Fixed Strike Volatility: Sticky Strike vs Sticky Delta

Key Takeaways

• Fixed strike volatility tracks IV at one absolute strike as spot moves; in a sticky-strike regime it stays constant, in a sticky-delta regime it changes as the moneyness shifts.
• On SPX shock days, empirical data shows fixed-strike downside IV often rises even as that strike gets closer to ATM, neither sticky-strike nor sticky-delta, but a level-change regime.
• A common mistake: defaulting to sticky-strike in risk systems without testing, on equity shock days this understates the vol move on short-dated surface by a material amount.
• The regime can shift intra-day: rallies in calm news tend toward sticky strike; shocks and crashes tend toward sticky-delta or full upward vol-level shift across the surface.

What It Is

Think of the SPX 5,000 strike option. Today with SPX at 5,000, that strike is at-the-money. Tomorrow if SPX moves to 5,100, the same 5,000 strike option is now 100 points in the money for the call. Its IV is not automatically the ATM IV anymore. Under different vol-surface dynamics, the IV of the fixed 5,000 strike behaves differently as spot drifts away from it.

Fixed-strike vol is simply the implied vol assigned to that specific strike at each moment. Traders, risk managers, and structured-product desks care about it because many books hold positions at specific strikes for long periods, and daily P&L depends on how those strikes reprice.

The Intuition

Black-Scholes predicts a single flat IV across all strikes. Real markets have a skewed surface. As spot moves, there are three popular rules of thumb for how the surface reshapes:

• Sticky strike: IV at each absolute strike stays the same. When spot rises, the ATM strike changes, and the new ATM picks up whatever IV the surface already priced at that strike.
• Sticky delta (sticky moneyness): the surface shifts with spot, so a 25-delta put today still has the same IV as a 25-delta put tomorrow, even though the absolute strike backing that delta has changed.
• Sticky local vol: the rule implied by a calibrated local-vol model, which sits between sticky strike and sticky delta.

Fixed-strike vol is the quantity you measure to tell which regime you are in. In a pure sticky-strike world, fixed-strike vol is a constant. In a pure sticky-delta world, fixed-strike vol changes whenever spot moves, even if nothing else changes.

How It Works

For an options book with positions at specific strikes, the daily IV-change P&L on a strike is:

Vol P&L ~= Vega(strike) * d(IV_fixed_strike)

Where IV_fixed_strike is the implied volatility assigned to that specific absolute strike across the day. Two days with the same ATM IV can produce different P&L on the same position depending on how fixed-strike vols moved.

The regime can be tested empirically with a simple regression. For each strike K, regress the daily change in IV(K) on the daily return of the underlying:

d(IV(K)) = a + b * r_underlying + epsilon

• If b is close to 0, the surface behaves sticky strike (IV at K does not depend on where spot is).
• If b is large and negative for downside strikes (put IV rises when spot falls), the surface behaves sticky delta or steeper.
• In practice on SPX, empirical studies (Derman 1999, Hull et al.) find a regime close to a "sticky implied tree" or "sticky local vol," between the two extremes.

The rule of thumb on equity indices: when spot rallies on calm news, vol behaves roughly sticky strike. When spot drops on a shock, vol behaves closer to sticky delta, with the whole surface shifting up.

Worked Example

SPX opens at 5,000. The 4,800 strike put has IV of 16 (a 96 percent moneyness OTM put). Spot sells off 100 points on a macro headline to 4,900.

• Sticky strike prediction: 4,800 strike put IV stays at 16. The 4,800 strike is now 98 percent moneyness, closer to ATM, but we are tracking the absolute strike, so its IV does not change.
• Sticky delta prediction: the skew curve shifts laterally to follow spot. The new 96 percent moneyness strike is 4,704. The 4,800 strike, now at 98 percent moneyness, picks up the IV that previously sat on a 98 percent strike, roughly 15. Fixed-strike vol at 4,800 moved from 16 to 15.
• Empirical observation on SPX shock days: in practice, the whole surface often rises as spot falls. The 4,800 strike IV might actually rise to 17 or 18 even though it got closer to ATM. That is not sticky strike or sticky delta, it is level-change dominating regime dynamics.

Which regime you assume has large consequences for vega P&L on a large book.

Common Mistakes

1. Assuming sticky strike without testing. Many risk systems default to sticky strike because it is the simplest rule. On equity index surfaces in stressed regimes, that assumption materially understates the vol move on short-dated surface.

2. Confusing fixed-strike vol with ATM vol. ATM vol is spot-dependent: as spot moves, the ATM strike changes. Fixed-strike vol tracks an absolute strike. The two can move in opposite directions on the same day.

3. Ignoring the skew regime dependence. On calm days, sticky strike is a reasonable approximation. On shock days, the whole surface moves up, and fixed-strike vols on downside strikes rise sharply even though they got closer to ATM.

4. Using one regime for every asset. FX markets typically behave sticky delta. Equity indices are closer to sticky local vol. Single stocks can flip regimes around earnings. The right hedging rule depends on the asset.

5. Forgetting dividends and carry. Forward-strike vol and spot-strike vol differ by a carry term. Comparing fixed-strike IV over horizons where carry changed needs to net that out.

Frequently Asked Questions

Q: What is fixed-strike volatility in simple terms? Fixed-strike volatility is the implied vol assigned to a specific absolute option strike (like SPX 4800) as the underlying moves around. It tells you how the market reprices that one contract over time, which is what drives P&L on any position held at a fixed strike.

Q: How does fixed-strike volatility affect investment decisions? When the underlying moves, your option's P&L comes from two sources: delta (the price move) and the change in IV at your specific strike. If you only monitor ATM vol, you may miss that your fixed-strike IV has moved in the opposite direction on the same day.

Q: What is a real-world example of fixed-strike volatility in practice? SPX opens at 5000, the 4800-strike put has IV 16. A shock sends SPX to 4900. Under sticky-strike, the 4800 IV stays at 16. Under sticky-delta, it might drop to 15. In a real shock, it often rises to 17 or 18 as the whole surface lifts, a regime-dependent outcome that most simple risk models miss.

Q: How can practitioners use fixed-strike volatility in hedging? Estimate which regime your underlying is in before sizing vega hedges. On equity indices, model tests (regress dIV(K) on underlying returns) typically show a regime between sticky-strike and sticky-delta. On shock days, plan for the whole surface to lift, do not assume your downside strikes will hold their IVs just because they moved closer to ATM.

Q: How is fixed-strike volatility different from ATM volatility? ATM vol is spot-dependent, as spot moves, the ATM strike changes and so does the ATM vol reference. Fixed-strike vol stays anchored to one absolute price level. The two can move in opposite directions: ATM vol can fall (surface flattens) while a specific OTM strike's IV rises (surface steepens at the wings).

Sources

1. Derman, E. "Regimes of Volatility." Goldman Sachs Quantitative Strategies Research Notes, January 1999. http://pricing.online.fr/docs/regimes.pdf
2. Daglish, T., Hull, J., Suo, W. "Volatility Surfaces: Theory, Rules of Thumb, and Empirical Evidence." Rotman School of Management. https://www-2.rotman.utoronto.ca/~hull/downloadablepublications/DaglishHullSuoRevised.pdf
3. Delta Quants. "Volatility: Sticky Strike vs Sticky Delta." http://deltaquants.com/volatility-sticky-strike-vs-sticky-delta
4. Natenberg, S. Option Volatility and Pricing. McGraw-Hill. https://archive.org/details/optionvolatility00shel

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.