Sticky Strike vs. Sticky Delta: Revaluing a Volatility Surface

Compare sticky-strike and sticky-Delta scenarios, solve the circular Delta-to-IV mapping, and use both conventions without mistaking either for a market forecast.

For educational purposes only; not investment advice. Investing may result in loss.

Direct answer

Sticky strike holds implied volatility fixed at each strike and expiration during a spot-only shock. Sticky Delta holds implied volatility fixed at each specified option-Delta coordinate and expiration. A fixed-strike contract usually moves to a different Delta coordinate after spot changes, so sticky Delta can assign it a different IV.

These are conditional surface-revaluation conventions, not contract terms, no-arbitrage identities, or predictions. Actual surfaces may move partly like either rule while also changing level, skew, curvature, term structure, and liquidity. Sticky Delta does not keep a contract’s Delta constant; it keeps an IV quote attached to a Delta coordinate.

The mechanics below concern vanilla options valued on a European-style model under an instantaneous spot shock with time held fixed. Delta quoting is common in FX, while strike and moneyness views are common in equity and index options; exact conventions vary by product and venue. Derman’s cited evidence concerns SPX observations from 1997-09 through 1998-10, not every market or a current forecast. The OCC disclosure concerns U.S. exchange-traded standardized options and U.S. brokerage accounts. American-style exercise, futures options, employee options, OTC agreements, non-U.S. accounts, taxes, and legal rights require their own terms and jurisdiction-specific analysis. This page is current through 2026-08-22, does not evaluate any reader’s circumstances, and provides no individualized investment, legal, or tax advice.

What each convention fixes

For one expiration, write the pre-shock surface as σ₀(K) in strike coordinates or σ₀(Δ) in Delta coordinates. After spot moves from S₀ to S₁:

Sticky strike sets σ₁(K) = σ₀(K) at every fixed strike.
Sticky Delta sets σ₁(Δ) = σ₀(Δ) at every stated Delta node.

For a contract with strike K, sticky Delta is circular because Delta depends on IV. A reproducible calculation must:

State expiration, Call/Put side, spot or forward Delta, premium adjustment, rates, dividends, day count, and interpolation.
Choose an IV guess for the contract at S₁.
Compute its Delta, read or interpolate IV from the old σ₀(Δ) curve at that coordinate, and update the guess.
Repeat until both IV and Delta satisfy a stated tolerance; otherwise report non-convergence or an out-of-grid rule.

A label such as 25Δ Put is therefore not a universal strike. Call/Put sign, absolute-Delta labeling, forward versus spot Delta, and premium adjustment can map the same label to different contracts.

For a small move, the difference enters valuation through:

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

Sticky strike makes fixed-strike dσ_imp = 0 by assumption. Sticky Delta can make dσ_imp ≠ 0 as that contract migrates across Delta nodes, changing effective Delta and hedge P/L. For a large move, revalue every leg on the full shocked surface; local Greeks and one-step interpolation are not enough.

Delta is not moneyness

Sticky moneyness fixes a curve in K/F or ln(K/F) coordinates. It can resemble sticky Delta because both move with the forward, but Delta also depends on IV, time, rates, dividends, option side, and quoting convention. A risk report should name its coordinate and inputs rather than say only “floating smile.”

Example: one fixed-strike Call, two surfaces

Assume one expiration has these simplified pre-shock Call-Delta nodes:

Call Delta	IV
`50Δ`	`24%`
`70Δ`	`22%`

Spot starts at S₀ = $100; the K = $100 Call is initially at 50Δ with IV 24%. Spot rises instantly to S₁ = $105, with time, rates, dividends, and the declared Delta convention held fixed. For illustration, assume the iterative sticky-Delta calculation under those declared inputs converges to 70Δ.

Sticky strike: the fixed K = $100 Call retains IV 24%.
Sticky Delta: the old 70Δ node assigns the same contract IV 22%.

The same contract differs by 24% − 22% = 2 volatility points across scenarios. If dollar Vega is $18 per volatility point per contract, the first-order difference is 2 × $18 = $36 per contract, or about $360 for 10 contracts.

The 70Δ convergence is an explicit scenario input, not a result derivable from the table alone and not a claim about a listed chain. The $360 estimate excludes Delta, Gamma, Theta, higher-order interactions, bid-ask spreads, commissions, margin, taxes, and model error. Under sticky Delta, the new 50Δ option inherits 24%; it need not be the original K = $100 contract.

Building a decision-useful comparison

Capture synchronized executable option quotes, spot or forward, rates, dividends, timestamps, and contract specifications.
Record the exact Delta definition and whether wing labels use signed or absolute Delta.
Use one arbitrage-aware interpolation and extrapolation policy in both scenarios.
Iterate sticky Delta to a documented tolerance and flag nodes outside the calibrated grid.
Shock each expiration separately and distinguish an instantaneous shock from passage of calendar time.
Separate IV level, skew rotation, curvature, term structure, and coordinate migration in P/L attribution.
Revalue every leg, then aggregate by signed quantity, multiplier, currency, and account.
Compare assumptions with product-specific historical conditional moves without treating a sample average as a law.
Stress jumps, event-IV collapse, stale wings, wider bid-ask spreads, and inability to execute a theoretical hedge.
Size and govern risk from executable stress loss, liquidity, mandate, and account constraints, not the convention producing the smaller number.

Local-volatility, stochastic-volatility, and SABR-type models imply different smile dynamics. Dupire and Derman–Kani show how an option-price surface can be embedded in local-volatility or implied-tree frameworks; that static fit does not validate future surface motion. Hagan and co-authors document that local-volatility smile dynamics can oppose observed behavior in their rates/FX context. Moving any result to another asset class, maturity, venue, or regime requires fresh calibration and out-of-sample hedge testing.

Common misconceptions

“Sticky Delta keeps the option’s Delta fixed.” It fixes IV by Delta coordinate; the contract moves across coordinates.
“Sticky strike leaves every risk unchanged.” Fixed-strike IV is unchanged, but moneyness, Delta, value, and hedge needs move.
“Sticky Delta equals sticky moneyness.” Their coordinates depend on different inputs and may produce different values.
“One rule is always conservative.” The larger loss depends on position, move direction, skew, maturity, and interactions.
“A calibrated surface supplies its own dynamics.” Today’s cross-section does not determine tomorrow’s conditional motion.
“The Vega difference is complete P/L.” Spot, Gamma, time, execution, funding, and model residuals remain.