Gamma Options Greek: Why Delta Moves So Fast on Nifty Options Near Expiry

Picture a trader who sells an at-the-money Nifty option on expiry day. At 11 am the position looks safe. By 1:30 pm a 150-point move has turned a small, comfortable short into the biggest loss of the month. Delta alone doesn’t explain that. The gamma options greek does. Gamma tells you how fast delta itself changes when the Nifty moves, and close to expiry that speed goes up sharply for at-the-money strikes.

This guide walks through what gamma measures, why it peaks at the money and near expiry, and what that means for buyers and sellers. The worked examples use a hypothetical Nifty level of 25,000 and option values we calculated ourselves with the Black-Scholes formula, assuming 13% implied volatility and a 6% interest rate. They are illustrations of how the maths behaves, not live market prices or forecasts.

Delta first, because gamma only makes sense next to it

Delta is the rupee change in an option’s premium for a one-point move in the underlying. A call with a delta of 0.5 gains roughly 50 paise for every point the Nifty rises. Simple enough, and most traders stop there.

The catch is that delta doesn’t sit still. Zerodha Varsity’s chapter on gamma makes the point plainly: delta is a variable, and it changes with every move in the underlying. An out-of-the-money call that starts with a small delta picks up delta as the Nifty climbs towards its strike, and keeps picking it up once the option slips into the money. If you work out your exposure using today’s delta and then forget about it, your numbers drift away from reality as soon as the market moves.

That drift is what gamma measures. If you’ve already read our explainer on delta hedging on Nifty, gamma is the reason those hedges need constant adjusting.

How the gamma options greek fits with delta

Gamma is the change in delta for a one-point change in the underlying. Varsity describes delta as the first-order derivative of the premium and gamma as the second-order derivative, and uses the physics comparison most textbooks use: if delta is speed, gamma is acceleration. Investopedia’s gamma definition uses the same speed-and-acceleration analogy.

In practice the arithmetic is short:

• New delta is roughly old delta plus gamma multiplied by the points moved.
• A gamma of 0.001 means delta changes by about 0.1 for every 100 points the Nifty moves.
• Gamma itself shifts as the market moves, so this shortcut works best for small moves. For big ones, recalculate.

The numbers look tiny on an option chain, often three zeros after the decimal point for an index like the Nifty. Don’t let that fool you. Multiply a gamma of 0.002 by a 150-point move and delta shifts by 0.3, which is a big change in how much your position makes or loses per point.

Who is long gamma and who is short

Investopedia puts the sign rule simply: long options have positive gamma and short options have negative gamma. That holds for calls and puts alike.

• Option buyers are long gamma. When the market moves their way, delta grows and the position makes money faster. When it moves against them, delta shrinks, so losses slow down. The most a buyer can lose is the premium paid.
• Option sellers are short gamma. Varsity spells out what this does to a short trader: when the market moves against the position, the deltas add up and the position gets riskier at every step. The loss speeds up, it doesn’t slow down.

Futures, for what it’s worth, have no gamma. A Nifty futures contract moves one point for one point however far the index goes, so its delta never changes.

Why gamma is highest at the money

Both sources agree on the shape. Gamma is largest for at-the-money options and falls away as an option goes deep in the money or far out of the money. The intuition is easy once you think about where delta has room to move.

A deep in-the-money call already behaves almost like the futures contract, with a delta close to 1. It can’t go much higher. A far out-of-the-money call has a delta near zero and needs a huge move before it starts to matter. The at-the-money strike is the one sitting on the fence. A modest move either way decides whether it ends up worth something or nothing, so its delta swings the most.

Here’s what our hypothetical numbers show with 30 days to expiry, Nifty at 25,000:

With a month to go, the gap between strikes is small. The 25,300 call has almost the same gamma as the at-the-money one, because 300 points isn’t far when there are 30 days left for the index to travel. Now watch what happens as expiry gets closer.

Gamma near expiry: the part that catches people out

Investopedia notes that gamma is largest for options with near-term expirations relative to longer-dated ones. That single line explains a lot of expiry-day drama on the Nifty. Same three strikes, same Nifty level, same volatility, only the days to expiry change:

Two things stand out. First, the at-the-money gamma climbs from 0.000423 at 30 days to 0.002344 with one day left, about 5.5 times higher in our example. Second, the strikes away from the money go the other way at the end. With one day left, the 24,500 call has a delta of 0.999 and a gamma of almost nothing. It’s basically a futures contract now. The 25,300 call has a delta of just 0.042. Its fate is close to decided.

Close to expiry, gamma piles onto the at-the-money strike. That’s the one strike where a normal intraday move can flip an option from worthless to valuable, or the other way round, within hours.

A worked example: the same 100 points, two very different results

Take the 25,000 call in our model and move the Nifty from 25,000 to 25,100. Compare a contract with 30 days left against one with two days left.

• 30 days to expiry: the premium goes from Rs 435.51 to Rs 493.61, a gain of Rs 58.10, or about 13%. Delta moves from 0.560 to 0.602.
• 2 days to expiry: the premium goes from Rs 100.12 to Rs 159.79, a gain of Rs 59.67, or about 60%. Delta jumps from 0.516 to 0.675.

The rupee gain per unit is almost identical. The percentage gain is about four and a half times larger for the short-dated option, and its delta has moved nearly four times as much (0.159 against 0.042). Push the Nifty another 100 points to 25,200 and the two-day call’s delta reaches 0.807. A position that started as a coin toss is now behaving mostly like a long futures position.

It’s worth checking the shortcut too. Starting gamma for the two-day call is 0.001657, so the estimate says delta should rise by about 0.166 on a 100-point move, to roughly 0.682. The full calculation gives 0.675. Close, but not exact, because gamma itself fell to 0.00149 along the way. This is why the rule of thumb is fine for a quick read and not for sizing a hedge.

The downside works the same way for a buyer. Drop the Nifty 100 points to 24,900 and the two-day call falls from Rs 100.12 to Rs 56.79, a loss of about 43%. The 30-day call falls from Rs 435.51 to Rs 381.64, about 12%. Short-dated at-the-money options are high-gamma instruments in both directions.

What short gamma does to an option seller

Now look at it from the seller’s side, which is where gamma does the real damage. Say a trader sells the 25,000 straddle, meaning both the call and the put, with the Nifty at 25,000. In our model:

The two-day seller collected about a quarter of the premium, and the same 200-point move costs them more in rupees and far more as a share of what they took in. That’s short gamma in one table. Near expiry the straddle starts close to delta-neutral, but a 200-point move pushes the short call’s delta to about 0.81 in our model, so the position now loses roughly 0.6 of a rupee per unit for every further point higher. Multiply that by your lot size and the number of lots and you can see how a “safe” expiry-day short gets out of hand.

Varsity’s own guidance in its second gamma chapter goes further than most traders like to hear: since at-the-money options carry the highest gamma, it suggests avoiding shorting them, and it warns against shorting at-the-money or in-the-money options in the hope that they expire worthless.

Selling options near expiry pays you through time decay, but you are short gamma the whole time. The premium is the price someone pays you to carry that risk.

That trade-off between collecting time value and carrying gamma risk is the other half of the story. Our guide to theta decay in options trading covers the time-decay side in detail.

Using gamma in your own trading

Most retail traders won’t hedge gamma the way a dealing desk does. Investopedia describes gamma hedging as buying and selling options so that their gammas offset, leaving a position with net gamma near zero, which is usually a job for institutions running large books. You can still use gamma as a practical risk check:

1. Look at gamma before you sell. If your broker’s option chain shows the Greeks, use them. If you’re short an at-the-money strike with a day or two left, its gamma is telling you how quickly your delta will turn against you.
2. Size short positions on a bad move, not the current delta. Ask what your delta would be after a 150-point or 200-point move, using gamma as a rough guide. Size for that number.
3. Prefer defined risk near expiry. Buying a further out-of-the-money option against a short one caps the loss and cuts your net short gamma. Spreads give up some premium, but they stop a gamma spike from becoming an open-ended loss.
4. If you buy, know what you’re paying for. A cheap short-dated at-the-money option is a high-gamma bet. It can double fast on a sharp move, and it can lose a big chunk of its value just as fast if the Nifty stalls. In our model, the two-day at-the-money call slips from Rs 100.12 to Rs 69.93 a day later with the Nifty unchanged at 25,000.
5. Recheck after big moves. Gamma changes with the index level and with time. A hedge that was right at 10 am may be badly off by 2 pm on an expiry day.

A quick mental model

We find it helps to think of gamma as a measure of how unstable your delta is. Low gamma means your exposure stays roughly where you set it. High gamma means the market can rewrite your position for you within a session. Near expiry, at the money, the market is doing a lot of that rewriting.

Common mistakes with gamma

• Ignoring it because the number is small. Index option gammas are small numbers because the index is a big number. What matters is gamma multiplied by the points the market can realistically move in a session.
• Treating delta-neutral as risk-free. A short straddle can be close to delta-neutral at entry and still be heavily short gamma. Neutral today doesn’t mean neutral after a 1% move.
• Assuming gamma stays fixed. As our worked example showed, gamma itself falls or rises as the Nifty moves and as days pass. Use the estimate for direction, then recalculate.
• Forgetting that time works on gamma too. A position you put on with a week to go has a very different risk profile on the last day, even if the Nifty hasn’t moved at all.

If you’re still getting comfortable with calls, puts and how option premiums are built, start with our options trading for beginners in India guide before trading short-dated contracts.

The short version

Gamma is the rate at which delta changes as the underlying moves. It’s highest for at-the-money options and highest of all close to expiry, which is why at-the-money Nifty options can swing so violently in the final sessions. Buyers are long gamma and benefit when big moves happen. Sellers are short gamma and pay for those moves, faster the closer expiry gets. In our hypothetical example, at-the-money gamma with one day left was about 5.5 times its level with 30 days left, and a 200-point move cost a two-day straddle seller 35.5% of the premium collected against 5.4% for a 30-day seller. If you sell options, gamma is the Greek to check before anything else.

Disclaimer: This article is for information and education only and is not investment advice or a recommendation to buy or sell any security or derivative. The definitions and behaviour of gamma described here are from Zerodha Varsity’s two gamma chapters (the first is linked above) and the Investopedia page linked above. All Nifty levels, premiums, deltas and gammas in the tables and examples are hypothetical values we calculated with the Black-Scholes model under stated assumptions (13% implied volatility, 6% interest rate); real option prices will differ. Options trading carries a high risk of loss; consult a SEBI-registered investment adviser before making investment decisions.