What Is Delta, Gamma, and Theta in Options?

Options are financial contracts granting a buyer the right, but not the obligation, to buy or sell an underlying asset at a predetermined price on or before a specific date. Their value derives from an underlying asset, such as stocks, bonds, commodities, or currencies. Option Greeks are measurements that quantify an option’s sensitivity to factors like the underlying asset’s price, time decay, and volatility.

Understanding Delta

Delta measures the expected change in an option’s price for every one-dollar change in the underlying asset’s price. For example, a call option with a Delta of 0.60 suggests that if the underlying stock increases by $1, the option’s price is expected to rise by $0.60.

Call options have a positive Delta, ranging from 0 to 1.00, reflecting their value increasing as the underlying asset’s price rises. Conversely, put options have a negative Delta, ranging from -1.00 to 0, indicating their value increases as the underlying asset’s price falls. An option with a Delta near 1.00 or -1.00 behaves much like owning or shorting 100 shares of the underlying asset.

Delta’s value changes based on an option’s “moneyness,” which refers to its relationship between the underlying asset’s price and the option’s strike price. Options that are deep in-the-money (ITM) have Delta values closer to 1.00 for calls and -1.00 for puts, meaning they move almost dollar-for-dollar with the underlying asset. Out-of-the-money (OTM) options, far from their strike price, have Delta values closer to 0, indicating less sensitivity to small price changes.

At-the-money (ATM) options, where the strike price is close to the current underlying asset price, exhibit a Delta near 0.50 for calls and -0.50 for puts. As an option approaches its expiration date, its Delta can become more extreme. ITM options will see their Delta move closer to 1.00 or -1.00, while OTM options will see their Delta move more rapidly towards 0.

Understanding Gamma

Gamma measures the rate at which an option’s Delta changes in response to a one-dollar change in the underlying asset’s price. For instance, if a call option has a Delta of 0.50 and a Gamma of 0.10, a $1 increase in the underlying asset’s price would cause the Delta to increase to approximately 0.60.

Gamma is highest for at-the-money options and diminishes as options move further into or out of the money. This is because Delta experiences its most significant changes when the underlying asset’s price is near the option’s strike price. Options that are deep in-the-money or far out-of-the-money have Deltas that are already close to their maximum or minimum values, so their Deltas do not change as dramatically with further price movements.

The impact of Gamma becomes more pronounced as an option approaches its expiration date. Near expiration, even small movements in the underlying asset can cause rapid and substantial shifts in Delta, especially for at-the-money options. For example, an ATM option with high Gamma near expiration could see its Delta swing dramatically from near 0.50 towards 1.00 or 0 with only a slight price change in the underlying asset.

Gamma is always positive for both call and put options. A higher Gamma indicates that Delta will be more volatile, meaning the option’s price sensitivity to the underlying asset can change rapidly. Conversely, a lower Gamma suggests a more stable Delta, where the option’s price sensitivity changes more gradually with movements in the underlying asset.

Understanding Theta

Theta quantifies the rate at which an option’s price erodes or loses value over time, assuming all other factors remain constant. This decay is often referred to as time decay, as options have a finite lifespan and become worthless at expiration if not exercised. Theta is expressed as a negative number, representing the daily decrease in an option’s value. For example, a Theta of -0.05 indicates that the option’s price is expected to decrease by $0.05 each day.

Time decay is a constant force acting against an option’s value, as the probability of the underlying asset reaching a favorable price before expiration diminishes with each passing day. Both call and put options experience time decay, meaning their value naturally declines as they approach their expiration date.

Theta’s impact accelerates significantly as an option approaches its expiration date, especially for at-the-money options. Options with a longer time until expiration decay more slowly because there is more time for the underlying asset to move favorably. However, in the final weeks or days before expiration, the rate of decay dramatically increases, causing a more rapid loss of value.

This accelerated decay near expiration is particularly pronounced for at-the-money options because they possess the most extrinsic value, which is solely composed of time value and implied volatility. As expiration nears, this extrinsic value evaporates quickly, leading to a higher negative Theta. For deep in-the-money or out-of-the-money options, Theta tends to be less negative because they hold less time value to begin with.

The Collective Influence of Delta, Gamma, and Theta

Delta, Gamma, and Theta, when considered together, provide a comprehensive picture of an option’s characteristics and how its price is likely to behave under various conditions. Delta establishes the initial sensitivity of the option’s price to movements in the underlying asset. It provides a foundational understanding of how much an option’s value is expected to change for each dollar movement in the underlying security.

Gamma then refines this understanding by revealing how Delta itself will react to changes in the underlying asset’s price. A high Gamma indicates that Delta will change rapidly, meaning the option’s price sensitivity is not fixed but will accelerate or decelerate quickly. Gamma essentially describes the curvature of an option’s price movement.

Concurrently, Theta introduces the dimension of time decay, illustrating the constant erosion of an option’s value as expiration approaches. Theta ensures that the option’s extrinsic value diminishes with each passing day. This decay becomes particularly pronounced for options nearing their expiration, especially at-the-money options, due to the rapid evaporation of their time value.

Therefore, an option’s overall price behavior is a result of these forces acting simultaneously. Delta provides the immediate directional exposure, Gamma describes how that directional exposure changes, and Theta accounts for the inevitable passage of time. Together, these Greeks help to describe the multifaceted nature of an option’s value, showing how its price is influenced by the underlying asset’s movement, the rate of change of that movement, and the relentless march towards expiration.