Zomma

What it is

Zomma measures how an option’s gamma changes as implied volatility changes. It is a third‑order risk metric—formally d(gamma)/d(vol)—and is one of the “minor Greeks” used to manage higher‑order risks in options trading. The term “zomma” is trader jargon (not a Greek letter).

Relationship to other Greeks

• Delta: first‑order sensitivity of an option’s price to changes in the underlying asset’s price.
• Gamma: second‑order sensitivity (the rate at which delta itself changes as the underlying moves).
• Zomma: third‑order sensitivity (the rate at which gamma changes as implied volatility changes).

How it works

Zomma quantifies how a change in implied volatility (IV) alters the curvature of an option’s delta profile. Because gamma determines how quickly delta responds to price moves, changes in gamma driven by volatility shifts will change the option’s directional exposure. Zomma can be positive or negative:
– Positive zomma: gamma increases when IV rises.
– Negative zomma: gamma decreases when IV rises.

Units follow the units used for IV in the calculation (e.g., per percentage point of IV).

Why it matters

• Risk management: traders use zomma to evaluate and manage the stability of gamma‑hedged positions as volatility moves.
• Sensitivity of hedges: a portfolio that is gamma hedged at one volatility level may become under‑ or over‑hedged if gamma shifts with volatility; zomma quantifies that effect.
• Directional risk: a large absolute zomma means small volatility changes can create substantial changes in directional exposure as the underlying price moves.

Example

If an options position has zomma = 1.00 (using the same IV units as the zomma calculation), then a 1 percentage‑point increase in implied volatility would raise gamma by 1 unit. That higher gamma increases how much delta will change for a given move in the underlying, altering directional risk and hedging requirements.

Interpreting values

• Small zomma (near zero): gamma is relatively insensitive to volatility; gamma hedges remain more stable across IV moves.
• Large positive zomma: rising IV amplifies gamma — hedges may require more frequent adjustment and directional exposure can grow quickly.
• Large negative zomma: rising IV reduces gamma — hedges can become less responsive to underlying moves.

Key takeaways

• Zomma = d(gamma)/d(vol) measures how gamma responds to changes in implied volatility.
• It is useful for assessing the durability of gamma hedges and anticipating how volatility shifts affect directional risk.
• Traders monitor zomma alongside delta and gamma when managing complex option positions.