The options greeks explained
By Faizan Ahmad. Updated .
The greeks are four numbers that explain why an option's price changes. Delta is how much the option moves when the stock moves $1, gamma is how fast delta itself changes, theta is how much value one day of time costs, and vega is how much the option gains or loses when implied volatility moves 1 point. Read together, they turn "my option went down" into a breakdown you can act on: was it the stock, the clock, or volatility?
What does each greek measure?
| Greek | The question it answers | For a long option | Biggest when |
|---|---|---|---|
| Delta | How much does the option move per $1 in the stock? | 0 to 1 for calls, 0 to -1 for puts | Deep in the money |
| Gamma | How much does delta change per $1 in the stock? | Always positive | At the money, close to expiry |
| Theta | How much value does one day cost? | Always negative | At the money, close to expiry |
| Vega | How much does the option move per 1 point of implied volatility? | Always positive | At the money, far from expiry |
| Rho | How much does the option move per 1 point of interest rates? | Positive for calls, negative for puts | Long-dated options |
Greeks are quoted per share. One standard contract covers 100 shares, so multiply by 100: a delta of 0.50 means about $50 per contract for each $1 the stock moves, and a theta of -0.17 means about $17 a contract lost per day.
How do the greeks work together? A real example
On October 30, 2026, Nvidia fell 3.94% to close at $205.25, a drop of about $8.42 from the prior close near $213.67. The same day, Tradytics showed NVDA's implied volatility up 5.9 points to 45.7%. Take an illustrative one-month NVDA $215 call bought at the prior close with implied volatility near 40%. A standard pricing model gives it a price of about $9.48 and these greeks: delta 0.51, gamma 0.016, theta -0.17, vega 0.24. Here is what each greek says happened to it, assuming the call's volatility rose by the same 5.9 points:
| Greek | Arithmetic | Effect per share |
|---|---|---|
| Delta (the stock fell) | 0.51 × -$8.42 | -$4.29 |
| Gamma (delta shrank on the way down) | ½ × 0.016 × 8.42² | $0.57 |
| Vega (volatility rose) | 0.24 × 5.9 points | $1.42 |
| Theta (one day passed) | one day | -$0.17 |
| Total | -$2.47, about -$247 a contract |
A full reprice of the same call in the model lands at about -$2.60, so four multiplications get you close. The breakdown is the useful part: the stock drop cost $4.29 a share, but the jump in volatility handed back $1.42. Had volatility stayed flat, the call would have lost about $3.90. A put holder that day was paid twice, since a long put gains from a falling stock (negative delta) and from rising volatility (positive vega).
The gamma line is why long options are lopsided in your favor: as the stock fell, the call's delta shrank, so each extra dollar of drop hurt a little less. On the way up it works the other way, and each extra dollar earns a little more.
How do the signs flip for long and short options?
Selling an option flips every sign. That is the whole trade-off between buying and selling premium in one table.
| Position | Delta | Gamma | Theta | Vega |
|---|---|---|---|---|
| Long call | Positive | Positive | Negative | Positive |
| Long put | Negative | Positive | Negative | Positive |
| Short call | Negative | Negative | Positive | Negative |
| Short put | Positive | Negative | Positive | Negative |
Buyers pay theta every day in exchange for positive gamma and vega: big moves and rising volatility help them. Sellers collect theta and carry negative gamma and vega: quiet days help them, sharp moves and volatility spikes hurt. Market makers on the other side of public trades carry these exposures in size, which is what gamma exposure (GEX) tries to measure.
Which greek matters most for your trade?
| Trade | Greeks to watch | Why |
|---|---|---|
| Buying weekly or same-day options | Gamma and theta | Huge swings per $1, and fast daily decay |
| Buying options months out | Delta and vega | Moves a lot like stock; sensitive to volatility; small daily decay |
| Buying before earnings | Vega | Implied volatility usually drops after the report |
| Selling options for income | Theta and gamma | You earn decay but pay when the stock moves hard |
Where do the greeks come from, and how far can you trust them?
Greeks come out of a pricing model (Black-Scholes or a binomial model) fed with the stock price, strike, time left, interest rates, dividends and the option's implied volatility. That has three consequences. They are estimates for small moves, which is why the example above was close but not exact. They change all the time, because every input changes. And two platforms can show slightly different greeks for the same contract, because they plug in slightly different volatilities or models. Treat them as a dashboard for the next move, not a forecast.
How to see it on Tradytics
The options strategy builder shows any strategy's payoff at expiry and before, and its P&L by price and date, so you can watch time decay and the stock's moves work on it before you place a trade; its chain shows each contract's delta as odds, the rough chance it finishes in the money. For the market's side, each stock's research options page, such as NVDA options, shows implied volatility by expiry and strike and dealer gamma by strike.
Common questions
Which greek is the most important?
For most option buyers, delta first, because it says how much you make or lose on the stock move you are betting on. Theta comes next for short-dated options and vega for anything held through earnings.
Are greeks per share or per contract?
Per share. Multiply by 100 for a standard contract, and by the number of contracts for the whole position.
Why does my broker show different greeks than another platform?
Each platform calculates greeks with its own volatility input, model and timing. Small differences are normal; large ones usually mean one side is using a stale price.
Do I need to care about rho?
Rarely. Rho measures sensitivity to interest rates and only adds up for options with many months or years left.
Can the greeks tell me where the stock will go?
No. They describe how an option reacts to moves, time and volatility. They say nothing about which way the stock will go.
Sources
- Cboe, "Learning the Greeks: An Expert's Perspective" (April 27, 2021): short definitions of delta, gamma, theta, vega and rho.
- Cboe rule filing SR-CBOE-2019-126 (SEC Form 19b-4): definitions of delta, gamma, theta and vega with worked numbers.
- OCC and the US options exchanges, Characteristics and Risks of Standardized Options (June 2024): what goes into an option's premium, and intrinsic versus time value.
- SPY options traded $331.78M in premium on 2026-11-02: $193.21M in calls and $138.57M in puts, a net bullish lean of $31.95M.
- Put/call ratio 0.72.
- Options price a move of about ±$6.07 by 2026-11-02.
- Max pain for 2026-11-02 is $765.0.
Updated 2026-11-02 16:02 UTC