Gamma: why it grows so fast near expiry

On Monday 29 Jun 2026, one day before the monthly expiry, Nifty closed at 23,946.25 and its future at 23,972.90. The 23,950 call cost Rs 87.65 a unit and had a delta of 0.55. Its gamma was 0.00209. That means each point the index climbs adds 0.00209 to the delta, so after 50 points the delta is about 0.65. On Wednesday 10 Jun 2026 the at the money call with 48 days left had a gamma of 0.00032. The one day option reacts 6.6 times as sharply. I read gamma before I read delta on any short dated option, because it tells me how long today's delta will stay true.

The idea, plainly

Module F21 called delta a speedometer. Gamma is the acceleration: how much delta changes for one point of the index. It is a slope of a slope. A gamma of 0.00209 looks tiny, so I read it two ways. Per lot of 65 units it is 0.136 units of the future for every point. Over a move of 50 points it is the delta added: 0.10. The other Greeks sit beside it: theta is time, vega is volatility (module I10) and rho is the interest rate (module I11).

The formula, and why it peaks at the money

DF is the small interest discount factor, phi the bell curve at d1 (module F21), F the future, s the implied volatility and T the years to expiry.

Gamma = DF * phi(d1)
/ (F * s * sqrt(T))

Two parts matter. As T shrinks, sqrt(T) at the bottom shrinks and gamma grows. And phi on top is largest when d1 is near zero, the strike nearest the future. So gamma peaks at the money and rises as expiry nears.

Why the hump narrows

With little time left, the market is nearly sure which side of the strike the index will finish, except in a narrow band around it. Inside that band delta swings from near 0 to near 1, so it changes fast. With weeks left the band is wide and delta changes slowly.

The rupees: half gamma times the move squared

Delta alone treats an option as a straight line. Gamma adds the curve. For a move of x points the extra rupees per unit, on top of delta times x, are:

Gain = gamma * move
* move / 2

Because the move is squared, doubling it quadruples the gain. A lot with one day left gains about Rs 169 from a 50 point move and Rs 678 from a move of 100 points.

Long gamma and short gamma

The buyer of an option is long gamma: positive. The seller is short gamma: negative, and the same curve works against the seller. A long straddle, a call and a put together, has almost no delta at the start, so what shows in the grid is gamma. A move either way helps the buyer, and theta is what the help costs.

Worked example: what one day left does to gamma, 10 and 29 Jun 2026

Four at the money calls, four distances to expiry. At the money means nearest the future for the monthly expiries and nearest the parity forward for the weekly. Gamma is from Black 76 at each strike's own implied volatility. Gamma is per point. Delta added is for a move of 50 points, and the gain column uses the half gamma rule for that move, before any theta. Gain and theta, a day, are for one lot of 65 units.

Gamma against theta

The gamma column rises 6.6 times from 48 days to one day. The square root of 48 is about 7, so gamma follows the square root rule closely. Now read the last column beside the one before it. Gamma is not free. The same shrinking time that builds gamma also builds theta, the daily price of holding it (module F22). Set the two equal and you can solve for the move at which gamma pays for one day of theta. It comes to the index level times the implied volatility, divided by 19.1 (the square root of 365), which is one day of implied movement. For the one day option that is about 190 points. For the 48 day option it is about 180. A buyer needs the index to move more than the market priced for the day, or gamma does not cover its cost.

Reading gamma off the chain

The NSE option chain shows prices, open interest and implied volatility, but no gamma column. You work it out from the formula with the strike's own implied volatility, or let the Greeks calculator do it. A call and a put at one strike and volatility have the same gamma. On this chain each side's price implies its own volatility, so the 23,950 put shows a gamma of 0.00192 against 0.00209 for the call.

What short gamma looks like to a seller

A seller collects theta and pays out gamma. When the index runs, the loss does not grow in a straight line: each extra point costs more than the one before. SEBI treats the last day of an expiry as a time of special risk. Since 20 Nov 2024 a short index option that expires that day carries an extra 2% of extreme loss margin on top of the normal margin. Module F05 shows the stack. Nifty is the only index with weekly options at NSE (NSE circular FAOP64506 of 10 Oct 2024), so the one day picture comes round every Tuesday, not once a month. Traders who want zero delta can add futures to cancel it, a delta hedge, but that leaves the gamma in place. Neutral on delta is not neutral on gamma (module I12 adds the legs of a whole position).

The common mistake

The claim: On expiry day gamma is at its peak, so a cheap far option can multiply many times in minutes. The 24,150 call cost Rs 22.65 a unit. To make a rupee it needed the index above 24,172.65 at settlement, which was the index close for expiries before 7 Dec 2026, 226 points or 0.95% above the close, against a straddle that priced one standard deviation at 0.83%. Nifty closed at 23,865.75 on 30 Jun, 81 points lower, and the call expired at nothing. Gamma pays only when the index travels, as from 10 to 16 Jun, when the 23,250 weekly call went from Rs 163.60 to Rs 739.15. The seller collected the first number and paid the second. For the buyer such a payoff is a lottery ticket: rare big wins, many small losses. What is a gamma blast? has its own page.

Key takeaways

• Gamma is the change in delta for one point of the index.
• At the money gamma rises roughly with one over the square root of time.
• With one day left, gamma was 6.6 times that of 48 days left.
• The buyer is long gamma and the seller is short gamma.
• Gamma costs theta, so the move must beat a day's implied move.
• A cheap far option needs a large move before gamma matters.

Before you trade. Derivatives trading carries a high risk of loss. SEBI's study "Profitability of Individual Traders in the Equity Derivatives Segment (FY25 to FY26)" (August 2026) found that 87.7% of individual traders in equity F&O made net losses in FY26, with aggregate net losses of Rs 91,685 crore. Read the SEBI study