Options Gamma Explained: Why It Spikes Near Expiry

What gamma measures

Delta estimates how much an option's price changes for a $1 move in the underlying stock. Gamma goes one level deeper: it estimates how much delta itself changes for that same $1 move. The Options Industry Council puts it simply: how delta is expected to change given a $1 move in the underlying is called gamma.

A common analogy is speed and acceleration. If delta is how fast the option's price moves with the stock, gamma is how quickly that speed picks up or slows down. Mathematically, gamma is the first derivative of delta, or the second derivative of the option price, with respect to the stock price.

Gamma is quoted as a positive number for both calls and puts on most option chains. Like the other Greeks for US equity options, it is usually shown per share, so a contract covering 100 shares has 100 times the displayed exposure.

Delta: how much the option price moves per $1 in the stock.
Gamma: how much delta moves per $1 in the stock.
Gamma is a local estimate. After a large move, gamma itself has changed, so the estimate drifts.

A hypothetical worked example

Take a hypothetical $100 stock and a $100 strike call with about 30 days left. Suppose the chain shows a delta of 0.50 and a gamma of 0.05.

If the stock rises to $101, gamma suggests delta will rise to about 0.55. If the stock falls to $99, delta should drop to about 0.45. The option becomes more sensitive to the stock as it moves into the money and less sensitive as it moves out.

This is why delta alone can understate how an option behaves over a larger move. Gamma is what captures that curve.

These figures are illustrative only. Real gamma values depend on the stock price, strike, time to expiration, implied volatility and interest rates, and they change constantly.

Why gamma is highest at the money

Delta for a call ranges from roughly 0 for a far out-of-the-money option to roughly 1.00 for a deep in-the-money option. Puts run from roughly 0 to -1.00.

A deep in-the-money call already has a delta near 1.00, so it has little room to change. A far out-of-the-money call has a delta near 0 and a small move barely affects its odds of finishing in the money. Both have low gamma.

An at-the-money option sits in the middle, with delta around 0.40 to 0.60. A move in either direction meaningfully changes whether it is likely to finish in or out of the money, so its delta responds strongly. That is where gamma peaks.

Why gamma spikes near expiration

Time changes the shape of the picture. With months to go, there is plenty of time for the stock to wander across many strikes, so a $1 move today does not change much. Delta shifts gradually and gamma is spread out and modest.

As expiration approaches, there is less time for the stock to move, and the outcome narrows to a simple question: will the option finish above or below the strike? At expiration an in-the-money call behaves like 100 shares (delta near 1.00) and an out-of-the-money call is worth nothing (delta near 0). In the final days, delta for an at-the-money option has to travel from about 0.50 toward one of those two ends, and a small move in the stock can push it most of the way.

That rapid swing in delta is exactly what high gamma means. Merrill notes that for near-the-money options, gamma tends to rise as expiry approaches and time value erodes. Using a standard pricing model with the same hypothetical $100 stock and the same volatility, a $100 call with one day left can have a gamma several times larger than the same strike with 30 days left. In that hypothetical one-day case, delta might move from about 0.50 to about 0.75 on a single $1 move.

The spike is concentrated near the strike. Options that are clearly in or out of the money see their gamma fall toward zero as expiration nears, because their delta has already settled near 1.00 or 0. Once expiration arrives and the outcome is decided, gamma goes to zero.

Long-dated at-the-money options: moderate gamma, delta changes gradually.
Short-dated at-the-money options: high gamma, delta can swing sharply.
Short-dated options far from the strike: very low gamma.

Long gamma and short gamma

Gamma is positive when you own options and negative when you sell them, for both calls and puts. Stock has no gamma, because one share always has a delta of 1.00.

Long gamma means your delta moves in your favor. If you own a call and the stock rises, your delta grows, so the position becomes more sensitive to further gains. If the stock falls, delta shrinks, so further losses are smaller per dollar. The cost of that shape is time decay: the option loses extrinsic value each day.

Short gamma works the other way. If you sold a call and the stock rises, your negative delta grows, so each additional dollar hurts more than the last. Option sellers collect premium and benefit from time decay, but they carry the risk that a sharp move accelerates against them.

Near expiration both effects are magnified. A short at-the-money option in its final days can go from a small exposure to a large one on a modest move, which is why sellers often watch gamma closely in expiration week. Expiration also brings assignment and pin risk for options that finish near the strike.

Gamma, theta and the trade-off

Gamma and theta tend to travel together. The same at-the-money, short-dated options that carry the most gamma also tend to lose extrinsic value the fastest. Owners of those options are paying daily time decay for their sensitivity to movement, while sellers are collecting that decay in exchange for taking on the acceleration risk.

Neither side gets something for nothing, which is why time to expiration is a risk decision as well as a pricing one.

How to use gamma when reading a chain

Most retail traders do not need to calculate gamma, but checking it on the chain answers useful questions before you take a position.

How stable is my delta? A low gamma means your exposure will not change much on a normal move. A high gamma means your position can behave very differently after even a small move in the stock.

How does expiration change my risk? Comparing the same strike across a near and a far expiration shows how much faster delta will move in the shorter one.

Am I long or short gamma overall? For spreads and multi-leg positions, the net gamma tells you whether the position gains sensitivity as the stock moves or loses it. Many platforms show position-level Greeks for this purpose.

The Short Version

Gamma measures how much an option's delta changes for a $1 move in the underlying.
Gamma is highest for at-the-money options and lowest for deep in- or out-of-the-money options.
As expiration nears, at-the-money gamma rises sharply because delta must settle near 0 or 1.00.
Owning options gives positive gamma; selling options gives negative gamma.
High gamma usually comes with high time decay, so the two should be read together.

Questions

What is gamma in options in simple terms?

Gamma is the rate at which an option's delta changes when the stock moves $1. If delta is the option's speed relative to the stock, gamma is its acceleration.

Why does gamma increase near expiration?

With little time left, an at-the-money option's outcome hinges on which side of the strike the stock finishes. Its delta must move from around 0.50 toward 0 or 1.00, so small stock moves cause large delta changes, which is what high gamma means.

Is gamma positive for puts?

Yes. Long calls and long puts both have positive gamma. Short calls and short puts both have negative gamma. The sign depends on whether you bought or sold the option, not on whether it is a call or a put.

Does gamma go to zero at expiration?

Once an option expires, its delta is fixed at either 0 or 1.00 (or -1.00 for puts), so gamma is zero. Just before expiration, options right at the strike can have very high gamma while options away from the strike have gamma close to zero.

What is gamma risk?

Gamma risk is the risk that your position's delta changes quickly and against you. It matters most for sellers of short-dated, at-the-money options, where a modest move in the stock can sharply increase the size of their exposure.

How is gamma shown on an options chain?

Most chains show gamma per share as a positive decimal for both calls and puts. For a standard 100-share equity option contract, multiply by 100 to see the change in the contract's share-equivalent delta per $1 move.

Sources

More guides: Options Delta Explained: How It Works in Practice · Theta and Time Decay in Options, Explained

This article is for educational purposes only and is not financial, investment, or tax advice. Options involve substantial risk and are not suitable for all investors. All examples are hypothetical.