Gamma: Changing Delta & Near-Expiry Risk

Delta is the change in an option’s value for a one-point move in the underlying. Gamma is the change in that Delta for a one-point move. Gamma of 0.000307 means a one-point NIFTY rise lifts Delta by about 0.000307. It is a change in sensitivity. It is not a ₹0.000307 gain in premium, not a percentage and not a probability.

The baseline is the same as in the last three lessons: NIFTY 25,000, strike 25,000, 30 days left (30/365 years), implied volatility 18%, interest 6% and dividend yield 1% a year. The model is Black–Scholes–Merton for a plain European option, which can be exercised only at expiry. These are teaching inputs, not exchange quotes. Here the Call is worth ₹565.99, its Delta is 0.541541 and its Gamma is 0.000307264 per NIFTY point.

Delta alone estimates a ₹54.15 rise per unit for a 100-point rise. Gamma adds a curvature correction of about ₹1.54, giving ₹55.69. Full repricing gives ₹55.68, from ₹565.99 to ₹621.68. The tiny gap is the approximation. It is not a cost and not a profit from some other Greek.

The curvature term uses the square of the move, so it is positive for a fall too. For a 100-point fall, the same correction is added to a negative Delta estimate: −₹52.62 by estimate, −₹52.61 by full repricing. The Call still lost value. Positive Gamma means the price curve lies above the straight Delta line. It does not mean a bought Call profits in both directions.

Before expiry, a bought Call and a bought Put both have positive Gamma. Selling to open either one reverses the sign: a written Call and a written Put have negative Gamma. Selling an option you already own just closes that long position. Call and Put name the contract. Long and short name the position. One does not replace the other.

Take 65 units of the baseline contract, a teaching quantity, not the current NSE lot. A long Call has position Delta +35.2002 and Gamma +0.0199722. A long Put has Delta −29.7464 and the same Gamma +0.0199722. A short Call flips both Call numbers and a short Put flips both Put numbers. Position Gamma is how much the whole position’s Delta changes for a one-point move.

Close to expiry, a small move near the strike decides whether the option finishes with value or without. Delta can therefore swing quickly over a narrow range. As time falls, Gamma gathers into a taller, narrower peak near the strike, other inputs being comparable.

The picture fixes the strike at 25,000 and varies NIFTY, with curves for 30, 7 and 1 day left. At spot 25,000, Gamma rises from about 0.000307 to 0.000639 and then 0.001693 per point. The peak is near the strike, not always exactly at it: interest, dividend, volatility and time shift it a little.

A Delta hedge adds an opposite exposure to cancel the position’s sensitivity to a small move. Our 65-unit long Call starts with Delta +35.2002. In the ideal case, adding −35.2002 units of plain exposure makes the total Delta zero. These are divisible units for the arithmetic, not an order to sell fractions of NIFTY or a futures lot.

NIFTY rises 100 points, other inputs fixed. The Call position’s Delta, recalculated, is now +37.1833. The old hedge is still −35.2002, so +1.9832 is left over. To get back to zero you would sell another 1.9832 units. The option’s changing Delta pushed the hedge out of balance.

Gamma is the curve, not the cost of owning it. A bought option can still lose value through time, an IV fall or a bad move, despite positive Gamma. Re-hedging a long-Gamma position again and again is called Gamma scalping. Whether it pays depends on the actual moves, the price paid, time decay, volatility, financing and trading costs. Curvature gains on a worksheet are not an income stream. Gamma against Theta is the usual trade-off, but not every bought option has negative Theta.

Negative Gamma calls for care with large moves and funding. A naked short Call has no upper limit on loss. A naked short Put’s loss is large but capped, because the underlying cannot go below zero: the most is the strike minus the premium, before costs. Both can lose far more than the premium collected. Margin is security, not a cap on loss. In a volatile market, a broker can ask for more funds or close the position. Assess a multi-leg position leg by leg, with its settlement obligations.

A Gamma squeeze is a possible feedback loop, not something you can read off one option-chain number. Dealers, such as market makers, quote both buying and selling prices for options. If they are net short Gamma and keep re-hedging their Delta, they buy the underlying as it rises and sell as it falls. That can reinforce a move when it is large against the available liquidity. Dealers who are net long Gamma hedge the other way. Which case applies depends on their actual positions and behaviour.

Open interest counts outstanding contracts, and every contract has a long side and a short side. Open interest alone does not say which side dealers hold, what their net Gamma is after offsets, or how they will hedge. Other strikes, expiries and products can offset it. Cboe’s 2023 research uses US data to show that gross activity is not net dealer risk. It says nothing about NIFTY dealers. The SEC’s October 2021 review described how a Gamma squeeze could work but found no evidence of one in the GameStop period it studied. Treat a squeeze claim as a hypothesis that needs position and flow evidence, not a forecast from high open interest.

Before comparing Gamma readings, check the contract, strike, expiry, underlying, timestamp, IV input and units. Does the screen show Gamma per unit or for your whole position? Prices and Greeks can update at different times, and another IV convention or model gives another number. Decimals matter: rounding our baseline Gamma to two places shows 0.00 and hides it completely.

To stress a position, move spot to the level you fear, then recalculate the option value and every exposure, stating what you assume for time and IV. Compare with your entry price only if you want the outcome of a position. A model value is not a fill. Costs, taxes, spreads, liquidity and the real exit price decide realised profit or loss.

Settlement matters beside the Greeks. NIFTY index options settle in cash. NSE stock options are European and physically settled under the current contract terms. An exercised long stock Call needs full payment for the shares at the strike. An exercised long stock Put needs shares to deliver. The seller has the matching obligation. A bought option’s loss is limited to the premium, but that does not remove these funding and delivery needs. Check the exchange rules and your broker’s expiry handling before calling a Greek-based hedge a complete risk plan.

You now have four lenses on one option: Delta for direction, Gamma for how Delta changes, Theta for time and Vega for volatility. The next lesson is implied volatility itself: how it is read from a quote, why it differs across strikes and expiries, and why a high or low reading needs context. That helps you choose the volatility assumption in a full scenario instead of freezing it.