Definition
Gamma is a second-order option Greek that quantifies the rate of change of an option’s delta with respect to changes in the underlying asset’s price. It is typically expressed as the amount delta will change for a one-unit move in the underlying, making it a curvature measure of the option’s price sensitivity. High gamma indicates that delta is very responsive to small price moves, while low gamma implies a more stable delta profile.
As part of the broader set of Option Greeks, gamma is central to understanding the non-linear payoff structure of options in both traditional and crypto markets. It is generally highest for at-the-money options with shorter time to expiration and decreases as options move deep in- or out-of-the-money. Because it reflects how convex an option position is, gamma is closely linked to how an option’s risk profile evolves as markets move.
Context and Usage
In advanced options theory, gamma is used to describe second-order price risk, complementing delta’s first-order sensitivity and interacting with Volatility to shape an option’s overall risk surface. It helps characterize how rapidly hedging requirements change as the underlying asset price moves, since shifts in delta are governed by gamma. Positions with substantial gamma exhibit more pronounced non-linear behavior, which can lead to large changes in exposure over small price intervals.
Within the framework of Option Greeks, gamma is often analyzed together with vega and theta to understand how price curvature, volatility sensitivity, and time decay jointly affect an option’s valuation. In crypto derivatives markets, where Volatility can be elevated and abrupt, gamma provides a formal way to describe how quickly an option’s directional sensitivity can accelerate. As a conceptual metric, it underpins the mathematical models used to represent convexity and higher-order risk in option pricing.