Higher-Order Greeks: Speed, Color, Ultima

Delta measures how an option's price moves with the underlying; gamma measures how delta itself moves. The next layer down measures how gamma and vega move — and for a large enough options book, those third-order effects stop being academic and start showing up on the P&L.

Speed is the rate of change of gamma with respect to the underlying price — it tells a market maker how much their gamma exposure will shift if the stock jumps, which matters because gamma near expiry can swing from small to enormous over a narrow price range. Color is the rate of change of gamma with respect to time — how gamma decays or grows as expiry approaches, which is why a book that looked safely hedged on Monday can look very different by Thursday even with the stock unchanged. Ultima is the third derivative of the option price with respect to volatility — the rate of change of vomma (which is itself the rate of change of vega), relevant mainly to books running large, complex volatility positions where vega's sensitivity to vol itself needs tracking.

None of these are quoted or hedged individually the way delta and gamma are; they're monitored as an aggregate signal that a book's second-order Greeks are about to become unstable, most often near expiration on options that are close to the money, where gamma and vega are both largest and most sensitive to small moves.