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

Compare where implied volatility stays attached after spot moves, solve the recursive Delta mapping, and quantify how the two conventions change option valuation and hedging.

Canonical: https://wiki.fcontext.com/options/sticky-strike-sticky-delta/
Fact checked: 2026-07-22

> For educational purposes only; not investment advice.

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## 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.

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## 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:

1. Start with an IV guess.
2. Calculate the contract's Delta at `S₁` under the stated convention.
3. Read or interpolate IV from the old `σ₀(Δ)` curve at that Delta.
4. 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.

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## 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.

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## 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.

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## 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.

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## Related topics

- [Skew dynamics](/options/skew-dynamics/)
- [Implied volatility](/options/implied-volatility/)
- [Local volatility model](/options/local-volatility-model/)
- [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)