What do delta, gamma, theta and vega mean on a real option?

The option Greeks are four numbers that describe how an option price reacts when one input changes and the others stay put. Delta is the change in the option price for a 1-dollar move in the stock. Gamma is how much delta itself changes for that same move. Theta is the change in the option price from one day passing. Vega is the change in the option price for a 1-point change in implied volatility. Read together, they show which forces are acting on a contract at a given moment.

This post is part of our lingo series. Instead of four separate definitions, it puts all four Greeks on one real contract from the options tape, so you can see what each number measures, in what unit, and how they fit side by side.

What the Greeks are, and where the definitions come from

The definitions below follow the Options Industry Council (OIC), the education arm of the options industry, which publishes a page for each one.

• Delta: the change in the option price for a 1-dollar change in the underlying stock, per share.¹
• Gamma: the change in delta for a 1-dollar change in the underlying stock.²
• Theta: the change in the option price for one day passing, all else equal, per share.³
• Vega: the change in the option price for a 1-percentage-point change in implied volatility, per share.⁴

Two details in those definitions matter more than they look.

First, every Greek is a sensitivity to ONE input with the other inputs held fixed. Delta answers "what if only the stock moves?" Theta answers "what if only a day passes?" In a real market several inputs move at once, and the Greeks themselves shift as they do.

Second, the numbers are quoted per share. A standard US equity option covers 100 shares (the contract multiplier), so to see the effect on one contract you multiply by 100.

The contract: one call from the tape

As of 2026-10-08, at 10:36 ET, the CaymanBot options flow tape showed a call on NRG with a 140 strike, expiring 2027-03-19.⁵ The print was bought to open across 24 trades, for total premium of $6,563,870. Each contract traded at $6.10, with the stock at $108.16, so the strike sat well above the stock price at the time. This was someone else's trade on the public tape; it is used here only because it shows all four Greeks on one line.

The data feed reported these values for the contract at that print:

The cost of one contract comes straight from the price and the multiplier. In dollars:

Now each Greek in turn, on this one contract.

Step 1: Delta, the stock-price sensitivity

Delta of 0.298886 means that if the stock rose by 1 dollar, with nothing else changing, the option price per share would be expected to rise by about 30 cents. In dollars per share:

On a full contract, the same delta is often read as a share count:

So for small moves, this one contract reacts to the stock roughly like 29.9 shares would. A call's delta sits between 0 and 1. A strike far above the stock price tends to sit lower in that range, and a strike below the stock price tends to sit higher.

Step 2: Gamma, the change in delta

Delta is itself a moving number, and gamma measures how fast it moves. Gamma of 0.009632 means that a 1-dollar rise in the stock would add about 0.009632 to delta, and a 1-dollar fall would take about that much away.

On a contract basis:

That reads as about 1.0 share of extra stock-equivalent exposure for each 1-dollar move in the stock. This is why delta is described as a snapshot: after a large move, the delta in the table above no longer describes the contract, and gamma is the number that tells you how quickly it drifts.

Step 3: Theta, the cost of one day

Theta on this contract was -0.041861 per share, which rounds to -$0.042. Holding the stock price and implied volatility fixed, one day passing would be expected to take about 4 cents per share off the option price. In dollars per contract:

So the contract would lose about $4.19 of value for each day that passes with nothing else changing. The minus sign is the convention for a bought option: time works against the holder. Our earlier post on why an option loses value when the stock does not move walks through this effect on its own.

Step 4: Vega, the volatility sensitivity

Implied volatility is the volatility level that the option's market price implies. The feed reported 0.495063 for this contract, which is 49.5%.

Vega was 0.252661 per share, about $0.253. If implied volatility moved up by one percentage point, with the stock and time held fixed, the option price would be expected to rise by about 25 cents per share. A one-point fall would take about that much away. In dollars per contract:

So one percentage point of implied volatility is worth about $25.27 on this contract, against about $4.19 for one day of time.

Reading the four numbers side by side

Put the per-contract figures next to each other and the contract's exposures become concrete:

• A 1-dollar move in the stock: about 29.9 shares' worth of exposure (delta).
• How that exposure shifts with the move: about 1.0 share per dollar (gamma).
• One day passing: about -$4.19 (theta).
• One point of implied volatility: about $25.27 (vega).

A few general things show up when you read Greeks this way.

Each number assumes the others stand still. In practice the stock, the calendar and implied volatility all move at once, so the real change in the option price is a mix of all four effects, and the Greeks are recomputed as the inputs change. The table above describes this contract at 10:36 ET on 2026-10-08 and no other time.

Units differ, so compare them in dollars. Delta is in shares, gamma is in delta per dollar, theta is in dollars per day and vega is in dollars per volatility point. Turning each into a per-contract dollar figure, as above, is what makes them comparable.

Time to expiration shapes the mix. This contract had months left until 2027-03-19. Contracts with more time left generally carry more vega, and contracts close to expiration generally carry more theta and gamma relative to their price. That is a general property of option pricing, and it says nothing about what NRG or this contract will do.

When you look at prints on the tape, our guide on how to read options flow shows where the strike, expiry and premium sit on each line, and the Greeks add the "what is this contract sensitive to" layer on top.

How to practice this

The quickest way to learn the Greeks is to watch them change. Open a call in a paper account, note its delta, gamma, theta and vega, and check them again after the stock moves, after a weekend, and after implied volatility shifts.

CaymanBot gives you a $100K paper trading account, so you can hold a contract like this one with no real money at stake and compare the Greeks from day to day.

In the first two Learning Mode stages, each trade on the feed comes with a plain-English sentence you can check against the strike, expiry and premium.

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Educational only, not investment advice.