What is zomma and how does it connect gamma and volatility?

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AcadiFi · Accepted Answer

Zomma is the derivative of gamma with respect to volatility, describing how the gamma profile reshapes when implied vol shifts.

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A fund named Larksfield Quant running a short-vol strategy might have a negative gamma position of minus 0.09 per share at current vol of 22. If zomma equals minus 0.012 per vol point, a jump to vol 28 pushes gamma toward minus 0.162 even before spot moves. That sharper negative gamma means the hedger must rebalance more aggressively for every subsequent spot move, amplifying transaction costs and slippage.

Zomma is highest for near-the-money options with meaningful time to expiry because the gamma profile there is most sensitive to vol reshaping. Deep ITM or OTM options have low zomma because their gamma is already small. For CFA candidates, the linkage to remember is that vanna connects delta and vol, volga connects vega to vol, and zomma connects gamma to vol. All three are lenses on the same smile effect: when vol moves, every first-order Greek moves, and zomma is the gamma-specific slice.

```mermaid
graph TD
    V[Vol shift] --> G[Gamma]
    V --> D[Delta]
    V --> E[Vega]
    G -. zomma .- V
    D -. vanna .- V
    E -. volga .- V
```

What is zomma and how does it connect gamma and volatility?

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