NISM Series VIII, Chapter 5. Updated Jun 2026, 10-minute read.

Option Greeks — Delta, Gamma, Theta, Vega, Rho

Option Greeks quantify how sensitive an option's price is to market changes. They are essential risk management tools and a consistently high-weightage topic in NISM Series VIII.

Key takeaways

Delta: change in option price per ₹1 change in underlying. Calls: 0 to +1; Puts: -1 to 0
Gamma: rate of change of Delta. Highest for ATM options near expiry
Theta: daily time decay of option value. Always negative for option buyers
Vega: sensitivity to implied volatility changes. Long options have positive Vega
Rho: sensitivity to interest rate changes. Less material for short-dated options
ATM options have the highest time value and Vega; deep ITM/OTM options have highest/lowest Delta

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	+	-

Frequently asked questions

Why is Gamma highest for ATM options near expiry?

Near expiry, a small price move can flip an ATM option from OTM (worthless) to ITM (valuable). This causes Delta to change rapidly, hence high Gamma. This is why selling ATM options near expiry is very risky.

What does it mean to be 'Theta positive'?

Being Theta positive means you profit from time decay — you have net short options positions. Option sellers (writers) are Theta positive. Strategies like covered calls and short straddles are Theta positive.

Written by Arpan Das.

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