The Greeks
What Are the Greeks?
The Greeks are mathematical measures that describe how an option's price changes in response to various factors. Understanding the Greeks is essential for managing options positions effectively.
Delta (Δ)
Delta measures how much an option's price changes for a $1 move in the underlying asset.
- Call deltas range from 0 to +1.00
- Put deltas range from -1.00 to 0
- ATM options have deltas near ±0.50
A call option with delta of 0.60 will gain approximately $0.60 for every $1 increase in the stock price.
Gamma (Γ)
Gamma measures how much delta changes for a $1 move in the underlying. It's the rate of change of delta.
- Gamma is highest for ATM options
- Gamma increases as expiration approaches
- Long options have positive gamma
Theta (Θ)
Theta measures the rate of time decay — how much an option loses in value each day.
- Expressed as a negative number for long options
- Time decay accelerates as expiration approaches
- ATM options have the highest theta
A theta of -0.05 means the option loses $0.05 in value each day, assuming all other factors remain constant.
Vega (ν)
Vega measures sensitivity to changes in implied volatility.
- Expressed as change per 1% change in IV
- Long options have positive vega
- Longer-dated options have higher vega
Rho (ρ)
Rho measures sensitivity to changes in interest rates. Generally the least significant Greek for short-term options.
Summary Table
| Greek | Measures | Long Calls | Long Puts |
|---|---|---|---|
| Delta | Price sensitivity | Positive | Negative |
| Gamma | Delta sensitivity | Positive | Positive |
| Theta | Time decay | Negative | Negative |
| Vega | Volatility sensitivity | Positive | Positive |
| Rho | Interest rate sensitivity | Positive | Negative |