Option Greeks explained: delta, gamma, theta, vega

An option's price depends on a handful of inputs: the stock price, time to expiration and volatility. Each Greek measures how much the option price reacts to one of them. All examples below come from the AAPL option chain on October 19, 2026 (expiring October 21, with AAPL near $343):

Delta: how much the option moves per $1 in the stock

The 345 call has a delta of 0.410: for every $1 AAPL rises, this option gains about $0.41.

• Call deltas run from 0 to 1, put deltas from -1 to 0. Puts have negative delta because they lose value when the stock rises.
• The further out of the money, the closer delta gets to 0; the 355 call is only 0.096. Deep in-the-money options approach 1 or -1.
• At-the-money options sit around ±0.5. Many traders also read delta as a rough probability of finishing in the money.

Gamma: how fast delta changes

Gamma is how much delta changes for each $1 move in the stock. The 345 call has a gamma of 0.0368: after a $1 rise in AAPL, its delta goes from 0.410 to about 0.447.

Gamma peaks at the money and grows as expiration approaches. That's why near-expiry at-the-money options swing so violently.

Theta: what the option loses each day

Theta is the change in option price per day with everything else held constant, and it's usually negative. The 345 call has a theta of -0.836: if nothing else moves, it drops from about 3.08 to 2.24 in one day.

This contract is two days from expiration, so time decay is steep. Option buyers pay theta; option sellers collect it.

Vega: price change per 1 point of volatility

Vega is the change in option price for each 1 percentage point change in implied volatility. The 345 call has a vega of 0.114: if its implied volatility rose from 37.3% to 38.3%, the price would rise by about $0.11.

Longer-dated options have more vega, so they're more sensitive to changes in volatility. What implied volatility itself means is covered in What is implied volatility.

Getting the Greeks from an API

Every contract in the chain snapshot endpoint /v3/snapshot/options/{underlying} carries a greeks object with delta, gamma, theta and vega, so you don't need to run a pricing model yourself:

"greeks": {
  "delta": 0.410,
  "gamma": 0.0368,
  "theta": -0.836,
  "vega": 0.114
}

Two things to keep in mind:

• Rho (sensitivity to interest rates) isn't provided. For short-dated options it's usually tiny.
• Deep in-the-money or long-untraded contracts have no reliable implied volatility, so they have no greeks field. Check that it exists before reading it.

Complete Python code is in Get a US option chain with Greeks in Python.

Related

• What is implied volatility (IV)?
• Get a US option chain with Greeks in Python
• US option symbols explained