Second-order: Vomma and Dual Delta
Vomma measures vega's own convexity — how much vega itself changes as implied volatility moves. Positive vomma means an option's sensitivity to volatility grows as volatility rises, a detail that matters to anyone sizing a vega hedge in a fast-moving vol regime.
Dual Delta measures sensitivity to the strike rather than the spot, and roughly equals the risk-neutral probability the option finishes in the money — a cleaner read on "probability of finishing" than raw delta offers.
Third-order: Speed, Zomma, Color, and Ultima
Speed measures how fast gamma itself changes as price moves — it tells you whether a gamma wall building ahead of price is likely to strengthen or evaporate as price actually gets there. Zomma measures how gamma changes as implied volatility moves, which means a vol spike can quietly reshape the entire gamma profile even while price sits still.
Color measures gamma's own decay over time — the third-order sibling of Charm — and explains why gamma walls near expiration can shift from strike to strike day over day, not just intraday. Ultima, the rate of change of vomma with respect to volatility, is a pure convexity-of-convexity term used mainly by desks stress-testing tail scenarios.
Lambda and Veta
Lambda is an option's leverage ratio — the percentage change in the option's value per percentage change in the underlying — a direct read on how much more, or less, exposure the option gives relative to owning the stock outright. Veta measures vega's decay over time: how much an option's sensitivity to volatility erodes simply from time passing, independent of any actual change in implied volatility.
None of these need memorizing to use a terrain map day to day — they surface through the exposure metrics and the regime read rather than as raw numbers on their own — but each has a precise, linkable definition behind it for the moment a reading calls one out by name.