SPX Volatility Surface: Sticky Moneyness vs. Constant Delta

External question — Quantitative Finance Stack Exchange Author: Spasski Original post: https://quant.stackexchange.com/questions/85380 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I am trying to understand how the $SPX$ implied volatility skew reacts to changes in the spot price $S$ , specifically regarding options at fixed percentage offsets (e.g., 10% OTM, 20% OTM). If $S$ moves, but we look at a strike $K$ that maintains a constant moneyness ratio (e.g. $K/S = 0.9$ ), does the market typically adjust the Implied Volatility at that new strike to ensure the option delta remains constant? I understand there are two primary theoretical models for skew dynamics: Sticky Strike: The volatility at a fixed numerical strike $K$ remains constant, regardless of spot moves. Sticky Delta / Sticky Moneyness: The volatility skew "slides" with the spot price, such that the volatility at a fixed moneyness (or fixed Delta) remains constant. My question is: Does SPX typically (calm markets) exhibit "Sticky Moneyness" behavior where the implied volatility at fixed percentage offsets ( $K/S$ ) remains stable, effectively preserving the option delta? Or does the volatility surface deform in a way that breaks this relationship at least in the short run (intra-day or a few days).

External answer — Quantitative Finance Stack Exchange Author: QuantCalc.net Original post: https://quant.stackexchange.com/a/85853 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. This is not an either-or scenario. Market behavior is typically quantified using the Skew Stickiness Ratio (SSR), where an SSR of 0 indicates sticky delta and 1 indicates sticky strike. An SSR greater than 1 signals an overreaction, driven by a strong spot-volatility correlation. For the SPX, the ratio sits around 1.4 for short tenors and approaches 1 for long tenors. Consequently, SPX dynamics lean toward sticky strike or overreaction, never sticky delta.