Gamma
Gamma measures how delta changes as the underlying moves. Largest at ATM, especially near expiration. Why long-gamma and short-gamma positions behave so differently, and why 0DTE gamma is the structural reason short-premium trades blow through their expected ranges.
Delta tells you how the option moves with the underlying. Gamma tells you how delta itself moves. It's the "acceleration" greek — the rate at which delta changes as the underlying changes.
For 0DTE in particular, gamma is the force that turns small underlying moves into outsized P&L swings. Understanding gamma is the difference between knowing why a short-premium position blew through its expected range and being surprised by it.
The definition
The change in an option's delta for a $1 change in the underlying. Mathematically, the second derivative of price with respect to the underlying. Units: delta change per $1. Long options always have positive gamma; short options always have negative gamma. Calls and puts at the same strike share the same gamma.
If a call has delta 0.40 and gamma 0.05, then after a $1 rise in the underlying its delta is approximately 0.45. After a $2 rise, approximately 0.50. The relationship is approximate because gamma itself changes as the underlying moves — but for small moves, the linear approximation is close.
A few mechanical notes:
- Gamma sign is about long vs short, not call vs put. Long anything = positive gamma; short anything = negative gamma.
- A call and a put at the same strike and expiration share the same gamma. Their deltas move in lockstep — when one's delta moves up, the other's moves up by the same amount (just from a different starting point).
- Gamma units are delta-per-dollar. For position-level numbers, multiply by the contract multiplier (100 for SPX/SPY) to get how many deltas the position gains per $1 underlying move.
The shape of the gamma curve
Gamma is largest when the underlying is at the option's strike — i.e., when the option is ATM — and falls off symmetrically toward deep ITM and deep OTM. The curve is bell-shaped, peaking right at the strike and dropping off in both directions.
The chart below plots gamma as a function of the underlying. Drag the time-to-expiry slider toward zero and watch the bell narrow and grow taller. With weeks left, gamma is spread out — strikes meaningfully away from ATM still have some gamma. With an hour left, gamma is concentrated almost entirely in strikes immediately around the underlying.
- Gamma at $5,000
- 0.0038
- Call strike · time
- $5,000 · 7.0 d
The bell shape isn't a coincidence. Gamma peaks at ATM for the same reason every other ATM concentration shows up: ATM is the strike where the outcome is most uncertain. A small move in the underlying produces the biggest change in the option's probability of finishing ITM — which is the biggest change in delta — which is exactly what gamma measures.
Long gamma vs short gamma
The single most important practical concept about gamma is the asymmetry between long and short.
Long gamma works for you. When you're long an option and the underlying moves your way, gamma accelerates your delta — you make more per dollar as the move continues. When the underlying moves against you, gamma decelerates your loss — your delta shrinks toward zero, so further adverse moves cost you less per dollar. Long gamma is convex: favorable outcomes amplified, unfavorable outcomes dampened.
Short gamma works against you. When you're short an option and the underlying moves your way, your delta moves toward zero — you stop making money even as the trade keeps going in your direction. When the underlying moves against you, gamma accelerates your loss — your delta grows in the wrong direction, so further adverse moves cost you more per dollar. Short gamma is concave: favorable outcomes capped, unfavorable outcomes compounded.
A concrete example. Short an ATM 5000 straddle (sell the 5000 call and 5000 put) for combined premium of $40. Position is delta-neutral at entry. Underlying moves up $10 to 5010 over the next hour:
- The call you sold is now ITM by $10. Its delta moved from ~0.50 toward ~0.70.
- The put you sold is now OTM by $10. Its delta moved from ~-0.50 toward ~-0.30.
- Your position delta is now meaningfully negative — you're short the rally on net.
- The position's mark-to-market loss is several dollars more than what the entry-delta-times-move would predict. That extra loss is gamma.
If the underlying continues higher, the position keeps bleeding faster. If it reverses and comes back to 5000, you get some of the loss back — but not all of it, because the time-value decay and any IV expansion that happened during the move stay with you.
Gamma scalping, briefly
The flip side of long gamma being convex is that you can capture the convexity by trading the underlying.
A strategy of being long options (long gamma) and hedging the position's delta continuously by trading the underlying. As the underlying moves and the option's delta changes, you re-hedge by buying or selling the underlying. The convex profile of long gamma means you systematically buy low and sell high on the hedges — which harvests the underlying's realized volatility as P&L.
Market makers run gamma scalping continuously on their books. Some funds run it as a primary strategy: long gamma at relatively low IV, paying theta to maintain the position, harvesting realized volatility through systematic hedging.
For retail 0DTE traders, gamma scalping shows up less directly but matters as context. The market makers on the other side of your trades are typically gamma-hedging, and their hedging flow contributes to intraday dynamics — especially in the final hours of 0DTE expiration when their gamma exposure is highest.
What makes 0DTE gamma extreme
Gamma scales roughly as 1/√T. As time-to-expiry shrinks, gamma at ATM grows fast. The same strike that had small gamma a week ago has gamma roughly an order of magnitude larger with one day to expiry, and another order of magnitude larger in the final hour.
Mechanically: the option's delta needs to converge on either 0 (OTM) or 1 (ITM) by the closing print. The closer you are to expiration, the more violently delta has to swing across the strike. That violent swing is high gamma.
A concrete intuition. A 5000 SPX call with the underlying at 4995 (a few points OTM):
- With 7 days to expiration, delta might be around 0.45. A $10 move from 4995 to 5005 shifts delta to maybe 0.55 — a 0.10 swing.
- With 1 hour to expiration, the same OTM starting position has lower delta (maybe 0.27 — the S-curve is steeper, so OTM strikes have less probability of finishing ITM). But the same $10 move from 4995 to 5005 takes delta from ~0.27 to ~0.73 — a swing of nearly 0.50 in delta in the time it takes the underlying to make that move.
Why pin risk is gamma risk
Pin risk — the danger that the underlying pins right at a short strike at expiration — is fundamentally a gamma phenomenon.
With the underlying oscillating around a short strike in the final minutes, the position's delta swings between very negative and very positive. The short leg is alternately ITM (delta ±1) and OTM (delta 0) as the underlying ticks back and forth across the strike. Each crossing is a P&L event — and the closing print determines whether the option settles ITM or OTM, which can produce meaningfully different final P&L.
For SPX (cash-settled), pin risk is purely a P&L distribution issue — there's no assignment to handle. For SPY and equity options (physically-settled), pin risk also creates assignment uncertainty: whether you wake up Monday with no position or with 100 shares per contract you didn't expect.
The full mechanism with concrete examples is covered in Pin Risk and the Gamma Trap.
Reading gamma from a chain
Gamma on a typical SPX chain is shown as a small decimal:
- For options with weeks to expiration, ATM gamma is small — typically in the low single-digit thousandths per share.
- For 1-day options, ATM gamma is roughly an order of magnitude larger.
- In the final hour of a 0DTE option, ATM gamma is another order of magnitude up from there.
The exact numbers depend on the underlying price, the IV at that strike, and the contract specifications — but the qualitative pattern (gamma grows fast as time-to-expiry shrinks at ATM) is what matters for position management.
To translate gamma into position terms, multiply by the contract multiplier (100). A position-level gamma of 5 means the position's net delta moves by 5 per $1 underlying — so a $5 move shifts net delta by 25. For short-premium positions, gamma exposure tells you how fast your delta can move against you. Watching gamma — not just delta — is what tells you when you're approaching the position's danger zone.
Key takeaways
- Gamma is the rate of change of delta as the underlying moves. The "acceleration" greek. Long options have positive gamma; short options have negative.
- The gamma curve is bell-shaped across strikes, peaking at ATM. As time-to-expiry shrinks, the bell narrows and grows taller at the strike.
- Long gamma is convex (favorable outcomes amplified, adverse ones dampened). Short gamma is concave (favorable outcomes capped, adverse ones compounded). The structural reason short-premium trades blow up is gamma, not theta.
- 0DTE gamma is large in the final hour, especially at ATM. Short ATM 0DTE positions are mechanically leveraged bets on the underlying staying near a narrow range.
- Pin risk — the danger of the underlying ending right at a short strike — is fundamentally a gamma phenomenon, covered in its own article.