The Greeks — delta, gamma, theta, vega (what they actually mean)

Change in option price per $1 change in underlying.

• Call delta: 0 to +1. At-the-money ≈ 0.50. Deep ITM → 1.
• Put delta: 0 to −1. ATM ≈ −0.50.
• Practical reading: delta ≈ probability of expiring ITM. A 0.30-delta call has roughly a 30% chance of being ITM at expiry.

Rate of change of delta. Highest at-the-money, lowest deep ITM/OTM.

• High gamma means your delta shifts fast as spot moves. Good for scalpers, bad for hedgers.

Time decay per day, in dollars per share. Always negative for long options — you LOSE money just from time passing.

• A 7-DTE at-the-money SPY call might have theta −$0.15/day. Hold it 3 days without spot moving = −$0.45 per share = −$45 per contract.
• Theta accelerates exponentially in the last week.

Change in option price per 1% change in implied volatility (IV).

• High vega means your position is sensitive to IV. Before earnings → IV pumps → vega works FOR you. After earnings → IV crushes → vega works AGAINST you.

When buying options:

• You need spot to move enough to overcome theta decay + IV crush
• Delta tells you your directional sensitivity
• Theta tells you the ticking clock

When selling options:

• You collect premium
• You WANT theta (time passing = free money)
• You HATE gamma (spot moving against you = unbounded losses possible)