Gamma Meaning: How Fast an Option's Delta Changes

How gamma works

Delta is not fixed. A call deep in the money has a delta near 1 and behaves like the index. A call far out of the money has a delta near 0 and barely moves. Between the two, delta rises as the index rises, and gamma measures how fast.

• Bought options have positive gamma. When the market moves your way, delta grows, so each further point is worth more. When it moves against you, delta shrinks, so each further point costs less.
• Sold options have negative gamma. Each point against you costs more than the last, and each point in your favour earns less.
• Gamma is highest at the money and falls for options deep in or far out of the money, because a deep option's delta is already near 1 or 0 and has little room to change.

A worked example on one Nifty lot

Nifty is at 25,000 with 12 days to expiry and implied volatility of 14%. The 25,000 call costs ₹280.50, with a delta of 0.54 and a gamma of 0.00063. One lot is 65 units.

Delta alone predicts a gain of 0.54 × 100 × 65 = ₹3,510 on one lot for a 100-point rise. The option gains ₹3,702 (from ₹280.50 to ₹337.45), ₹192 more, because the delta rose from 0.54 to 0.60 during the move. For a 100-point fall the delta falls to 0.48, so the loss is ₹3,299, less than delta predicted. That difference in both directions is gamma at work: it favours the buyer and costs the seller.

Gamma rises as expiry nears

The same at-the-money call, at the same 14% IV:

With one day left, a 100-point move changes the delta by about 0.22, more than five times the change with 30 days left. On expiry day an at-the-money option can go from almost worthless to moving one for one with the index within a few hundred points. That is why expiry-day option selling carries the sharpest losses and why SEBI added an extra 2% exposure margin on short index options expiring that day.

Gamma and theta: two sides of one trade

Gamma and theta rise and fall together. The 12-day call has a gamma of 0.00063 and loses ₹12.85 a day to time; the 2-day call has a gamma of 0.00154 and loses ₹28.10 a day. A buyer pays theta every day for the chance that gamma turns a large move into a large gain. A seller collects theta and accepts that a large move will cost more than delta suggests.

The chart shows the trade-off for a sold straddle at 25,000 with 12 days left: a gain of about ₹1,411 on a flat day, a loss of ₹1,213 after a 200-point rise and ₹6,916 after a 400-point rise. The loss grows roughly with the square of the move, which is the signature of negative gamma.

Gamma and hedging

A delta-neutral position has no exposure to small moves at the start, but gamma changes its delta as the market moves. A seller with large negative gamma must rebalance often to stay neutral, buying after rises and selling after falls, which costs money. A buyer with positive gamma can do the opposite, selling after rises and buying after falls, and lock in small gains from each swing. That technique is called gamma scalping, and it pays only if the market moves more than the theta paid for the position. See the delta neutral strategy.

When gamma matters most

• Expiry day and the day before, when gamma on at-the-money options is highest.
• Around events, when a large move can push options from out of the money to deep in the money quickly.
• Short straddles and strangles, whose losses accelerate with the move.
• Bought straddles and strangles, which need the move to arrive before theta erodes them.
• Delta-hedged positions, which need rebalancing at a rate set by gamma.

Related terms

• Delta meaning: how much an option moves for a 1-point move in the underlying
• Theta meaning: what an option loses each day to time
• Vega meaning: how an option responds to implied volatility
• Expiry meaning: when contracts settle

Learn more

• Option greeks: delta, gamma, theta, vega and rho with Nifty examples
• Expiry day trading strategies: where gamma risk is highest
• Option selling strategies: managing negative gamma with stops and hedges

Frequently asked questions