What Is Gamma in Options and How Does It Work?

Options contracts allow individuals to manage risk or speculate on the future price movements of an underlying asset, such as stocks or commodities. These financial instruments derive their value from the performance of another asset. Market professionals use “Greeks” to quantify an option’s sensitivity to different market variables, helping assess and manage risks. Gamma is an important Greek that sheds light on a deeper layer of option behavior.

Gamma: The Rate of Delta Change

Gamma quantifies how much an option’s Delta is expected to change for every one-point movement in the underlying asset’s price. Delta represents the sensitivity of an option’s price to changes in the underlying asset’s price, indicating the approximate change in an option’s value for a $1 change in the underlying asset. If Delta is the speed of a car, Gamma is its acceleration, showing how quickly the speed (Delta) itself is changing. A higher Gamma suggests that the option’s Delta will shift more significantly with even small movements in the underlying asset.

For instance, if an option has a Delta of 0.50 and a Gamma of 0.10, a $1 increase in the underlying asset’s price would increase the option’s value by approximately $0.50 and increase its Delta to roughly 0.60. This change in Delta means the option becomes more sensitive to subsequent price movements. This reveals the non-linear nature of options pricing.

Gamma is typically highest for options that are at-the-money (ATM), meaning their strike price is very close to the current market price of the underlying asset. As an option moves further into or out of the money, its Gamma tends to decrease. This means that ATM options experience the most rapid changes in their Delta as the underlying asset fluctuates.

Key Determinants of Gamma

The magnitude of an option’s Gamma is influenced by several factors. As an option approaches its expiration, its Gamma tends to increase, especially for options that are at or near the money. This acceleration becomes most pronounced in the final weeks or days before expiry, reflecting a heightened sensitivity of Delta.

Moneyness, the relationship between an option’s strike price and the underlying asset’s current market price, also plays a substantial role. At-the-money options typically exhibit the highest Gamma values. This occurs because the probability of these options finishing in-the-money or out-of-the-money changes most dramatically with small movements in the underlying asset, leading to rapid shifts in their Delta. As options move deeper into-the-money or further out-of-the-money, their Gamma tends to decrease.

Implied volatility, a forward-looking measure of expected future price fluctuations, also affects Gamma. Higher implied volatility generally leads to lower Gamma for options. This relationship exists because when volatility is high, the option’s Delta is expected to change less rapidly across a wider range of possible prices. Conversely, lower implied volatility typically results in higher Gamma values.

How Gamma Shapes Option Payouts

Gamma directly impacts the profit and loss profiles of option positions, introducing a non-linear dynamic known as convexity. Individuals who purchase options hold a positive Gamma position. This positive Gamma means that as the underlying asset’s price moves in their favor, the option’s Delta increases, accelerating potential profits. Conversely, if the underlying moves against them, their Delta decreases, decelerating losses.

For example, if a long call option holder has a positive Gamma, and the underlying stock price rises, the option’s Delta will increase. This means that for every subsequent dollar increase in the stock price, the option’s value will increase by a larger amount. This accelerating profit potential is a significant benefit for option buyers. If the stock price falls, the call option’s Delta will decrease, reducing the rate at which the option loses value.

Individuals who sell options hold a negative Gamma position. This implies that as the underlying asset’s price moves against their position, their Delta increases, leading to accelerating losses. If the underlying asset moves in their favor, their Delta decreases, decelerating potential profits.

For instance, a short put option holder with negative Gamma experiences an increasing negative Delta as the underlying stock price declines. This means that for every additional dollar the stock falls, the put option’s value will increase by a larger amount, leading to more substantial losses for the seller.

Gamma represents the sensitivity of a position’s Delta to changes in the underlying asset’s price, indicating how much the position’s exposure to price movements will fluctuate. It explains why options exhibit a curved profit and loss diagram, where gains or losses can grow at an increasing rate.