answer:

this is actually a very important concept, but its represented backwards here IMO. the floating strike volatility surface is the primitive, the stationary variable over time. https://twitter.com/bennpeifert/status/1383986749689372674

If S&P is up 5% today, 1-month skew is -1.5 points per 1%, and the ATM vols come down 7 points on the rally, fixed strike implied volatility goes *up*, despite floating strike going down a lot. This is a mechanical skew delta effect. But is it meaningful to say "vol is up"?

If i slept for a couple years (sounds amazing!), I'd ask where the ATM vol and the 25 delta call & put vols are, not where the 4175 strike vol is.

If we've rallied to SPX 8000, and 1m ATM IV is crushed to 10, the 4175 vol will still be super high because they're winger puts, probably much higher than it is today. Doesn't mean "vol went up a lot"; there isn't a "bid to fixed strike vols" just because we keep rallying.

The risk properties of options (how much spot gamma and vol gamma they have, how much long or short vanna, etc) are all driven by where the strike is relative to spot. Implied volatility reflects the "market prices" of those risk properties at a point in time.

As a result, all interesting time series properties of volatility surfaces are stationary with respect to floating strike, not with respect to fixed strike.

IMO this confusion is reasonable and common! And it comes from the fact that vanilla fixed-strike options are the primitive observable instruments.

But conceptually:

-Spot moves
-Floating strike surface does *something*
-Fixed strike moves relative to floating strike, [1] sliding along the shape of the surface, and [2] moving with any changes in the shape of the surface

Importantly, that doesn't mean that floating strike trades are driving changes in the surface (they might or might not be!) but rather that the dynamic properties of options are driven by (forward - strike)/ (vol * sqrt(t)), not by strike

apologies that the above could be written much more precisely by someone who likes writing equations in a blog/document, but that someone is not me