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Delta: Why the Index Moved and the Option Barely Did

In short

is the fraction of the underlying's move that an option's picks up. An at-the-money option has a delta near 0.5. A 100-point move in the index then moves its premium by roughly 50 points. A far out-of-the-money option can have a delta of 0.1 or less, so the same 100 points moves it about 10. Being right about direction is not enough. The decides how much of that being right is paid out.

Where this sitsStep 4of 9 in What you are actually buying
Things to check6Before you rely on it
Common mistakes4Named, with the reason

Read these first

2

How it unfolds, step by step

  1. The setup

    Index X sits at 20,000 and a call struck at 20,400 trades at ₹22. The strike is 400 points away, with eight sessions to run. The option's delta is low. Most of the premium is a bet on a move that has not happened.

  2. What happens next

    Over the next eight sessions the index rises 180 points to 20,180. That is a real, sustained, correctly predicted move. The premium goes from ₹22 to ₹34.

  3. What it means — and does not

    The index gained 180 points and the option gained ₹12. That is delta. The premium picked up under a tenth of the move, because at 400 points away the option was still unlikely to finish with any intrinsic value at all. Everything worked exactly as an option is defined to work. The holder was right about direction and still barely paid. This is the arithmetic behind almost every 'my option did not move' question. Delta is only the FIRST of three reasons a bought call can lose while the underlying rises, and it explains the smaller move. The second is time. The part of the premium paid for the sessions still to run shrinks every day, whether or not the level moves. That is /learn/options-theta-expiry-trap. The third is implied volatility. When the market lowers its assumption about how far the underlying might travel, the premium falls with it, even on a correct call. That is /learn/implied-volatility-crush-after-event. The three act at once, and they can add up to less than nothing. On a separate example a call is bought at ₹80 and the underlying then rises by ₹20. Delta adds ₹10, and the way delta itself steepens adds ₹2. A fall in implied volatility takes ₹10 away, and three sessions of time take ₹3. The premium ends at ₹79, a rupee below where it started, after a move in the right direction.

An index move of 100 gives an ATM option about 50 and far OTM 10, beside gamma, theta, vega.
  • Index level
  • Option premium (₹)
  • Strike 20,400 · 20,400

The index climbs 180 points while the premium on a strike 400 points away climbs ₹12. Both lines rise. They do not rise together.

Show the underlying data
The numbers behind the chart above.
DayIndex levelOption premium (₹)
120,000₹22
220,025₹23
320,055₹24
420,080₹25
520,105₹27
620,130₹29
720,160₹32
820,180₹34

What this does not establish

The low-delta reading stops applying as the level approaches the strike. Delta rises as the option moves toward the money. That is why the last leg of the move above is worth more per point than the first. The assumption to check is distance, not direction. A position taken because the underlying 'will go up' carries a hidden second assumption. It assumes the move will be FAR ENOUGH and SOON ENOUGH to drag the strike into the money, and the strike is the level at which that second assumption is settled.

Things to check

6

How far is the strike from the current level, in points?

Roughly what fraction of a move would this strike actually pick up?

Is the expected move big enough to cover the premium paid, not just to be in the right direction?

If the premium fell while the underlying rose, which of the three is it? The strike too far away, the sessions used up, or the market's assumption about movement falling?

Is the figure on the screen a mid-price between the best bid and the best offer, or the bid a seller would actually be paid?

Check delta, time and implied volatility together when explaining a premium change.

Common mistakes

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  • Assuming a correct directional call pays out in proportion to the move. The strike decides the fraction.

  • Buying the furthest strike because it is cheapest, without noticing that cheap and low-delta are the same fact stated twice.

  • Blaming delta for every disappointing premium. Time passing and implied volatility falling do the same damage on their own, and a page that only knows delta explains a third of the cases.

  • Treating the figure on the screen as the price it can be sold at. A mid-price sits between the best bid and the best offer, and a holder selling straight away is paid the bid.

Check yourself

The index rises 180 points and a call held on a strike 400 points away gains 12 rupees. What went wrong?

  • The premium should have tracked the index and the quote is stale
  • Nothing — a far strike picks up only a small fraction of a move
  • The position lost its value to time decay instead
Show the answer

B. Nothing — a far strike picks up only a small fraction of a move

Delta is the fraction of the underlying's move a premium picks up, and a strike that far out has a low one. The direction was right and the arithmetic still gave back very little, which is the mechanic rather than a fault.

Frequently asked

5
What is a typical delta for an at-the-money option?

Around 0.5. It is the strike where the option is about as likely to finish with intrinsic value as without, so the premium picks up roughly half of each move in the underlying.

Does delta stay the same?

No. It changes as the underlying moves and as expiry approaches. The rate of that change is called gamma. A strike far away has a low delta that rises as the level comes toward it.

Why is a far strike cheaper?

Because it is less likely to finish with any intrinsic value. The low price and the small response to a move are the same fact seen from two sides.

The index rose and my call still lost money. What are the three things to check?

Delta first: how far the strike sits from the level, which is what this page works through. Time value comes next. The part of the premium paid for the sessions still to run falls every day, and that is /learn/options-theta-expiry-trap. Implied volatility comes third. If the market lowers its assumption about how far the underlying may travel, the premium falls with it, and that is /learn/implied-volatility-crush-after-event. All three can be acting at the same time, and together they can cancel a correct direction out completely.

Why can I not sell at the premium shown on the screen?

Because a screen often shows a mid-price. That is the midpoint between the best bid and the best offer, and nobody is obliged to trade there. On an example a holder buys at ₹80, the screen later shows ₹81, and the real quote is ₹79.50 bid against ₹82.50 offered. Selling at once means selling at ₹79.50. That is fifty paise below what was paid, on a screen that appeared to show a rupee of gain. On fifty units that is ₹25 of loss before any charge.

Where this comes from. This way of reading a chart is widely taught. It is not a rule from any circular, so there is no document to cite.

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The strike price is the level at which an option can be exercised.

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