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The volatility skew often changes based on multiple factors, such as moneyness of the option, time to expiration, movement in the underlying instrument, etc..

How does one best model the skew? Is there a way to forecast how the skew will change as underlying moves and time passes?

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what type of modelling what you like to do exactly? Are you interested in getting a good surface / smile from market data or do you really want to stochastically model the skew/surface ? –  Probilitator Mar 1 at 7:35

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