An option's price changes with the underlying, with time, and with volatility. The Greeks measure each of those sensitivities. You don't need the formulas, but you do need to know what each one tells you about your position.
| Greek | Measures | Quick reading |
|---|---|---|
| Delta (Δ) | Change in option price per $1 move in the underlying | 0.50 delta call gains about $0.50 if the stock rises $1 |
| Gamma (Γ) | Change in delta per $1 move | How quickly delta speeds up; highest at the money near expiry |
| Theta (Θ) | Change in option price per day that passes | −0.05 theta loses about $0.05 a day (×100 per contract) |
| Vega (ν) | Change in option price per 1-point change in implied volatility | 0.10 vega gains $0.10 if IV rises 1 point |
Delta
Calls have delta between 0 and 1; puts between 0 and −1. At the money options are around ±0.50. Delta is also a rough guide to the chance an option finishes in the money, and it tells you the equivalent share position: one 0.50-delta call behaves like 50 shares.
Gamma
Gamma is how fast delta changes. Near expiry, at-the-money options have huge gamma: delta can swing from 0.2 to 0.8 on a small move. That makes short-dated options explosive for buyers and dangerous for sellers.
Theta
Theta is time decay: the value an option loses each day, all else equal. Buyers pay theta; sellers collect it. Decay accelerates in the last few weeks, which is why sellers like short-dated options and buyers need moves to happen quickly.
Vega
Vega is sensitivity to implied volatility. Long options gain when volatility rises; short options gain when it falls. Longer-dated options have more vega.
Worked example
You own 2 calls with delta 0.40, theta −0.06 and vega 0.12. The stock rises $2, a day passes, and IV is unchanged.
Approximate change = 2 contracts × 100 × (0.40 × $2 − $0.06) = +$148 (ignoring gamma, which would add a little more).
Key takeaways
- Delta is price sensitivity, and approximates the equivalent share position.
- Gamma is how fast delta changes; it peaks at the money near expiry.
- Theta is daily time decay; it speeds up in the final weeks.
- Vega is sensitivity to implied volatility; long options benefit when it rises.