Gamma in Options Explained: Why Delta Keeps Moving
Delta tells you how much an option’s price moves when the underlying moves one point. Gamma tells you how fast that delta itself changes, which is why a position that felt small this morning can feel enormous by afternoon.
Gamma is the rate of change of delta for a one point move in the underlying. If a Nifty call has a delta of 0.50 and a gamma of 0.0008, a 100 point rise takes delta to roughly 0.58 without you touching the position.
Ahead: where gamma is largest, what it does to a payoff in rupees, and why sellers dread expiry day.
The intuition before the maths
Think of delta as speed and gamma as acceleration. A car at 40 km/h with heavy acceleration is not really a 40 km/h car, and an option with delta 0.50 and high gamma behaves the same way. Gamma is always positive for anyone who bought an option, call or put, and always negative for anyone who sold one. That sign decides whether movement helps you or hurts you.
Where is gamma highest?
At the money
An option deep in the money already has a delta near 1, so it barely reacts to further moves and gamma is small. One far out of the money has a delta near 0 and also barely reacts. The at-the-money strike is the tipping point where a small move genuinely changes whether the option finishes worth anything, so that is where gamma peaks.
Close to expiry
With a month left, a 100 point Nifty move barely settles where the index expires. With two hours left, it settles it completely. Gamma at the money therefore climbs steeply into expiry, and on expiry afternoon it can be several times its Monday value.
- At the money plus near expiry: gamma at maximum, the most dangerous zone for sellers.
- Deep in or far out of the money: low gamma at any expiry.
- High implied volatility spreads gamma across more strikes; low volatility crams it into strikes nearest spot.
Gamma and time decay peak at the same strike near expiry, so they are two faces of one trade-off. The seller collects theta decay as rent and pays for it by carrying negative gamma.
A worked example in rupees
Nifty is at 25,000. Take the 25,000 CE at a premium of Rs 120, delta 0.50, gamma 0.0008. Suppose the lot size is 75, so one lot costs 120 times 75, or Rs 9,000. Confirm the current lot size on the exchange website.
Nifty rises 100 points to 25,100. The delta-only estimate is 0.50 times 100, so Rs 50 of premium gain. The gamma correction is 0.5 times 0.0008 times 100 times 100, which is Rs 4.
Total gain: Rs 54, so a premium near Rs 174. Per lot that is Rs 4,050 rather than the Rs 3,750 delta alone predicted.
Four rupees sounds trivial. Now run a 400 point fall. Delta predicts a Rs 200 loss. The gamma term is 0.5 times 0.0008 times 400 times 400, which is Rs 64, and it again favours the buyer, so the actual loss is nearer Rs 136. The buyer’s losses decelerate and the seller’s accelerate. That is why a 400 point move against a short option hurts more than four times as much as a 100 point move.
| Nifty spot | Approx delta of 25,000 CE | Change | What the seller feels |
|---|---|---|---|
| 24,800 | 0.34 | reference | Small exposure |
| 24,900 | 0.42 | +0.08 | Exposure creeping up |
| 25,000 | 0.50 | +0.08 | Half a short Nifty lot |
| 25,100 | 0.58 | +0.08 | Losing faster per point |
| 25,300 | 0.72 | +0.14 | Near a full short future |
Those deltas are illustrative. The pattern is the point: a seller who wrote one lot at delta 0.50 holds something near a naked short future once spot has run 300 points, without placing a single extra order.
Long gamma versus short gamma
Long gamma means you bought options. Movement helps in both directions: your position improves as you are proved right and gets less bad as you are proved wrong. The bill arrives as time decay every single day.
Short gamma means you sold options. A quiet market pays you daily. A sharp move punishes you at an increasing rate, worst exactly where your premium collection was highest.
They are opposite bets on whether realised movement beats what the option price implies, so gamma is best read alongside the full set of options Greeks.
Why do option sellers fear expiry day?
Because gamma goes near vertical, and a strike that was safely out of the money becomes a coin toss in minutes.
Picture a trader who sold the 25,000 CE on expiry morning with Nifty at 24,900 and collected Rs 25. Delta was maybe 0.30. By 2 PM Nifty is 25,010, delta has crossed 0.55, and every further point costs more than the last. NSE index options are European style, so there is no early exercise, but that is no protection against premium repricing violently in the final hour.
The practical responses, ordered by how much they help:
- Move away from the at-the-money strike. Selling further out cuts premium and gamma, and the gamma reduction is proportionally larger.
- Sell a further expiry instead of the current week. Gamma per unit of premium is much lower with more days left.
- Convert a naked short into a defined-risk spread by buying a further strike, giving up premium to cap the loss.
- Set a hard exit level on the underlying, not on the premium. Premium based stops get skipped on wide spreads.
- Cut lot size. Halving lots halves your gamma, the only lever that always works.
A plain risk note: short gamma positions can lose several times the premium collected in one session, and margin calls arrive then too.
Gamma and hedging: what actually happens
Desks neutralise delta by trading futures. Gamma forces them to keep doing it, because delta drifts as spot moves and a hedge set at 10 AM is stale by 11.
A short gamma hedger is forced to sell as the market falls and buy as it rises, the worst possible sequence. A long gamma hedger does the reverse and books a small profit at each rebalance. That is gamma scalping, and for retail traders brokerage, STT at 0.15% on the sale of options and bid-ask spreads normally eat the entire edge, as delta hedging sets out.
There is a market-wide version too. When many dealers are short gamma around a heavily traded strike, their hedging amplifies moves in that direction, one reason indices accelerate through round numbers on expiry day.
Frequently Asked Questions
Can gamma be negative for an option I bought?
No. Any long option, call or put, has positive gamma. Negative gamma comes only from being short options. A spread can show net negative gamma if the option you sold sits closer to the money than the one you bought, so check the net figure for the whole position rather than each leg separately.
What is a normal gamma value on a Nifty option?
There is no standard number, since it depends on spot level, days to expiry and volatility. Index options show small decimals such as 0.0005 to 0.002 at the money simply because Nifty is a large number. Comparing gamma across two underlyings is not meaningful; compare across strikes within one expiry.
Does gamma affect sellers even if price finishes where it started?
Yes, if they hedged along the way. A seller who adjusted a delta hedge through a round trip in the index will have bought high and sold low several times and can end up with losses even though spot closed flat. An unhedged seller who held on keeps the premium. Hedging short gamma has a cost.
How does implied volatility change gamma?
Higher implied volatility spreads probability across a wider range of strikes, so gamma is lower at the money and higher at distant strikes. When volatility collapses, gamma concentrates tightly around spot. That is why the same strike can behave calmly one week and violently the next.
Is gamma the same for a call and a put at the same strike?
For European options on the same underlying, strike and expiry, gamma is effectively identical for the call and the put. Their deltas differ, one positive and one negative, but the rate at which those deltas change is the same. That follows directly from put-call parity.
Key Takeaways
- Gamma measures how much delta shifts per one point move: positive for every long option, negative for every short one.
- It peaks at the at-the-money strike and rises steeply into expiry, exactly where premium sellers are most exposed.
- Estimate premium change as delta times the move plus 0.5 times gamma times the move squared. That second term makes large moves disproportionately costly for sellers.
- Long gamma pays on movement and bleeds on time; short gamma pays on stillness and loses at an accelerating rate.
- Cutting lot size is the only gamma reduction that always works. Further out strikes and later expiries come next.
