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

For educational purposes only; not investment advice.

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.

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.

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.

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.

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.