Sticky Strike vs. Sticky Delta: Two Volatility-Surface Scenarios

For educational purposes only; not investment advice.

Direct answer

Sticky strike holds implied volatility fixed at each strike and maturity when the underlying moves. Sticky Delta holds implied volatility fixed at each option-Delta coordinate and maturity; after spot moves, a fixed-strike contract generally maps to another Delta node and therefore another IV.

They answer a conditional question: “If spot changes and other chosen inputs follow this rule, what surface should be used to revalue the portfolio?” They are scenario conventions, not contractual terms, no-arbitrage identities, or forecasts. Actual equity-option surfaces can move partly like either convention, rotate, shift in level, change curvature, and switch behavior across regimes.

Sticky Delta does not mean an option’s Delta stays constant. It means the IV quote remains attached to a Delta coordinate. The contract’s Delta changes with spot, IV, time, rates, dividends, and the Delta convention.

What remains fixed

Represent a fixed-maturity surface as either σ(K) or σ(Δ). After a spot move from S₀ to S₁:

Sticky strike applies σ₁(K) = σ₀(K) for each fixed strike.
Sticky Delta applies σ₁(Δ) = σ₀(Δ) for each fixed Delta node.

For a contract with strike K, Sticky Delta requires solving a recursive problem because Delta depends on IV:

Start with an IV guess.
Calculate the contract’s Delta at S₁ under the stated convention.
Read or interpolate IV from the old σ₀(Δ) curve at that Delta.
Recalculate Delta and repeat until the IV and Delta mapping converge.

The result is undefined unless the report specifies at least maturity, Call/Put side, forward or spot Delta, premium-adjusted or unadjusted Delta, rates, dividends, and interpolation. A quoted “25 Delta Put” is a coordinate, not a universal strike.

For small moves, the valuation difference can be understood through:

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

Sticky strike sets the fixed-strike dσ_imp to zero by construction. Sticky Delta may assign nonzero dσ_imp to that same contract as it migrates through Delta nodes. This changes effective Delta and hedge P/L. For large moves, revalue every leg on the full shocked surface rather than adding local Greeks.

Coordinates are not interchangeable

Sticky moneyness holds a curve in K/F or ln(K/F) coordinates. It is often loosely grouped with Sticky Delta because both surfaces move with the forward, but they are not identical: Delta also depends on IV, time, rates, dividends, and convention. A risk report should name the actual coordinate instead of using “floating smile” as shorthand.

Example: the same 100 Call under two rules

Assume one maturity has these simplified Call-Delta nodes before the move:

Call Delta	IV
`50Δ`	`24%`
`70Δ`	`22%`

The underlying starts at S₀ = $100, and the K = $100 Call is at the 50Δ node with IV 24%. Spot rises to S₁ = $105; time, rates, and dividends are held fixed for this controlled example.

Sticky strike: the K = $100 Call keeps IV 24%.
Sticky Delta: an iterative Delta/IV solve maps the now in-the-money fixed-strike Call to 70Δ, where the old curve assigns IV 22%.

The same contract therefore differs by 24% − 22% = 2 volatility points between scenarios. If its dollar Vega is $18 per volatility point per contract, the first-order valuation difference is:

2 × $18 = $36 per contract

For 10 contracts, it is about $360 before Delta, Gamma, time, and higher-order interaction effects. These Delta nodes and the solved 70Δ result are illustrative inputs, not a claim about a particular listed chain.

The coordinate view also explains a different question. Under Sticky Delta, the new 50Δ option near the new at-the-money strike inherits 24%; it is not necessarily the original K = $100 contract. Confusing “same contract” with “same Delta bucket” reverses the comparison.

Building a usable comparison

Capture synchronized option quotes, spot or forward, rates, dividends, and timestamps.
State whether the surface is by strike, log-moneyness, forward Delta, spot Delta, or premium-adjusted Delta.
Keep Call/Put sign and absolute-Delta labeling explicit; 25Δ Put and 25Δ Call are different wings.
Use one arbitrage-aware interpolation and extrapolation policy across both scenarios.
Iterate Sticky Delta to convergence and report the tolerance; one lookup from stale Delta is inconsistent.
Shock every expiry separately; a spot move can coincide with term-structure changes.
Separate parallel IV level, skew rotation, curvature, and coordinate migration in P/L attribution.
Revalue all legs and aggregate by signed quantity and multiplier.
Compare assumptions with historical conditional surface moves, but do not treat a sample average as a law.
Stress jumps, event IV collapse, wider Bid-Ask, stale wings, and inability to trade the theoretical hedge.
Record the model residual when actual P/L is not explained by Delta, Gamma, Theta, and surface changes.
Size from executable stress loss and liquidity needs, not whichever convention produces lower risk.

Common misconceptions

“Sticky Delta keeps the option’s Delta fixed.” It keeps IV attached to a Delta coordinate; a fixed contract moves across coordinates.
“Sticky strike means the whole surface is unchanged.” IV at fixed strikes is unchanged, but moneyness and Delta labels move.
“Sticky Delta and sticky moneyness are the same.” Their coordinates depend on different inputs and can give different values.
“One convention is always conservative.” The larger loss depends on position, spot direction, skew, maturity, and interactions.
“The surface must follow one rule.” Actual surfaces can combine level, skew, curvature, and term changes.
“A two-point Vega estimate is complete P/L.” Spot, Gamma, time, surface response, execution, and model error remain.