The option’s gamma measures the rate of change of its delta with respect to the underlying price. Gamma of 0.10 means an approximate change of 0.10 in delta for a $1 underlying move, with other inputs held fixed. This is an absolute change in delta, not a 10% relative increase.
Like the delta, the gamma is constantly changing, even with tiny movements of the underlying stock price. It generally is at its peak value when the stock price is near the strike price of the option and decreases as the option goes deeper into or out of the money. Options that are very deeply into or out of the money have gamma values close to 0.
Example
Suppose XYZ trades at $47 and a FEB 50 call sells for $2 with delta 0.40 and gamma 0.10 per $1. A $1 rise to $48 gives an approximate new delta of 0.40 + 0.10 = 0.50, assuming gamma and other inputs remain close to their starting values.
For a $1 fall to $46, the corresponding first-order estimate is 0.40 − 0.10 = 0.30. Gamma itself changes, so these are approximations rather than exact repricing results.
Passage of time and its effects on the gamma
As the time to expiration draws nearer, the gamma of at-the-money options increases while the gamma of in-the-money and out-of-the-money options decreases.
The chart above depicts the behaviour of the gamma of options at various strikes expiring in 3 months, 6 months and 9 months when the stock is currently trading at $50.
Changes in volatility and its effects on the gamma
When volatility is low, the gamma of at-the-money options is high while the gamma for deeply into or out-of-the-money options approaches 0. This phenomenon arises because when volatility is low, the time value of such options is low but it goes up dramatically as the underlying stock price approaches the strike price.
In the illustrated model comparison, higher volatility spreads gamma exposure across a wider range of strikes and reduces its peak near the money. Gamma still varies with strike and other inputs; it is not constant across all strikes.
The chart above illustrates the relationship between the option's gamma and the volatility of the underlying security which is trading at $50 a share.
The charts illustrate model relationships with selected inputs held fixed. They are not current market quotes or universal curves for every option.
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Using the estimate
Greeks are local model sensitivities, not guaranteed price changes. They change as the stock, time and implied volatility change. Check whether a quoted value is per share or per contract, which volatility increment is used, and whether theta is measured per day or per year. Selling an option reverses the position’s Greek signs.
Short-term options applications
Explore Short-Term Options Trading to see how weekly, 1DTE and 0DTE expirations affect timing, price sensitivity and expiration risk. Availability and settlement depend on the selected product and series.
A price-path example
One standard call starts at delta 0.50 and gamma 0.04 per $1 underlying move. If stock rises $2, a local estimate gives delta 0.58. A delta-only value estimate is $100; including gamma gives 100 × [0.50 × 2 + ½ × 0.04 × 4] = $108. For a $2 fall, the corresponding approximation is −$100 + $8 = −$92.
The curvature term has the same sign for either direction because the price change is squared. Selling the call reverses both delta and gamma signs. These estimates freeze gamma and omit time and volatility changes; they should not be extended to arbitrarily large moves.
If the long call is hedged with 50 short shares, the $2 rise leaves roughly eight shares of net positive delta. Selling eight more shares resets that estimate. A later reversal can require buying shares back. This is the basis of dynamic hedging, but the stock transactions must be evaluated together with option decay, costs and borrow.
Near expiration, gamma can become concentrated around the strike. That makes a single start-of-day delta less informative and increases the importance of the path, timing and ability to execute a hedge.
