What does ultima measure in higher-order option analysis?

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AcadiFi · Accepted Answer

Ultima is the third derivative of option price with respect to volatility, capturing how volga accelerates as vol moves.

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Consider a structured note desk at a firm called Arenvale Structured Products selling volatility-linked products. Their long volga exposure of 1,200 per contract grows as vol rises: at vol 18 volga is 1,200, at vol 25 volga may be 2,000. Ultima quantifies this acceleration, say ultima equal to 115 per vol point. For large vol shocks, Taylor-expanding just to volga understates the gain from a vol spike, and ultima corrects that.

Ultima matters primarily for books heavily exposed to wings of the vol surface, such as long-dated OTM options, variance swaps, and VIX derivatives. For a vanilla hedging book, ultima is usually small and can be ignored. For CFA Level II candidates, ultima rarely appears directly but knowing it exists helps you understand why complex books quote a tower of Greeks: price, vega, volga, ultima, each one capturing a finer slice of vol sensitivity. The general principle is that risk management becomes an exercise in choosing where to truncate the Taylor series based on materiality.

What does ultima measure in higher-order option analysis?

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