What Are Third-Order Option Greeks? Explained
Learn third-order option Greeks: speed, zomma, colour, and ultima measure how gamma and vega change across price, volatility, and time.
Direct answer
Third-order Greeks measure how second-order sensitivities themselves move: speed tracks gamma's change with price, zomma tracks gamma's change with volatility, colour tracks gamma's decay over time, and ultima tracks vomma's change with volatility. Desk hedging uses them to stabilize large books; retail direction trades almost never need them beyond knowing they exist.
Third order means rates of rates of rates
Delta is first order, gamma second, and speed third: each layer differentiates the previous one against price, volatility, or time. Higher orders matter exactly when lower-order hedges stop holding still, which happens in large books, volatile regimes, and near expiration. Small directional positions feel these effects as noise long before they need names for them.
Option Greeks explained builds the first two layers these measures extend. Option gamma defines the second-order base that speed, zomma, and colour differentiate.
Speed, zomma, and colour split gamma's movement three ways
Speed, or gamma of gamma, gauges how fast gamma itself accelerates with price moves, critical near strikes into expiration. Zomma gauges gamma's sensitivity to implied volatility shifts, warning when vol regimes rewrite hedge ratios. Colour gauges gamma's time decay per day, telling desks how quickly gamma profiles age. Together they map every direction gamma can escape a static hedge.
Vanna and charm options covers the second-order cross Greeks traders meet first. Delta is not probability corrects the first-order misreading before higher orders compound it.
Ultima extends vomma where volatility itself swings
Ultima, or vomma of vomma, gauges how vega convexity changes with volatility, relevant when volatility-of-volatility runs hot around events and regime breaks. Like its siblings it refines rather than replaces full surface revaluation: no Greek chain substitutes for repricing the actual volatility surface under stress scenarios.
Volga vomma options explained defines the second-order volatility convexity ultima extends. Option vega grounds the first-order volatility sensitivity beneath both.
A higher-order checklist for the books that need it
Monitor speed into expiration pins, zomma across volatility regime shifts, colour on aging hedges, and ultima when vol-of-vol spikes, each with re-hedge triggers written beforehand. Everyone else should confirm first- and second-order controls work, then stop. Complexity earns its keep only where book size makes hedge drift expensive.
This guide explains higher-order mechanics for education. It does not recommend monitoring regimes, predict hedge performance, or promise any Greek profits. Risk system outputs and personal trade records govern real use.
Common questions
What is speed in options?
Gamma of gamma: how fast gamma itself changes with underlying price moves. It peaks near strikes into expiration where hedging needs constant adjustment.
What is zomma?
Gamma's sensitivity to implied volatility changes. It warns when volatility regime shifts rewrite hedge ratios that price moves alone would keep stable.
What is colour?
Gamma decay per unit time: how quickly gamma profiles age. Desks watch it on hedges held across sessions into expiration.
What is ultima?
Vomma of vomma: how vega convexity changes with volatility itself. It matters when volatility-of-volatility runs hot around events and breaks.
Should retail traders track third-order Greeks?
Almost never for decisions. Position size, liquidity, and exits dominate small-book outcomes where higher orders round to noise.