WealthJot.ai

Gamma: How Delta Changes

advanced7 min read

The acceleration behind delta — small near expiry for far strikes, explosive for near ones.

If deltaHow much an option moves per ₹1 move in the underlying. is your speed (how fast the optionThe right, not the obligation, to buy or sell at a set price. moves with the stock), **gammaHow fast an option’s delta changes with price. is your acceleration* — it measures how much deltaHow much an option moves per ₹1 move in the underlying. itself changes* when the underlying moves ₹1. GammaHow fast an option’s delta changes with price. is the Greek that makes delta a moving target rather than a fixed number.

GammaHow fast an option’s delta changes with price. is why optionsThe right, not the obligation, to buy or sell at a set price. are non-linear and why they can move shockingly fast near the strikeThe fixed price at which an option can be exercised. close to expiry. A low-gammaHow fast an option’s delta changes with price. optionThe right, not the obligation, to buy or sell at a set price. has a stable deltaHow much an option moves per ₹1 move in the underlying. (your exposure barely shifts); a high-gamma option has a deltaHow much an option moves per ₹1 move in the underlying. that swings wildly with small moves — your position can flip from barely-exposed to fully-exposed in a heartbeat. Gamma is *largest for ATMWhere an option’s strike sits relative to the current price. options near expiry*, which is exactly when a small move in the underlying can send the premium and delta lurching. This is the engine behind expiry-day fireworks: high gamma turns a tiny price wiggle into a violent P&LA record of revenue, costs and profit over a period. swing. Gamma is small and forgiving far from expiry, explosive and dangerous right at the strikeThe fixed price at which an option can be exercised. near the end.
ExampleAn ATMWhere an option’s strike sits relative to the current price. optionThe right, not the obligation, to buy or sell at a set price. a few hours from expiry can have huge gammaHow fast an option’s delta changes with price.: the stock ticks up ₹5 and its deltaHow much an option moves per ₹1 move in the underlying. leaps from 0.5 to 0.8; another ₹5 and deltaHow much an option moves per ₹1 move in the underlying. is near 1. The premium accelerates upward far faster than the earlier moves — wonderful for the buyer, terrifying for the seller who’s suddenly fully exposed.
Key takeawayGammaHow fast an option’s delta changes with price. measures how fast *deltaHow much an option moves per ₹1 move in the underlying.* changes per ₹1 move — the acceleration behind deltaHow much an option moves per ₹1 move in the underlying.. It’s highest for ATMWhere an option’s strike sits relative to the current price. optionsThe right, not the obligation, to buy or sell at a set price. near expiry, making them lurch violently on small moves (expiry-day fireworks). Buyers are long gammaHow fast an option’s delta changes with price. (helps); sellers are short gamma (the hidden danger).
FAQs
Why do option sellers fear gamma near expiry?

Because short gamma means their delta moves *against* them and accelerates losses: as the underlying approaches the strike near expiry, a small adverse move can rapidly turn a winning short option into a fast-growing loss. The high win rate of selling hides this gamma risk, which is most violent in the final hours — a key reason expiry-day option selling is so dangerous.