Suppose you are a market maker with a model that is producing an implied volatility surface for you. Suppose you quote bid/ask prices (vols) around the prices given by your implied vol surface. In order to manage inventory and deal with asymmetric information risks it is necessary to adjust you bid/ask quotes as you are hit/lifted. For example if you quote 10/12 and get lifted at 12 then you are net short at 12 and would like to move your spread to cover your short position. For example you may move the spread to 11/13. That way you are more likely to buy and less to sell and you may cover your short at 12 by buying back at 11 and making 1.
My question is this: how does this dynamic carry over to an environment where you are trading across strikes and maturities and have a vol surface? Say I get lifted on the December 100 XYZ call. It is intuitive that all the XYZ options are correlated products so I should adjust my spread up across the whole vol surface. But my question is how is this actually done. How does the change in the spread depend on where you are on the surface? In other words: how do I change my vol surface in response to a trade?