Module 8 · Lesson 4 of 13 · Options · About 5 minutes
The Option Greeks in Plain Language: Delta, Gamma, Theta, Vega
On this page
Before you read: Option Payoff Diagrams: Long and Short Calls and Puts
What you will learn
- What the four main Greeks measure and how to read them on an option chain.
- Why delta and gamma change as price moves, and why theta and vega matter even when price is still.
- What the Greeks cannot tell you.
What are the Greeks?
If an option’s price depends on several inputs, how could you measure the effect of each one separately?
The Greeks are sensitivity numbers that come out of an option-pricing model. Each one estimates how much the option’s price would change if one input changed a small amount and the others stayed the same. Most platforms show them per share, so you multiply by the contract multiplier for a per-contract figure. Check how your platform labels them. They are estimates from a model, and they change as the inputs change.
Delta: sensitivity to the underlying price
If the underlying rises $1, roughly how much does the option move?
Delta estimates the change in the option’s price for a $1 move in the underlying. Call deltas run from 0 to 1; put deltas run from 0 to −1. A call with a delta of 0.40 would be expected to gain about $0.40 per share, $40 per contract, if the underlying rose $1, other things equal. At-the-money options tend to have deltas near 0.50 (calls) or −0.50 (puts); deep in-the-money options approach 1 or −1; far out-of-the-money options approach zero.
Delta is also used to express an option position in share-equivalent terms: 10 calls with a delta of 0.40 on a 100-share multiplier behave, for a small move, roughly like 400 shares. Some people read delta as a rough probability of finishing in the money. That is an approximation that depends on the model, not a forecast.
Gamma: how fast delta changes
Why does an option’s delta keep shifting as the price moves?
Gamma estimates how much delta changes for a $1 move in the underlying. It is highest for at-the-money options and rises as expiration gets close. High gamma means delta, and so the position’s exposure, can change quickly. Option buyers have positive gamma; option sellers have negative gamma. That is one reason short options near expiration can change in risk very quickly.
Greeks diagram
Illustrative diagram constructed for teaching. Not real market data.
The diagram shows how the delta of a fictional call rises from near 0 far below the strike to near 1 far above it, changing fastest around the strike, where gamma is highest. It is constructed for teaching and is not real market data.
Theta: the effect of time
What happens to an option’s price if one day passes and nothing else changes?
Theta estimates the change in the option’s price from the passage of one day. It is usually negative for option buyers, because time value shrinks as expiration approaches, and positive for sellers. Time decay is not steady. For at-the-money options it tends to speed up in the final weeks and days.
Vega: the effect of implied volatility
Can an option’s price change because people expect more movement, even before any movement happens?
Vega estimates the change in the option’s price for a one-percentage-point change in implied volatility. Long options have positive vega; short options have negative vega. Vega is larger for longer-dated options. A drop in implied volatility, for example after a scheduled announcement passes, can reduce option prices even if the underlying barely moves.
What this does not tell you about the Greeks
- Greeks come from a model and its assumptions. Different platforms can show different values for the same option.
- Each Greek holds the other inputs fixed. In real markets several inputs change at once, and the estimates can be poor for large moves.
- Greeks describe sensitivity, not direction. They do not say what price will do.
- Aggregate “dealer positioning” figures built from Greeks rest on assumptions about who holds which side and should be read with that in mind.
Check yourself
- A put has a delta of −0.30. Roughly what happens to its price per contract if the underlying rises $1? Hint: delta × move × 100.
- Why is gamma highest for at-the-money options near expiration? Hint: how quickly can such an option switch between worthless and in the money?
- An option buyer sees the underlying unchanged after a big scheduled announcement, but the option fell in price. Which two Greeks could explain it? Hint: time and implied volatility.
Reflect on your own process
- Does your journal record the Greeks at entry, and do you note whether they were per share or per contract?
- Which Greek does your written plan check first for a position near expiration, and why that one?
- How would you compare your platform's Greek values with a second source before relying on them?