Option delta explained, in rupees per lot

Delta is the first number to understand on any option. It tells you how much the premium moves when the underlying index moves by one point, and so how much directional exposure you actually carry. It also turns option positions into a common currency that can be compared with futures or with the index itself.

The definition

• Call delta runs from 0 to 1. A call with delta 0.5 gains about 0.5 points of premium when the index rises 1 point.
• Put delta runs from 0 to -1. A put with delta -0.3 gains about 0.3 points when the index falls 1 point.
• At the money, delta is close to 0.5 (calls) or -0.5 (puts). Deep in the money it approaches 1 or -1; far out of the money it approaches 0.
• Selling flips the sign: a sold call has negative delta, a sold put positive delta.

Delta per lot in rupees

Premiums in India are quoted per unit, but you trade lots. Multiply delta by the lot size and you get the rupee change per index point for one lot. With a Nifty lot of 65, the illustrative numbers below show how different strikes behave with Nifty "at 25,000" and 7 days to a weekly expiry.

The 100-point column uses delta alone. For a move that large the real change differs, because delta itself changes as the index moves (that is gamma). For quick mental arithmetic on small moves, delta is good enough.

Delta as "equivalent index units"

A long 25,000 CE lot with delta 0.53 behaves, for small moves, like owning about 34.42 units of Nifty. A Nifty futures lot of 65 units has a delta of 65. This is useful for comparing positions: two lots of a 0.25-delta call carry roughly the same direction risk as one lot of a 0.5-delta call, but they behave very differently as expiry approaches.

Delta changes with the index and with time

• As the index rises, call deltas rise and put deltas move towards zero. That rate of change is gamma.
• As expiry approaches, deltas spread out: in-the-money options head towards 1 (or -1) and out-of-the-money options towards 0. On expiry day an at-the-money option can swing between the two within minutes.
• When implied volatility rises, deltas of far strikes move away from 0 and 1 because a big move looks more likely.

Hedging intuition

Market makers and many option sellers try to keep their overall delta near zero, so that small moves in the index do not change their profit much. The idea is simple: if you sold 2 lots of the 25,000 CE, your position delta is about -1.06 lots, or -68.83 index units. Buying one Nifty futures lot (+65 units) would bring the combined delta close to zero.

Three things make this less tidy in practice:

• Delta keeps changing. A hedge that was neutral at one index level is not neutral 100 points later, so the hedge has to be adjusted, and every adjustment pays charges.
• Lots are indivisible. You cannot buy 0.53 of a futures lot, so small positions can rarely be hedged precisely.
• A delta-neutral position is not risk-free. It still carries gamma and vega risk: a sharp move or a change in implied volatility can cause losses even when the starting delta was zero.

Is delta the probability of expiring in the money?

It is often quoted as a rough proxy, and for many strikes the two numbers are close. They are not the same thing, though, and the gap grows for longer-dated options and high volatility. Treat delta as a sensitivity first; if a tool shows a probability, it has been calculated separately, from a model with its own assumptions.

Examples use illustrative values, not current market data. This is general education, not investment advice.