What is gamma exposure?

Start with the option chain. For any expiry it lists call options at different strike prices — the price at which the owner has the right to buy the underlying. If a stock trades at $131, a call with a $120 strike lets you buy something worth $131 for $120: it's in the money. The strike nearest the current price is at the money (ATM), and strikes above it are out of the money.

Delta

Delta tells you how much the option price moves for a $1 move in the underlying. An ATM call worth $540 with a delta of ~0.54 would gain about $54 if the stock rose by $1 — a new price near $594. Delta is one of five option greeks.

Gamma

Gamma tells you how much delta itself changes for that same $1 move. As the underlying rises, an existing call's delta climbs by roughly gamma each dollar. Gamma ishighest at the money and fades as options move deep in- or out-of-the-money — the purple bell in the chart above.

Why gamma is “the delta of the delta”

Delta is already a rate of change: option price per dollar of underlying. Gamma is the rate of change of that rate — the second derivative of the option price, and the first derivative of delta. Hence the nickname. Delta tells you where you stand; gamma tells you how fast that is about to change underneath you.

You do not need calculus to see it — it is sitting in any option chain. Below is one for BTC: calls with 18 days to expiry, spot at $68,120, priced at 50% implied volatility (IV). Because a lower strike sits further in the money, moving down one row is the same as the underlying moving up. So subtract two neighbouring deltas, divide by the dollars between them, and you have measured gamma yourself.

One note on units. Gamma is normally quoted per $1 of movement, but with BTC in the tens of thousands a single dollar is noise — the numbers come out around 0.00004 and tell you nothing. So both gamma and the measured column below are scaled to $1,000 of movement, which is the size that actually matters here.

Take the $68,000 strike: delta 0.5285. Drop to $67,000 and delta is 0.5811 — a jump of 0.0526. The gamma on that row is 0.0526. Identical. Run the same subtraction down the whole chain and the last column never drifts more than about 0.0012 from the quoted gamma. That is the definition, made arithmetic.

The small gap that remains is itself instructive. Gamma is the instantaneous rate of change, while subtracting two rows measures the average across a $1,000 or $2,000 span — and gamma is changing over that span too. The wider the gap between strikes, the looser the approximation: the bottom rows jump $2,000 at a time, and drift furthest.

How gamma varies: ITM, ATM and OTM

Now read the gamma column top to bottom. Delta climbs steadily from 0.25 to 0.88 — a smooth S. Gamma does something else entirely: it rises from 0.0416 at the $74,000 strike to a peak of 0.0526 around $69,000–$68,000, then falls away to 0.0257 down at $60,000. A bell, not a ramp.

The reason is that deep in- and out-of-the-money options have nothing left to decide. A $60,000 call is almost certainly finishing in the money: its delta is pinned near 1 and a $1,000 move barely nudges it. A $74,000 call is almost certainly finishing worthless: delta near 0, equally unmoved. Only at the money is the outcome genuinely uncertain, so that is where a move shifts the odds — and therefore delta — the most. Gamma is a measure of uncertainty, and uncertainty peaks at the strike closest to spot.

Note that ITM and OTM are labels about direction, not about size. Both extremes of the chain have low gamma; what matters is distance from the money, not which side you are on.

Calls and puts share the same gamma

This is the part that surprises people. At a given strike and expiry, the call and the put have exactly the same gamma — not similar, identical. The table shows it: the $70,000 strike is an OTM call and an ITM put, with deltas of +0.4248 and −0.5752 pointing in opposite directions, yet one single gamma of 0.0518 serves both.

The algebra is short. Put-call parity fixes Δput = Δcall − 1. Differentiate both sides and the −1 disappears, because the derivative of a constant is zero. So the two deltas change at precisely the same rate, which is what gamma measures. Moneyness flips between the call and the put; curvature does not.

This is why gamma is aggregated per strike rather than per option type — and why a strike with heavy open interest matters regardless of whether that interest sits in calls or puts.

Gamma exposure (GEX)

Gamma exposure is what happens when you aggregate this across every contract dealers hold. Because each contract represents 100 shares, a dealer's hedge is roughly100 × delta shares per contract. When price moves, delta moves (via gamma), and the whole book must be re-hedged. That aggregate sensitivity — mapped by strike — is exactly what StrategyView renders for Bitcoin and Ethereum (BTC & ETH). And when that forced re-hedging feeds on itself, you get a self-reinforcing gamma squeeze.