The four main Greeks (delta, theta, gamma, vega) are not theory. Each one tells you how your trade's value changes if the stock moves, a day passes or volatility shifts.
| Measure | What it measures | What it is used for |
|---|---|---|
| Delta (Δ) | The change in the option's price for each dollar the stock moves | Sizing the position, and a rough estimate of the chance of expiring in the money (ITM) |
| Theta (Θ) | What the option loses each day as time passes | Choosing expiration dates |
| Gamma (Γ) | How fast delta changes | Watching jump risk |
| Vega (ν) | The change in the option's price for each point of implied volatility | Understanding what happens to options around earnings announcements |
One option, all four numbers
An at-the-money call on a stock priced at $100, expiring in 30 days, with implied volatility of 30%. Its approximate numbers: a premium of about $3.40, delta of about 0.50, gamma of about 0.05, theta of about −0.06 and vega of about 0.11. Here is what they mean:
- The stock rose a dollar: the option gains about $0.50, and delta becomes about 0.55 because gamma added 0.05.
- A day passed with no move: the option loses about $0.06 of its time value.
- Implied volatility rose one point (from 30% to 31%): the option gains about $0.11 even if the stock does not move.
How to read the four together
The option buyer wants a fast move in their direction: delta and gamma work for them, and they pay theta every day as the price of waiting. The option seller is the opposite: they collect theta every day and carry gamma if the stock moves hard. Vega governs what happens around big events, when volatility rises before them and falls after.
Common mistakes
- Reading delta as an exact probability: it is an approximation of the chance of expiring in the money, not a guaranteed number.
- Forgetting that theta speeds up in the last two weeks before expiration, so a near-dated option loses value faster than it looks.
- Piling up trades without calculating the delta of the whole position: ten contracts with a delta of 0.50 move like 500 shares.
Summary
The four Greeks answer four questions: how much do I make if the stock moves a dollar? (delta) · How much does that answer change? (gamma) · How much do I pay each day for waiting? (theta) · And what happens if volatility changes? (vega). Anyone who knows all four for a position before entering knows what they are really betting on, and what they could lose if the market goes the other way.
