Sticky Strike Vs Sticky Delta

Imagine a photograph of a hillside from a fixed spot on the ground, versus one from a drone that always hovers a fixed distance above wherever you're standing. Both show "the hill," but they capture different things when you walk somewhere new. A volatility smile has the same ambiguity: when spot moves, does the smile stay glued to specific strikes (the fixed camera), or move with spot so a given moneyness always sees the same vol (the drone)? These are the two classic, mutually exclusive assumptions about how a smile behaves.

The two rules, defined

Sticky strike: the implied vol quoted at each specific strike $K$ stays the same as spot moves.

$$\sigma(K, T) = \text{constant as } S \text{ changes}$$

In words: whatever vol the $100 strike traded at yesterday, it's still trading at today, even after spot moves from $100 to $95. The strike is the anchor.

Sticky delta (equivalently, sticky moneyness): the implied vol at a given moneyness — say, the vol for an option 5% out-of-the-money, or for an option with 25-delta — stays the same as spot moves, so the whole smile shifts sideways to follow spot.

$$\sigma(K/S, T) = \text{constant as } S \text{ changes}$$

In words: the vol assigned to "5% out-of-the-money" doesn't change; but because spot moved, that now corresponds to a different dollar strike than yesterday. The moneyness is the anchor, not the strike.

Worked example 1 — same move, different repricing

A stock trades at $100, with the $95 strike (5% OTM put) quoted at 24% vol and the $100 strike (ATM) at 20%. Spot drops to $95. Under sticky strike, the $95 strike's vol is unchanged at 24% — so the option that's now ATM is quoted at 24%, up from yesterday's 20% ATM vol. Under sticky delta, the new ATM vol stays at 20% — the smile shifted down with spot, so the strike now 5% OTM ($90.25), not $95, is the one trading at 24%. Same $5 drop, opposite predictions for at-the-money vol.

Worked example 2 — the P&L consequence for a hedged position

A dealer is long a $100-strike ATM call, delta-hedged, when spot is at $100 and vol is 20%. Spot falls 5% to $95. Under sticky strike, the call's vol (fixed to the $100 strike) is unchanged at 20% — no vega P&L, only the gamma/delta-hedging P&L. Under sticky delta, the smile shifts, so the vol appropriate for "the $100 strike, now 5% OTM" becomes whatever the OTM-put wing was quoting — 24% here — generating positive vega P&L on top. Same position, same market move, materially different P&L depending on the regime.

What this means in practice

Real markets are neither purely sticky-strike nor purely sticky-delta — they sit somewhere between, and which one dominates varies by asset class and regime (equity index smiles tend to behave closer to sticky-delta most of the time). This matters directly for hedging: the "correct" delta to use for hedging depends on how you expect the smile to move when spot moves, which is why some desks use a minimum-variance delta that blends both effects rather than committing to either extreme (see minimum variance delta).

Practice

1. Spot rises from $50 to $55. Under sticky delta, does the vol quoted for the strike that is now 10% OTM change from what the 10%-OTM strike was quoted at yesterday?
2. A trader delta-hedges an option using plain Black-Scholes delta in a market that is actually behaving sticky-delta. Will their realized hedging P&L tend to be biased, and in which direction relative to what they expected?