Sticky Strike and Sticky Delta

What are sticky strike and sticky delta?

Sticky strike and sticky delta are two rules for how an option’s implied volatility responds when the underlying price changes. Sticky strike holds IV fixed at each listed strike, while sticky delta holds it fixed at each delta. When the skew slopes, the rule you choose changes the option’s value after a spot move and the stock hedge that offsets its directional exposure.

Under sticky strike, a $100 strike with 30% IV keeps 30% IV after spot moves. At-the-money IV changes because the new spot sits at a different point on the fixed strike curve. Derman’s Regimes of Volatility shows the market switching between these rules.

Under sticky delta, each delta keeps its IV as spot moves. With time, interest rates, and dividends held fixed, sticky moneyness expresses the same relationship through strike divided by spot. The point at 100% moneyness stays at 100% moneyness as spot moves.

How the skew shifts under sticky strike and sticky delta

Start with a $100 stock and a linear skew: 30% IV at the $100 strike, falling by 0.35 volatility points for each $1 increase in strike. After spot rises to $105, sticky strike leaves the curve unchanged.

Under sticky moneyness, the new IV at strike K equals the original IV at K × 100 / 105. The $105 strike now receives the original $100-strike IV of 30%. The $100 strike takes the IV the original curve had at $95.24 (100 × 100 / 105), which is 31.67%. Each point keeps its strike-to-spot ratio.

How the sticky rule changes delta and the hedge

Effective delta includes both the direct price response and the IV response:

Effective delta = Black-Scholes delta + vega × fixed-strike IV change per $1 of spot.

For sticky strike, the IV response is zero. For sticky moneyness, it is -(K / S) × the local skew slope. Use vega per volatility point when the slope is measured in volatility points per dollar of strike.

In the 30-day call example, Black-Scholes delta is 0.51715 and vega is 0.11427 per share per volatility point. At S = K = $100, the IV response is +0.35 points per $1 of spot. The correction is 0.11427 × 0.35 = 0.03999, which lifts the effective delta to 0.55714.

For 50 calls with a 100-share multiplier, the stock hedge rises from 2,586 short shares to 2,786. Hedge on sticky-strike delta while the surface moves by sticky moneyness, and those 200 shares of directional exposure stay open.

How traders use sticky strike and sticky delta

Calculate the correction at each contract’s strike and expiration. Vega, the strike-to-spot ratio, and the local skew slope all contribute. Aggregate those contract-level results to connect the surface with the position’s stock-equivalent exposure. Repricing the same position under both rules after a spot move, leg by leg, shows how much the choice changes position value and the stock hedge.

Track each leg’s IV alongside its price. The VIX Index blends prices across a broad range of SPX option strikes, while your P&L runs on the IV of your own strikes. Read those contracts to see what the surface is doing to your position.

Sticky implied tree and minimum-variance hedging

Derman’s declining linear-skew example places sticky-strike delta between the higher sticky-moneyness delta and the lower sticky-implied-tree delta. A sticky implied tree holds a calibrated local-volatility model fixed and derives the response from that model. Treat the three deltas as the range for the hedge, and let the fixed-strike IVs show which one the market is trading.

Hull and White’s minimum-variance hedge research fits the relationship between spot changes and IV changes from market history and sets the stock hedge that cuts the variance of the option-and-stock position the most. Compare it with the sticky-rule deltas when you want the hedge the data supports.

Limitations of sticky strike and sticky delta

• Let the fixed-strike IVs pick the rule. Derman documented stretches when fixed-strike IV held steady and stretches when it moved against the index, so check which rule they follow before you size the hedge.
• Reprice after a large spot move. The correction is local: it uses today’s vega and the local skew slope, so recompute it instead of reusing the old one.
• Compute each contract’s correction at its own slope. Real skews curve, so the local slope moves away from the example’s constant 0.35 points per $1 as strike and expiration change.
• Recompute from the delta surface over a longer hold or after a rate or dividend change. The moneyness shortcut stands in for sticky delta only while time, rates and dividends hold still.
• For the hedge that leaves the smallest swings in position value, compare both sticky deltas with the minimum-variance hedge Hull and White fit from spot and IV history.

Bottom line

Sticky strike and sticky delta are two standard assumptions for how implied volatility responds to a spot move, and when the skew slopes, the choice changes both delta and the stock hedge. Run the position under both rules, compute the correction contract by contract, and watch the actual fixed-strike IVs to see which regime the market is in.