Stock Market · Options Theory

Delta

Delta is the rate of change in an option's price for every ₹1 change in the underlying asset's price. It's the most important and most used of the option Greeks.

Delta values

• Delta ranges from 0 to 1 for calls, 0 to −1 for puts
• Deep ITM call: delta ≈ 1 (moves almost ₹1 for every ₹1 Nifty move)
• ATM call: delta ≈ 0.5 (moves ₹0.50 for every ₹1 Nifty move)
• Far OTM call: delta ≈ 0.1 (barely moves with Nifty)

Puts have negative delta:

• ATM put: delta ≈ −0.5 (rises ₹0.50 when Nifty falls ₹1)
• Deep ITM put: delta ≈ −1

> Delta also approximates the probability that an option will expire ITM. A 0.2 delta OTM call has approximately 20% probability of expiring ITM.

Using delta in practice

1. Position sizing: a 0.5 delta call controls half the underlying. Two of them = equivalent to owning one futures lot.

2. Hedging: to hedge 100 shares of Reliance, you can buy puts with total delta = −1 (i.e., two ATM puts with delta −0.5 each).

3. Delta-neutral strategies: market makers and professional traders balance positive and negative delta to be neutral to market direction.

Delta ≈ 0.5ATM option. Moves ₹0.50 per ₹1 in underlying.

Delta is not constant

Delta changes as the underlying price moves and as time passes. This rate of change is Gamma. The next Greek to understand.

Takeaway. Delta = how much option price changes per ₹1 move in underlying. ATM ≈ 0.5. Deep ITM ≈ 1. Delta also approximates probability of expiry ITM. Use delta for position sizing and hedging.