Educational information only, not individualized investment, legal, or tax advice. Options involve risk and are not suitable for all investors; some written positions can lose more than the amount initially invested.
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 one cross-section. Hedging and scenario P/L require a convention, model, or empirical estimate for how the entire surface will respond to an 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” identify different surface points after spot moves. Sticky strike, sticky moneyness, and sticky Delta are scenario conventions, not market laws; observed behavior can change across selloffs, rallies, earnings, and liquidity shocks.
The mechanics below apply broadly to European-style valuation of vanilla options. The empirical discussion is mainly about U.S. equity and index options; Derman’s cited sample is SPX data from 1997-09 through 1998-10, not a current forecast. The OCC disclosure applies to U.S. exchange-traded, OCC-issued standardized options and U.S. brokerage accounts. American-style exercise, futures options, employee options, OTC contracts, and non-U.S. markets have different terms, account rules, taxes, and legal regimes. This page is current through 2026-08-22 and does not assess any reader’s objectives or circumstances.
Sticky conventions and option P/L
Sticky strike: for a fixed expiration and strike, IV 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 on that curve after the move.
Sticky Delta: IV at a specified option-Delta coordinate is held constant. This resembles sticky moneyness but is not identical because Delta also depends on volatility, time, rates, dividends, and the product’s Delta convention.
For a small move, an option’s value can be approximated by:
dV ≈ Δ_BS dS + Vega dσ_imp + ½Γ(dS)² + Θdt + ...
If implied volatility at the chosen surface coordinate responds to spot, the total spot sensitivity is approximately:
Δ_effective ≈ Δ_BS + Vega × (∂σ_imp/∂S)
Vega and ∂σ_imp/∂S must use consistent decimal or volatility-point units. Vanna is the local cross-sensitivity ∂²V/(∂S∂σ) and helps describe how Delta changes with volatility, but one Greek cannot capture a large deformation of level, skew, curvature, and term structure. Equity selloffs have often coincided with higher overall IV and richer downside Puts, but the sign, size, and local shape of the response are empirical rather than guaranteed.
Example: one 90 Put under two dynamics
Assume one expiration has this simplified IV curve against strike/forward:
K/F |
IV |
|---|---|
0.90 |
28% |
1.00 |
22% |
1.10 |
20% |
The 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
90strike remains at28%IV. - Under sticky moneyness, the fixed strike now has
K/F = 90/95 = 0.947. Linear interpolation between0.90and1.00gives approximately25.18%IV.
The assumptions differ by 28.00% − 25.18% = 2.82 volatility points for the same contract. If 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 other repricing effects.
This is a controlled arithmetic illustration, not a price forecast or trading recommendation. It assumes European-style valuation and excludes early exercise, discrete dividends, commissions, bid-ask spreads, margin, taxes, and model error. A production surface needs arbitrage-aware interpolation and simultaneous scenarios for term structure, skew, curvature, and liquidity.
Building and validating a dynamics assumption
- Record synchronized executable quotes, forward inputs, rates, dividends, and time conventions; stale wing quotes 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 changes by horizon, underlying, and market regime; daily equity behavior may not apply intraday, around events, or to rates and FX.
- Revalue every portfolio leg on the shocked surface instead of adding isolated Vega estimates.
- Attribute actual P/L to Delta, Gamma, Theta, surface level, skew/curvature, and execution, with an explicit 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. Dupire shows how a local-volatility model can fit an arbitrage-free European-option surface, while Hagan and co-authors show that fitting today’s smile does not establish realistic future smile motion. SABR was developed for rates and FX contexts; transferring any model to equity or listed-option portfolios requires product-specific calibration, hedge testing, and out-of-sample validation.
Common misconceptions
- “Skew is one number.” A slope depends on maturity, coordinates, strike range, and fitting method; dynamics also 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 the position and realized regime.
- “A steeper downside skew proves crash probability.” IV also reflects risk premia, supply and demand, constraints, and tail preferences.
- “Vega captures all volatility risk.” Parallel IV sensitivity misses skew, curvature, term structure, and spot-volatility interaction.
- “Today’s calibrated surface is a dynamics model.” Static fit and conditional evolution are separate requirements.