Speed and Color

Speed and color are third-order option Greeks. Speed measures how fast an option's gamma changes as the underlying moves - the rate of change of gamma with price. Color measures how gamma changes as time passes - the rate of change of gamma with time. Both are small for most positions but become meaningful for very short-dated, near-the-money options, where gamma itself is already large and unstable.

Speed extends the delta-gamma relationship one step further: gamma is not constant as price moves, and speed tells you how much it is about to change. For a position with large gamma near the money, speed describes whether that gamma is about to grow even larger as price continues in the same direction, or shrink as it moves past the strike - a meaningful distinction for anyone hedging a large, concentrated gamma position.

Color describes the analogous idea for time rather than price: how a position's gamma itself grows or decays as expiration approaches, holding price fixed. It is distinct from charm, which describes delta drifting with time, and from theta, which describes value decaying with time - color is specifically about the convexity (gamma) of the position changing shape as the clock runs down.

For most option positions, these third-order effects are negligible next to delta, gamma, theta, and vega. They become practically visible in 0DTE index options specifically because gamma itself is so concentrated and short-lived near expiration that its own rate of change is no longer a rounding error - a dealer's hedging obligation can be shifting quickly even before considering the next price tick.

Speed and color sit at the end of two Greek families: delta leads to gamma leads to speed (the price-sensitivity chain), and theta's time-decay concept extends through charm to color (the time-sensitivity chain applied to gamma). Understanding them is mostly relevant for reasoning about why dealer hedging obligations can themselves become unstable in the closing minutes of a same-day expiration, not for everyday option evaluation.

In the standard Greek hierarchy, delta is the first derivative of an option's price with respect to the underlying, gamma the second, and speed the third - each one measuring the rate of change of the Greek before it. Color occupies an analogous position in the time dimension: theta is the first derivative with respect to time, charm (delta decay) is the cross-derivative linking delta and time, and color is the derivative of gamma with respect to time.

For a market-maker managing a large, concentrated 0DTE book into the final hour of a session, both speed and color become part of the practical picture: a hedge that is correctly sized against today's gamma can become mis-sized within minutes if gamma itself is moving quickly, which is exactly what speed and color describe. This is a professional risk-management concern rather than something the average options participant needs to model directly.