The surface is not a fixed object. When the stock moves, the whole sheet of implied volatilities moves with it, and it can move in two different ways. Which way it moves changes what your position is really exposed to, so traders keep an eye on it.
Two rules
Take a stock at $100 with an ATM IV of 30%, and enough put skew that the $90 strike shows 34%. Now the stock falls to $90.
Under sticky strike, each strike keeps its own IV. The $90 strike still shows 34%, and since $90 is now at the money, ATM IV has risen from 30% to 34%. The smile stays nailed to the strike prices and the stock slides along it.
Under sticky delta, sometimes called sticky moneyness, the smile moves with the stock. ATM IV stays at 30% whatever strike is at the money now, so the $90 strike's IV drops from 34% to 30%, and the strike 10% below the new price, $81, picks up the 34%. Skew is attached to delta, not to dollar strikes.
IV by strike with the stock at $100: 30% at the money and 34% at the $90 strike, 10% below. Hover the 90% point. Under sticky strike that 34% becomes the ATM IV after a fall to $90; under sticky delta this whole picture moves with the stock and ATM stays at 30%. Raise skew and the gap between the two rules grows.
Both rules are simplifications. Real markets sit somewhere between them and drift from one to the other, and on a sharp fall the whole surface also shifts up. But the two rules are the yardsticks everyone measures against.
Why it changes your vega
Say you own the $90 put on that stock. The chain gives you its vega, the gain per one-point rise in IV. Under sticky strike, the fall to $90 leaves your put's IV at 34%, so vega does nothing and your gain is all delta. Under sticky delta the put's IV falls to 30% as it becomes the at-the-money option, so you give back four points of volatility through vega on top of the delta gain. Your model treated vega as a separate risk. The market tied it to the stock price.
A 30-day $90 put against the stock price, at its own skewed 34% and at the 30% it takes under sticky delta. At $90 the value gap is about 41 cents a share: four points of vega. Switch to Delta and the two lines nearly meet at the strike; the difference shows up in value, through vega.
The same logic runs in reverse for a call above the market, and it flips sign for short positions. A position's real exposure to a stock move is its delta plus its vega times the IV change that the move drags along with it. On a stock with steep skew that second term is not small. Some desks call the total the skew delta and hedge that, rather than the delta the model prints.
Reading the regime
Traders watch which rule is closer to holding, because it sets the hedge. In a slow, range-bound market, sticky strike tends to describe things: the stock wanders, the strikes keep their IVs, and ATM IV drifts up and down the smile as the stock passes over it. In a fast trending market, sticky delta does better: the smile rides along with the price. In a sharp sell-off neither works cleanly, because the entire surface jumps and the front jumps most.
The check is simple. Watch ATM IV across a stock move. If it changed by about what the smile at the old strikes predicted, the market is on sticky strike. If it hardly changed while the stock moved, sticky delta. The Terminal makes that check a two-number read.
The maths: the vega P&L between the two rules
For a fixed strike, the IV change a stock move drags along is zero under sticky strike. Under sticky delta the smile is fixed in moneyness, so a strike's IV moves with dIV/dS equal to the skew per dollar of stock. With 4 points of skew per 10% of a $100 stock, that is 0.4 points per $1. The position's effective delta becomes Δ_eff = Δ + vega × dIV/dS.
Worked example, with a 4% rate and 30 days to expiry, priced with the pricing model. The $90 put at 34% is worth about $0.61, with a delta of minus 0.12 and a vega of 0.058. Its sticky-delta effective delta is -0.122 + 0.058 × 0.4 = about minus 0.10: a fifth less downside protection than the chain's delta says.
Now the stock falls straight to $90. Under sticky strike the put keeps 34% and is worth about $3.35. Under sticky delta it is at the money on 30% and worth about $2.94. The difference is $0.41 a share, which is just its new vega of 0.103 times the 4 points lost. On 10 contracts that is $410: $2,730 of profit under one rule and $2,320 under the other, on the same stock move.
Your turn
Open the NVDA chain on the monthly expiration. Read the ATM IV, then read the IV printed two strikes lower. That second number is where ATM IV would go under sticky strike if the stock fell to that strike; the first is where it would stay under sticky delta. The next lesson stops treating skew as something that happens to your position and trades it directly.