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Why would the sensitivity of the implied volatility at fixed strikes depend on the mean-reversion of underlying?
Not an expert but eg if an index goes up 10% then you expect everything to rebase around the new level, no reason to expect reversion to the previous level so the old level ceases to matter. Another way to say it is that index level is scale free, the actual number has no meaning
But if swap rates go from 2% to 3%, that doesn’t mean the 2% level stops mattering. There might be a “natural level” of vol for 2% rates so the 2% strike is drawn to that level, but there is no natural level of vol for S&P 3000 or 4000 or 5000.
This is all very hand wavey and as I said, I’m not an expert, just conjecturing wildly on a sunny weekend afternoon.
An old slide: the skew P&L is the first order in price change times the difference between implied and realized betas of vol level V (atm vol) to price change. In equities empirically, beta[i] is 2*skewness and realized beat is close to 1.3*skewness. In FX both are close to zeropic.twitter.com/V4KLNnOu06
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