Skew Stickiness Ratio

An option's implied volatility surface has a skew: out-of-the-money puts typically trade at higher implied volatility than calls at a given moment in time. A separate question is how that whole surface moves when the underlying price moves — does the at-the-money implied volatility for a fixed strike shift by roughly what the static skew's slope would suggest, or does it move by more or less than that? The skew stickiness ratio (SSR) is defined precisely to answer this: it's the ratio of the actual observed change in at-the-money implied volatility, per unit move in the underlying, to the change predicted by the skew's slope alone (as if the whole surface just slid sideways one-for-one with spot).

An SSR near 1 means implied volatility behaves as if pinned to the strike ("sticky strike"): as spot moves, at-the-money vol changes by roughly what the skew's slope implies. An SSR near 0 means volatility is closer to "sticky delta" or "sticky moneyness," where the vol for a given strike barely moves and it's the vol for a given moneyness level that stays fixed instead. Real markets usually sit somewhere between these extremes, and the SSR is a convenient single number to quote how close to either regime the current market is behaving.

The ratio matters directly for hedging: a market maker's delta hedge for a skewed option book depends on assuming a vol dynamic, and mismeasuring the SSR (assuming sticky-strike when the market is closer to sticky-delta, or vice versa) leads to a systematically wrong hedge ratio and P&L bleed from unhedged vega-spot interaction, not just static skew risk.