How delta works
| Option | Delta | What it means |
|---|---|---|
| Deep in-the-money call | Near +1 | Moves almost one for one with the index |
| At-the-money call | About +0.5 | Moves about half as much as the index |
| Far out-of-the-money call | Near 0 | Barely moves until the index approaches the strike |
| At-the-money put | About −0.5 | Gains about half a point for each point the index falls |
| Deep in-the-money put | Near −1 | Moves almost one for one, in the opposite direction |
A call's delta is positive because a call gains when the index rises. A put's delta is negative because a put gains when the index falls. At any strike, the call delta and the absolute put delta add up to about 1.
A worked example on one Nifty lot
Nifty is at 25,000 with 12 days to expiry and implied volatility of 14%. Model prices and deltas at five strikes:
| Strike | Call price | Call delta | Call moves per point, one lot | Put price | Put delta |
|---|---|---|---|---|---|
| 24,500 | ₹617.65 | 0.81 | ₹53 | ₹65.35 | −0.19 |
| 24,800 | ₹398.30 | 0.66 | ₹43 | ₹145.35 | −0.34 |
| 25,000 | ₹280.50 | 0.54 | ₹35 | ₹227.10 | −0.46 |
| 25,200 | ₹187.50 | 0.41 | ₹27 | ₹333.70 | −0.59 |
| 25,500 | ₹92.10 | 0.25 | ₹16 | ₹537.65 | −0.75 |
If Nifty rises 100 points to 25,100, delta predicts the 25,000 call gains about ₹54, or ₹3,510 on one lot of 65. The model price moves from ₹280.50 to ₹337.45, a gain of ₹56.95 a unit or ₹3,702 a lot, a little more than delta predicted because delta itself rose during the move. That extra is measured by gamma.
Delta changes as the price moves
Delta is not fixed. As Nifty rises, every call's delta rises and every put's delta moves towards zero. The 25,000 call's delta goes from 0.54 at 25,000 to 0.60 at 25,100 and 0.66 at 25,200. Delta also changes with time: as expiry nears, at-the-money deltas stay near 0.5 while in-the-money deltas move towards 1 and out-of-the-money deltas towards 0.
Delta as a rough probability
Delta is also used as a quick estimate of the chance that an option finishes in the money. The 25,200 call's delta of 0.41 suggests a little under even odds; the 25,500 call's 0.25 suggests about one in four. The estimate is rough, because it assumes the model's volatility and ignores the drift of the market, but it is close enough for choosing strikes. Many option sellers sell strikes with a delta of 0.15 to 0.25, where the model gives a 75% to 85% chance of expiring worthless.
Delta of a position
The delta of a position is the sum of its legs' deltas, with the sign reversed for sold legs. A short straddle at 25,000 has a delta of −0.54 + 0.46 = −0.08 a unit, almost neutral. A bull call spread that buys the 25,000 call and sells the 25,200 call has a delta of 0.54 − 0.41 = 0.13, so it gains about ₹8.50 a point on one lot. A futures contract has a delta of exactly 1, so one lot of Nifty futures moves ₹65 a point. Traders who want no exposure to small moves build positions with a delta near zero; see the delta neutral strategy.
When delta matters most
- Choosing a strike. A higher delta costs more but tracks the index more closely; a lower delta is cheaper but needs a larger move.
- Sizing a trade. Two lots of a 0.25-delta option carry the same immediate exposure as one lot of a 0.50-delta option.
- Hedging. The number of futures or options needed to offset a position comes from its delta.
- Selling options. Delta sets the strike's distance from the money and the rough odds of expiring worthless.
Related terms
- Gamma meaning: how fast delta changes
- Theta meaning: what an option loses each day to time
- Vega meaning: how an option responds to implied volatility
- ITM ATM OTM meaning: where a strike sits against the index
Learn more
- Option greeks: all five Greeks with Nifty examples
- Strike price selection: choosing strikes by delta and distance
- Delta neutral strategy: positions built to a delta near zero
Frequently asked questions
What is a good delta for buying options?
Many buyers choose deltas between 0.40 and 0.60, where the option moves with the index and still costs less than a future. Lower deltas are cheaper but need a larger move before they pay.
Why is put delta negative?
A put gains when the index falls, so its price moves in the opposite direction to the index. The negative sign shows that.
What does a delta of 1 mean?
The option moves one for one with the index, like a futures contract. Deep in-the-money options approach a delta of 1 as expiry nears.
Does delta change during the day?
Yes. It changes with every move in the index, with time and with implied volatility, so a position's delta needs checking during a trending session.
Where can I see the delta of an option?
In an option chain that shows Greeks, such as QuantPower's option trading app, and in the black scholes option pricing calculator.