.
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This Peter Carr paper has some good details — https://poseidon01.ssrn.com/delivery.php?ID=887104096000094090107030026116070007059014046014006078009096019067075112006014090110126001100120033059005011077005074018001112016049064053067093018118113071001068088028055096108004065029105096024077124066116008093029119020107071097122088068006123022&EXT=pdf&INDEX=TRUE …
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