Options Greeks Cheat Sheet: Delta, Gamma, Theta, Vega & Rho Explained
The Five Greeks at a Glance
| Greek | Measures Sensitivity To | Range | Key Insight |
|---|---|---|---|
| Delta (Δ) | Underlying price change ($1 move) | Calls: 0 to +1.0; Puts: −1.0 to 0 | Directional exposure. Delta 0.50 ≈ 50% chance of finishing ITM. |
| Gamma (Γ) | Rate of change of Delta | Always positive for long options | Highest ATM near expiration. Measures Delta instability. |
| Theta (Θ) | Time decay (per day) | Negative for long options | Options lose value every day. Accelerates as expiration approaches. |
| Vega (ν) | Implied volatility change (1% move) | Always positive for long options | Long options benefit from rising IV; short options benefit from falling IV. |
| Rho (ρ) | Interest rate change (1% move) | Positive for calls, negative for puts | Usually minor, but matters for long-dated options (LEAPS). |
Delta Deep Dive
| Option Type | Deep ITM | ATM | Deep OTM |
|---|---|---|---|
| Call | ~0.90 to 1.00 | ~0.50 | ~0.05 to 0.20 |
| Put | ~−0.90 to −1.00 | ~−0.50 | ~−0.05 to −0.20 |
Position Delta: Multiply Delta by the number of contracts × 100. A portfolio with 10 call contracts at 0.60 Delta has a position Delta of +600 — equivalent to being long 600 shares of the underlying.
Gamma & Theta: The Trade-Off
Gamma and Theta are two sides of the same coin. Long options have positive Gamma (your Delta improves as the stock moves in your favor) but negative Theta (you pay for that advantage through time decay). Short options have the opposite: positive Theta income but negative Gamma exposure.
This is why ATM options near expiration are the most explosive — Gamma is at its peak, but so is Theta. The trade-off intensifies as expiration approaches.
Vega & Volatility
Vega measures how much the option price changes for every 1 percentage point move in implied volatility. A Vega of 0.15 means the option gains $0.15 if IV rises 1%. Long options are long Vega (benefit from rising volatility); short options are short Vega.
Vega is highest for ATM options and for longer-dated options. That’s why earnings plays and volatility trades focus on near-term ATM contracts.
Greeks for Common Strategies
| Strategy | Delta | Gamma | Theta | Vega |
|---|---|---|---|---|
| Long Call | Positive | Positive | Negative | Positive |
| Long Put | Negative | Positive | Negative | Positive |
| Covered Call | Positive (reduced) | Negative | Positive | Negative |
| Long Straddle | ~Neutral | Positive | Negative | Positive |
| Iron Condor | ~Neutral | Negative | Positive | Negative |
| Protective Put | Positive (hedged) | Positive | Negative | Positive |
Key Takeaways
- Delta = directional exposure. Gamma = how fast Delta changes. Theta = time decay. Vega = volatility sensitivity.
- Long options: positive Gamma and Vega, negative Theta. Short options: the reverse.
- Gamma and Theta are highest for ATM options near expiration — that’s where the action is.
- Use position Greeks (Greek × contracts × 100) to manage portfolio-level risk.
- Rho is usually negligible except for long-dated options like LEAPS.
Frequently Asked Questions
What is the most important Greek for options traders?
Delta is the starting point because it tells you your directional exposure. But Theta matters most for income strategies (selling options), and Vega matters most around events like earnings where implied volatility swings sharply.
Why does Delta approximate the probability of finishing ITM?
Under the Black-Scholes model, Delta of an option closely approximates the risk-neutral probability of expiring in the money. A 0.30 Delta call has roughly a 30% probability of finishing ITM at expiration.
How does Gamma risk work?
If you’re short Gamma (selling options), a big move in the underlying causes your Delta to move against you, amplifying losses. This is why market makers who sell options are constantly hedging — they need to adjust their stock position as Delta shifts.
What is Theta decay and when is it worst?
Theta is the daily dollar amount an option loses to time decay. It accelerates in the final 30 days before expiration, with the steepest decay in the last week. ATM options lose value fastest; deep ITM and deep OTM options have minimal Theta.
How do Greeks change for LEAPS?
Long-dated options (LEAPS) have lower Gamma, lower Theta, higher Vega, and higher Rho than short-dated options. They behave more like the underlying stock (higher Delta for ITM) and are much more sensitive to volatility and interest rate changes.