Gamma effect: Meaning, Criticisms & Real-World Uses

What Is Gamma Effect?

The Gamma Effect refers to the sensitivity of an option's Delta to changes in the Underlying Asset's price. As a second-order Derivative, gamma measures the rate at which delta will change for every one-point move in the underlying security. It is a crucial component within Options Trading and falls under the broader category of Option Greeks, which are risk measures that help traders and portfolio managers understand the various sensitivities of an options position.

History and Origin

The concept of "the Greeks," including gamma, emerged alongside the development of quantitative models for pricing options. While the basic concept of options contracts can be traced back to Ancient Greece, notably with Thales of Miletus and his predicted olive harvest, the formal mathematical framework for options pricing is a much more recent development.

The modern understanding and calculation of gamma became prominent with the advent of the Black-Scholes model in 1973⁸. Developed by Fischer Black and Myron Scholes, and later extended by Robert Merton, this seminal model provided a theoretical framework for valuing European-style options⁷. The mathematical derivations within such models inherently led to the identification of sensitivity measures like delta, and subsequently, gamma, as critical components for Hedging and Risk Management in the growing derivatives market.

Key Takeaways

The Gamma Effect measures how much an option's delta changes for a given movement in the underlying asset's price.
It is highest when an option is near the Strike Price (at-the-money) and for options with shorter times until expiration.⁶
Positive gamma indicates that a long option position will see its delta increase as the underlying asset moves favorably and decrease as it moves unfavorably, making the position more sensitive to price changes.⁵
Negative gamma (often held by option sellers or Market Makers who are short options) means their delta exposure becomes increasingly adverse with unfavorable price movements.⁴
Understanding the Gamma Effect is essential for dynamic hedging strategies, particularly for those aiming to maintain a delta-neutral portfolio.

Formula and Calculation

Gamma ($\Gamma$) is the second partial derivative of the option price with respect to the underlying asset's price, or equivalently, the first derivative of delta ($\Delta$) with respect to the underlying asset's price. In the context of the Black-Scholes model for a European Call Option, the formula for gamma is:

\Gamma = \frac{N'(d_1)}{S \sigma \sqrt{T-t}}

Where:

( N'(d_1) ) is the probability density function of the standard normal distribution evaluated at ( d_1 ).
( S ) is the current price of the Underlying Asset.
( \sigma ) is the Implied Volatility of the underlying asset.
( T-t ) is the time remaining until expiration (in years).

For a Put Option, the formula for gamma is identical to that of a call option with the same parameters.

Interpreting the Gamma Effect

The Gamma Effect provides insight into the convexity of an option's price relative to its underlying asset. A high gamma value indicates that the option's delta will change rapidly for small movements in the underlying price. This is particularly true for options that are at-the-money (where the strike price is close to the current underlying price) and those nearing their expiration.³

For traders, a positive gamma is generally desirable for directional bets, as it means their delta exposure increases when the market moves in their favor, accelerating profits. Conversely, a negative gamma position, often held by options sellers, implies that their Delta becomes more negative (for short calls) or more positive (for short puts) as the underlying moves against them, increasing their risk exposure. Understanding this sensitivity helps in adjusting positions and managing overall portfolio Volatility.

Hypothetical Example

Consider an investor holding a Call Option on Company XYZ stock.

Current stock price (S): $100
Option strike price: $100
Option's delta: 0.50
Option's gamma: 0.10

If Company XYZ's stock price increases by $1 to $101:
The delta of the option would not just remain 0.50. Instead, it would increase by the gamma value.
New Delta = Old Delta + Gamma = 0.50 + 0.10 = 0.60.

This means that for the next $1 increase in the stock price, the option's value is expected to increase by approximately $0.60, rather than $0.50. If the stock price then moves to $102, the delta would again adjust based on the new gamma (which itself can change, though for this simple example we keep it constant). This accelerating or decelerating sensitivity, driven by the Gamma Effect, highlights why gamma is crucial for understanding how an option's value changes with significant moves in the Underlying Asset.

Practical Applications

The Gamma Effect is fundamental in various aspects of financial markets, especially within Derivatives trading.

Hedging Strategies: Professional traders and Market Makers heavily rely on gamma for dynamic Hedging. They often aim to maintain a "delta-neutral" position, meaning their overall portfolio's delta is near zero, minimizing exposure to small price fluctuations. However, because delta changes with price movements (due to gamma), they must continuously adjust their hedges by buying or selling the underlying asset to re-establish delta neutrality. This is known as gamma hedging.
Volatility Trading: Traders who speculate on Implied Volatility often use gamma. A long gamma position benefits from large price swings (up or down) in the underlying asset, even if the direction is uncertain, as the positive gamma ensures delta moves favorably, increasing profits or mitigating losses.
Risk Management: For any institution involved in options, monitoring gamma is critical for Risk Management. A large negative gamma exposure, for instance, implies that adverse price movements could lead to accelerating losses, requiring substantial re-hedging efforts. The U.S. options market regulations set by bodies like the SEC ensure that brokers and market participants adhere to certain standards to manage such risks.

Limitations and Criticisms

While the Gamma Effect is a vital measure, it comes with limitations. Options pricing models, including those that calculate gamma, rely on certain assumptions that may not always hold true in real markets. For example, the Black-Scholes model assumes constant Volatility and continuous trading, which are idealizations.²

Furthermore, calculating and maintaining a perfectly gamma-hedged position in practice can be challenging due to transaction costs, illiquidity, and sudden market movements. High gamma near expiration can lead to significant and rapid changes in delta, requiring frequent and potentially costly adjustments to maintain a hedge. This can lead to what is known as "gamma risk," where unexpected price movements cause compounding losses for short-gamma positions¹.

A notable criticism arises when market dynamics become extreme, such as during phenomena like a "gamma squeeze," which can lead to rapid and unpredictable price movements.

Gamma Effect vs. Gamma Squeeze

The Gamma Effect is a fundamental concept in Options Trading that describes the rate of change of an option's delta. It is a measure of an option's sensitivity to price movements in its Underlying Asset.

In contrast, a Gamma Squeeze is a specific market event where a surge in demand for Call Options, particularly out-of-the-money options, compels Market Makers to buy large quantities of the underlying stock to hedge their positions. This forced buying can create a positive feedback loop, driving the stock price sharply higher. While the Gamma Effect is a continuous measure inherent in options pricing, a gamma squeeze is a rare and extreme manifestation of this effect in action, often characterized by rapid, dramatic price increases. The GameStop's dramatic surge in early 2021 is a well-known example of a gamma squeeze, often intertwined with a Short Squeeze.

FAQs

What does high gamma mean for an option?

High gamma means that an option's Delta will change significantly for even small movements in the Underlying Asset's price. This typically occurs when an option is at-the-money (its Strike Price is near the current stock price) and when it is close to expiration, as Time Decay becomes more pronounced.

Is positive or negative gamma better?

Whether positive or negative gamma is "better" depends on a trader's strategy and market outlook. Investors who are long options (buying Call Options or Put Options) have positive gamma, benefiting from accelerating profits as the underlying moves in their favor. Those who are short options (selling calls or puts) have negative gamma, which can lead to accelerating losses if the underlying moves against them, requiring more frequent Hedging.

How does gamma relate to delta?

Gamma is the rate of change of Delta. Delta measures how much an option's price is expected to change for a $1 move in the Underlying Asset. Gamma, in turn, tells you how much that delta itself will change with each $1 move. It's often referred to as the "delta of the delta."