Gamma (Γ)
Delta tells you how an option responds to a move. Gamma tells you how that response itself changes. It is why expiry days feel different from every other day.
In short: gamma is the rate at which an option's delta changes when the underlying moves one point. Long options have positive gamma (delta moves in the trader's favour as the market moves); written options have negative gamma (delta moves against the writer). Gamma is largest for at-the-money options close to expiry, which makes the last session before a Nifty Tuesday expiry the highest-gamma environment on NSE.
The intuition
Delta is the slope of the option's price against the underlying. Gamma is the curvature. A long call does not simply rise with the index; it rises faster the further the index goes, because its delta keeps climbing. That acceleration is gamma, and for the buyer it is the pleasant kind: gains compound on the way up and losses slow on the way down. For the writer, who holds the mirror image, it is the unpleasant kind: losses accelerate, gains decelerate.
Where the curvature is sharpest, gamma is largest. For an option with weeks to run, the price curve bends gently around the strike. For an option with hours to run, the curve is almost a corner: worth nothing below the strike, worth the full intrinsic amount above it. Standing at that corner is the maximum-gamma position, and on expiry day the whole market stands there together.
Formula
Gamma = change in delta ÷ change in underlying price
It is the second derivative of the option price with respect to the underlying, and it is the same for a call and a put at the same strike and expiry. From the Black-Scholes model: gamma = N′(d1) ÷ (S σ √T), where N′ is the standard normal density. Gamma rises as σ√T shrinks, which is the mathematical reason it explodes near expiry in calm markets.
Worked example (illustrative numbers)
Suppose NIFTY is at 24,000 two days before the Tuesday expiry with implied volatility at 14%. The 24,000 call is worth about ₹104 with delta 0.52 and gamma 0.0016. One lot is 65 units.
- Nifty rises 100 points to 24,100. Delta becomes roughly 0.52 + 0.0016 × 100 = 0.68; the model gives 0.67. The call now moves two-thirds of a point for every index point.
- Nifty falls 100 points to 23,900 instead. Delta becomes roughly 0.52 − 0.16 = 0.36. The call's response to the next move has shrunk by a third.
- The premium change over the 100-point rise is ₹104 to ₹163, about ₹59 per unit, ₹3,835 per lot, while a straight delta-0.52 estimate would have said ₹52. The extra ₹7 is gamma, and with one day less it would be larger still.
A trader who wrote that call and hedged it by buying 0.52 × 65 ≈ 34 units of Nifty futures was neutral at 24,000. At 24,100 the written call has delta −0.67, so the position is short about 10 units net: the writer is now short the index in a rising market and must buy more futures at the higher price to get back to neutral. Each re-hedge costs money; that is negative gamma made visible, and on expiry morning, when gamma is several times larger, the same 100 points would swing the hedge by far more.
Why it matters to an options trader
- It is the risk writers are paid for. Theta income and gamma risk are two sides of one coin: the strikes and expiries that pay the most theta are the ones with the most gamma. A writer who does not know their gamma does not know what they are selling.
- It explains expiry-day moves. When many participants are short gamma at a strike, their hedging pushes the index away from it; when they are long gamma, their hedging pins the index to it. The call and put walls on an OI chart are gamma concentrations in disguise.
- It is the buyer's edge in a volatile market. Long gamma means every move helps and re-hedging locks gains in; the cost is theta. Buyers win when the market moves more than implied volatility priced.
- It sets position sizing near expiry. A position that was comfortable with two weeks to run can be several times as sensitive two days before expiry at the same strikes.
Common mistakes
- Managing a written position by delta alone. Near expiry, delta can go from 0.2 to 0.8 inside an hour; the hedge that was right at 10 a.m. is wrong by 11.
- Holding short straddles into the last session. The theta left to collect is small; the gamma is at its maximum. The risk-reward of the final hours is the worst of the week.
- Reading a high gamma as "the option will move a lot". Gamma says the delta will move a lot; the premium change still depends on the size of the index move.
- Forgetting gamma falls as options go deep in or out of the money. A short strangle's gamma is low when the index is in the middle and becomes dangerous only as one strike is approached.
Indian-market specifics
- Nifty's weekly Tuesday expiry makes every Tuesday a high-gamma session on NSE; Bank Nifty and FinNifty, being monthly, have one such session a month on the last Tuesday. Sensex has its own on Thursday on BSE.
- NSE index options trade until 15:40 on expiry day, so the final ten minutes after the cash close are the most extreme gamma window of the cycle.
- Gamma per lot uses the current lot sizes: Nifty 65, Bank Nifty 30, FinNifty 60 (from January 2026), Sensex 20.
- SPAN margin for writers is scenario-based and rises as gamma rises, so margin calls on short positions tend to arrive exactly when gamma is biting.
FAQ
What does a gamma of 0.002 mean?
Delta changes by 0.002 per index point; a 100-point move shifts delta by about 0.2.
Why is gamma highest at the money near expiry?
Because the option sits on the edge between worthless and fully in the money, and a small move decides which.
What is gamma risk for an option writer?
The acceleration of losses as the market moves against a written option; the price of the theta collected.
What is gamma scalping?
Holding long options and re-hedging with futures after each move to lock in gains, profiting when realised volatility beats implied.
Gamma by strike, and where it is concentrated
The options calculator shows gamma with the other Greeks for any strike and expiry. In the app, Market Predictions reads dealer and gamma exposure across the chain as one of its inputs.