Gamma

Gamma measures the rate at which delta changes for every $1 move in the underlying stock. If a call has a delta of 0.50 and a gamma of 0.05, a $1 increase in the stock price would push delta from 0.50 to 0.55. Gamma applies equally to calls and puts but is always expressed as a positive number.

Why It Matters

Gamma tells you how stable or unstable your delta exposure is. High gamma means your delta shifts rapidly with stock price changes — your position's risk profile is changing fast. Low gamma means your delta is relatively stable and predictable.

This matters most for two groups: option buyers benefit from gamma because their winning positions accelerate (delta increases in their favor), while option sellers are hurt by gamma because losing positions accelerate against them. The gamma-theta tradeoff is one of the central tensions in options trading — you cannot have positive gamma (acceleration in your favor) without paying theta (daily time decay).

How It Works

Gamma is highest for ATM options and decreases the further you go ITM or OTM. This makes intuitive sense: ATM options are the ones most sensitive to whether the stock moves up or down — a small move can shift them from OTM to ITM or vice versa.

Gamma and time to expiration:

• Long-dated options: Low gamma. Delta changes slowly. More predictable.
• Short-dated options: High gamma. Delta changes rapidly. This is where gamma risk concentrates.

As expiration approaches, ATM gamma spikes dramatically. An ATM option near expiration can have a delta that swings from 0.30 to 0.80 in a single move. This is why the final days before expiration are called "gamma risk" — positions can gain or lose large amounts quickly.

The gamma-theta relationship:

• Long options = positive gamma + negative theta (you benefit from acceleration but pay daily decay)
• Short options = negative gamma + positive theta (you collect daily decay but face acceleration risk)

Gamma in spreads: Vertical spreads have lower net gamma than naked options because the long and short legs partially offset each other. This is one reason defined-risk strategies are popular — they reduce gamma exposure.

Quick Example

You own a call with delta 0.45 and gamma 0.06. The stock rises $3.

After the first $1: delta moves from 0.45 to 0.51 After the second $1: delta moves from 0.51 to 0.57 After the third $1: delta moves from 0.57 to 0.63

Your option gained approximately $0.45 + $0.51 + $0.57 = $1.53 in value (per share). Without gamma, using just the initial delta of 0.45, you would have estimated a $1.35 gain. Gamma gave you an extra $0.18 — and this effect compounds more with larger moves.