# Skew Dynamics: How the Implied-Volatility Surface Moves with Spot

Understand sticky-strike and sticky-moneyness assumptions, spot-volatility response, effective Delta, Vanna, and why a static skew cannot explain hedged option P&L.

Canonical: https://wiki.fcontext.com/options/skew-dynamics/
Fact checked: 2026-07-22

> For educational purposes only; not investment advice.

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## Direct answer

**Skew dynamics** describes how implied volatilities across strikes and maturities change when spot, forward, time, and market conditions change. A static skew is only today's cross-section. Hedging and scenario P/L require a rule, model, or empirical estimate for tomorrow's entire surface conditional on the underlying move.

The answer depends on coordinates. “IV at the same strike,” “IV at the same log-moneyness `k = ln(K/F)`,” and “IV at the same Delta” refer to different contracts after spot moves. Sticky-strike and sticky-Delta are scenario conventions, not laws; actual markets can switch regimes around selloffs, rallies, earnings, or liquidity shocks.

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## Sticky conventions and option P/L

**Sticky strike:** IV for a fixed calendar maturity and fixed strike is held constant when spot changes. The smile stays attached to strike coordinates.

**Sticky moneyness:** the IV curve is held fixed as a function of `K/F` or `ln(K/F)`, so it moves with the forward. A fixed strike samples a different point of that curve after spot moves.

**Sticky Delta:** IV at a given option Delta is held constant. It resembles sticky moneyness but is not identical because Delta also depends on volatility, time, rates, dividends, and convention.

For a small move, option value can be decomposed as:

`dV ≈ Δ_BS dS + Vega dσ_imp + ½Γ(dS)² + Θdt + ...`

If implied volatility at the relevant surface coordinate responds to spot, then approximately:

`Δ_effective ≈ Δ_BS + Vega × (∂σ_imp/∂S)`

with units handled consistently. Vanna captures the local cross-sensitivity of Delta to volatility, but one Greek cannot describe a large surface deformation. Equity selloffs often coincide with higher overall IV and richer downside Puts, yet the size and even local shape change are empirical, not guaranteed.

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## Example: one 90 Put under two dynamics

Assume one maturity has this simplified IV curve versus strike/forward:

| `K/F` | IV |
| ---: | ---: |
| `0.90` | `28%` |
| `1.00` | `22%` |
| `1.10` | `20%` |

Forward starts at `F = 100`, so a `K = 90` Put has `K/F = 0.90` and IV `28%`. The forward then falls to `F = 95`.

- Under **sticky strike**, the fixed `90` strike remains at `28%` IV.
- Under **sticky moneyness**, the fixed strike now has `K/F = 90/95 = 0.947`. Linear interpolation between `0.90` and `1.00` gives approximately `25.18%` IV.

The two assumptions differ by `28.00% − 25.18% = 2.82` volatility points for the same contract. If its assumed dollar Vega is `$20` per volatility point per contract, the first-order valuation difference is about `2.82 × $20 = $56.40` per contract, or `$564` for `10` contracts, before Delta, Gamma, time, and repricing effects.

This is a controlled illustration, not a forecast. Real surfaces need arbitrage-aware interpolation and simultaneous shocks to term structure, skew, and bid-ask spreads.

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## Building and validating a dynamics assumption

- Record synchronized executable quotes, forward inputs, rates, dividends, and time conventions; stale wings can fabricate skew moves.
- Compare surfaces in strike, log-moneyness, and Delta coordinates before naming a regime.
- Separate a parallel level shift, skew rotation, curvature change, and term-structure move.
- Estimate conditional moves by horizon and market regime; daily equity behavior may not apply to intraday or event windows.
- Revalue every portfolio leg on the shocked surface rather than adding isolated Vega numbers.
- Attribute actual P/L to Delta, Gamma, Theta, surface level, skew/curvature, and execution, leaving a model-residual bucket.
- Check calendar and butterfly arbitrage after interpolation and shocks; a smooth-looking surface can still be inconsistent.

Local-volatility, stochastic-volatility, and SABR-type models imply different smile dynamics. Calibration to today's surface does not prove tomorrow's response, so model selection must include hedging behavior and out-of-sample surface moves.

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## Common misconceptions

- “Skew is one number.” A slope depends on maturity, coordinates, strike range, and fitting method; dynamics requires changes through time.
- “Sticky Delta means fixed option Delta.” It means IV is attached to Delta coordinates; the contract's own Delta still changes.
- “Sticky strike is conservative.” It can understate or overstate risk depending on position and realized regime.
- “A steeper downside skew proves crash probability.” IV includes risk premia, supply-demand, constraints, and tail beliefs.
- “Vega captures all volatility risk.” Parallel IV sensitivity misses skew, curvature, term structure, and spot-vol interaction.
- “Today's calibrated surface is a dynamics model.” Static fit and conditional evolution are separate requirements.

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## Related topics

- [Implied volatility](/options/implied-volatility/)
- [Local volatility model](/options/local-volatility-model/)
- [Charm, Vanna, and Vomma](/options/charm-vanna-vomma/)
- [Option model risk](/options/option-model-risk/)

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## Authoritative sources

- [Derman: Regimes of Volatility](https://emanuelderman.com/wp-content/uploads/1999/04/gs-volatility_regimes.pdf)
- [Derman and Kani: Riding on a Smile](https://emanuelderman.com/wp-content/uploads/1994/01/gs-riding_on_a_smile.pdf)
- [Dupire: Pricing with a Smile](https://doi.org/10.1002/fut.3990140104)
- [Hagan et al.: Managing Smile Risk](https://www.next-finance.net/IMG/pdf/pdf_SABR.pdf)