Delta (Δ)
Delta measures how much an option's price changes for a ₹1 move in the underlying asset.
- Call Delta: 0 to +1 (positive — call price rises when underlying rises)
- Put Delta: -1 to 0 (negative — put price falls when underlying rises)
- ATM call ≈ 0.5; Deep ITM call ≈ 1; Deep OTM call ≈ 0
Delta also approximates the probability that the option will expire ITM (e.g., Delta = 0.7 → ~70% chance ITM at expiry).
Delta Hedging: To create a delta-neutral position, combine options with the underlying in the proportion of their deltas. A delta-neutral portfolio is insensitive to small price changes.
Gamma (Γ)
Gamma is the rate of change of Delta — it measures how fast Delta changes as the underlying moves.
- Highest for ATM options
- Increases as expiry approaches (Gamma risk spikes near expiry)
- Option buyers have positive Gamma (beneficial); sellers have negative Gamma (risk)
Theta (Θ) — Time Decay
Theta represents the daily erosion of option value due to the passage of time, all else equal.
- Always negative for option buyers (you lose money just by holding)
- Positive for option sellers (you gain from time decay)
- Accelerates as expiry approaches — highest in the last 30 days
- ATM options have the highest absolute Theta
Example: A Nifty ATM call with Theta = -50 means the option loses ₹50 per day purely from time decay (for one lot of 25: ₹1,250/day).
Vega (V)
Vega measures sensitivity to implied volatility (IV). A Vega of 20 means the option price changes by ₹20 for each 1% change in IV.
- Long options have positive Vega (benefit from rising IV)
- Short options have negative Vega (hurt by rising IV)
- ATM options have the highest Vega
- Vega decreases as expiry approaches
Rho (ρ)
Rho measures sensitivity to interest rate changes. For most short-dated Indian index options, Rho is negligible. Long-dated calls have positive Rho; long puts have negative Rho.
Summary Table
| Greek | Measures | Long Call | Long Put |
|---|---|---|---|
| Delta | Price sensitivity | + (0 to 1) | - (-1 to 0) |
| Gamma | Delta sensitivity | + | + |
| Theta | Time decay | - | - |
| Vega | Volatility sensitivity | + | + |
| Rho | Interest rate sensitivity | + | - |