Why does delta refuse to stay still?

Delta told you how much your option moves per dollar. Gamma tells you how much that answer is about to change. If delta is your speed, gamma is your acceleration — and it is the reason an options position can feel like a completely different trade after a 3% day.

The definition and a worked example

Gamma = the change in delta per $1 move in the underlying.

Stock at $100. An at-the-money call with delta 0.50 and gamma 0.06:

Stock to $101 → delta ≈ 0.56
Stock to $103 → delta ≈ 0.68
Stock to $97 → delta ≈ 0.32

Your exposure grew by more than a third on the way up and shrank by a third on the way down — automatically, without you doing anything.

What that does to your profit and loss

This is where gamma stops being trivia. Take the $3 rally. Your delta was 0.50 at the start and 0.68 at the end, so the average delta across the move was about 0.59. The option therefore gained roughly:

0.59 × $3 ≈ $1.77 per share (about $177 per contract)

A naive fixed-delta calculation would have predicted 0.50 × $3 = $1.50. Gamma added about $0.27.

Now the $3 decline. Delta fell from 0.50 to 0.32, averaging 0.41, so the loss was roughly:

0.41 × $3 ≈ $1.23 per share

Not the $1.50 a fixed delta implies. Gamma saved about $0.27.

Gains accelerate; losses decelerate. That curvature — convexity — is precisely what the buyer's time value paid for. Long options are long gamma, and it is the good half of owning an option.

The writer's mirror

The writer is short gamma, and their version reads: losses accelerate, gains decelerate. This is the mechanical engine underneath the previous unit's warning. A short options position does not just lose when it is wrong; it loses faster the more wrong it gets, which is what turns an uncomfortable move into a margin event.

Where gamma lives

Two rules cover almost everything:

Gamma peaks at the money. Deep ITM and far OTM contracts have gamma near zero, because their fate is nearly settled — an option that will certainly be exercised has a delta of 1 that no longer moves.
Gamma rises sharply as expiry approaches. A one-day at-the-money contract can see delta swing from 0.20 to 0.80 on a modest move, because the stock is racing toward a binary outcome.

Put those together and expiration week has a distinctive character: gamma at its maximum exactly when time value is at its thinnest. The position behaves violently and decays fastest at the same time. Nothing about that combination is gentle.

In the data

Gamma sits beside delta on the chain. Apple's is below, in the Terminal's options view, as the Γ column.

Open Apple's chain with IV and the Greeks in the EODHD Terminal

Both numbers were computed at one underlying price, at one moment, and the chain does not print that price beside them. Gamma exists because delta changes as the share moves, so a delta computed at this morning's price is already out of date by the afternoon. A published Greek is a snapshot of a curve taken at a point you were not shown.

Try it now

In the chain above, read gamma across strikes for a single expiry roughly two months out, and confirm the peak sits at the money, with tails falling to near zero on both sides.
Take the same strike at a near expiry and a far expiry. The near-dated gamma should be markedly higher. That difference is the entire reason short-dated options behave differently.
Pick a contract with roughly delta 0.50 and gamma 0.05 and compute by hand: what is the delta after a $2 rise? After a $2 fall? What is the average delta across each move, and what does each imply for the option's price change?