suppose we have the ability to perfectly model vol vs. spot behavior. ie. we know exactly what the vol surface will look like for a given spot level. i can see how this is useful for a market maker but i fail to see its usefulness for a risk taker.suppose im bullish on implied vols (of a give maturity and strike) and i buy a straddle there. if i delta hedge using my "perfect" model then my pnl would be zero even if i was correct in my view and vol increases.i guess the question really boils down to: how do i differentiate vol move due to spot move from "actual" vol move. (how do you even define "actual" vol move)

Paraphrasing somewhat, your question reads to me: how do I differentiate a `change in the implied volatility surface' due to a spot movefrom a change due to a move in some underlying (latent) volatility? Since particular spot levels are typically traversed many times, you could look at all the historical implied vol surfaces associated with a fixed spot level. Controlling for maturity, etc, the remaining differences are then due to 'something else'. The something else should include latent vol moves, but there also may be changes in other state variables and just trading noise. If you have a good model and the state variables are [$](t, S_t, V_t, \dots)[$],then the implied-vol surface is a function [$]\sigma_{imp}(t, S_t,V_t, \dots)[$], suppressing other parameters.So, [$]\Delta \, \sigma_{imp}(t, S_t,V_t, \dots)[$] is an Ito formula-type expansion. I'm not sure how far you can get until the results get very model-dependent. Also, with latent [$]V_t[$], you have to estimate those, so [$]V_t \rightarrow \hat{V}_t[$], where the hat denotes an estimate.

QuoteOriginally posted by: iniestasuppose we have the ability to perfectly model vol vs. spot behavior. ie. we know exactly what the vol surface will look like for a given spot level. i can see how this is useful for a market maker but i fail to see its usefulness for a risk taker.suppose im bullish on implied vols (of a give maturity and strike) and i buy a straddle there. if i delta hedge using my "perfect" model then my pnl would be zero even if i was correct in my view and vol increases.i guess the question really boils down to: how do i differentiate vol move due to spot move from "actual" vol move. (how do you even define "actual" vol move)So you are saying something like, you have a perfect model, you are bullish on implied vol, your model was indeed right but your p&l is zero. Maybe that means you shouldn't have been bullish in the first place?