When you hold an option contract, its price doesn't move in a direct relationship with the stock. It is affected by the stock price, time, volatility, and interest rates together. The Greeks are the mathematical measures that define all of these sensitivities.
| Greek | What it measures | Range |
|---|---|---|
| Delta (Δ) | Option price change / dollar stock move | 0→+1 (Call) / −1→0 (Put) |
| Theta (Θ) | Value lost per day (time decay) | Always negative for buyers |
| Gamma (Γ) | Rate of change of delta / dollar stock move | Highest at the money |
| Vega (ν) | Option price change / 1% change in IV | Positive for buyers |
* This is a hypothetical illustration and does not reflect actual results. Results vary with market conditions and execution timing.
Delta (Δ): your directional exposure
Delta at work: AAPL $185| Call at 185 (ATM) · Delta 0.50 | AAPL rose $2 → option $+1.00 ($100 total) |
| Call 200 (OTM) · Delta 0.15 | AAPL rose $2 → option $+0.30 ($30 total) |
* This is a hypothetical illustration and does not reflect actual results. Results vary with market conditions and execution timing.
Delta as probability. Delta ≈ the probability the option expires in the money. A Call with delta 0.30 ≈ 30% probability. That is why professional sellers target the 0.20-0.30 range.Theta (Θ) · The silent killer
Theta = what an option loses each day from the passing of time alone. It speeds up sharply over the last 30 days.
Theta from two viewpoints. For the buyer, theta is an enemy: every day without a move leaks value. For the seller, theta is a friend: every day that passes, the sold option loses value in your favor.Gamma (Γ) · Acceleration
Gamma measures how fast delta changes. High gamma = delta changes quickly, a big risk for sellers. At-the-money options near expiration have the highest gamma.
Vega (ν) · Volatility sensitivity
Vega = how much the option price changes with each 1% change in IV. Before earnings, IV rises → it inflates prices. After the announcement, IV collapses (IV Crush) → it destroys the value of options you bought.
