How does the implied vol surface move over time?

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AcadiFi · Accepted Answer

The surface doesn't move rigidly. Three canonical regimes capture most dynamics: 1. Sticky strike: for a given strike K, implied vol sigma(K, T) stays constant as spot moves. This is the classic Black-Scholes world. It implies that ATM vol falls when spot rallies (because what was ATM becomes OTM put territory). 2. Sticky delta (or sticky moneyness): for a given moneyness K/S or delta, implied vol is constant. When spot rallies, the whole skew shifts right with it. This is typical for FX and short-dated index options in calm regimes. 3. Sticky local vol: dictated by Dupire's local vol equation. The ATM skew implies a specific relationship, and ATM vol changes with spot by approximately 2 * skew_slope * dS/S. ```mermaid flowchart LR A[Spot
Rallies] --> B{Regime} B --> C[Sticky
Strike] B --> D[Sticky
Delta] B --> E[Sticky
Local Vol] C --> F[ATM Vol
Drops] D --> G[Skew
Shifts] E --> H[ATM Vol
Drops 2x Skew] ``` A concrete example: Silverline Asset Management runs a vega-neutral book on SPX. They hedge by strike under sticky-strike and by delta under sticky-delta. In a 2% rally on a calm day the ATM 1-month vol typically drops roughly 40-60 bps under sticky local vol given the prevailing skew. In a crash, vol of vol explodes and the sticky-delta assumption fails — skew steepens sharply. FRM exam tip: know that the Derman regime choice dictates the vanna/volga hedge ratios and the cross-gamma between spot and vol.

How does the implied vol surface move over time?

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