Zomma (∂Γ/∂σ)
Third-order Greek measuring how gamma changes when implied volatility moves — the gamma-vol cross.
The partial derivative of gamma with respect to implied volatility. Zomma quantifies how an option's gamma changes when IV moves — most significant for wing positions and books with concentrated out-of-the-money gamma exposure.
Where Γ is gamma, d₁ and d₂ are the standard Black-Scholes terms, and σ is implied volatility. Zomma is largest at the wings and approaches zero at the money.
- Positive zomma: gamma grows when IV rises. Long-zomma positions gain convexity in vol rallies — useful for tail hedges.
- Negative zomma: gamma shrinks when IV rises. Short-zomma positions lose convexity exactly when vol shocks hit — a classic wing-seller failure mode.
- Near ATM: zomma is near zero. Most retail trades have negligible zomma exposure.
- Wing positions: zomma is largest out of the money. Wing-heavy books need to monitor zomma alongside vomma during vol regime shifts.
Where Zomma Lives
Vega tells you how option value changes when IV moves. But vol changes don't only affect option price — they also reshape the option's gamma profile. Zomma is the partial derivative of gamma with respect to IV: it tells you how much your convexity itself will move when vol shifts.
Zomma is essentially zero at the money (gamma is already at its peak there) and largest at the wings. A book of OTM options will see meaningful zomma exposure during vol regime shifts; an ATM-only book barely registers it.
The most common practical use is in wing-heavy structures — variance swaps, dispersion trades, and tail-hedge programs — where understanding how gamma evolves under vol stress is critical. For retail traders running ATM strategies, zomma is background noise managed implicitly through strike selection.
Get Zomma via API
spot(required) — underlying pricestrike(required) — option strike pricedte(required) — days to expirationsigma(required) — implied volatility (decimal)type(required) —callorputr(optional) — risk-free rate (default 0.05)q(optional) — dividend yield (default 0.0)
{
"third_order": {
"speed": number,
"zomma": number,
"color": number,
"ultima": number
}
}curl -H "X-Api-Key: YOUR_KEY" \
"https://lab.flashalpha.com/v1/pricing/greeks?spot=550&strike=560&dte=30&sigma=0.18&type=call"Why Zomma Matters for Trading
Zomma is how gamma changes with vol. Long zomma profits when vol and moves rise together — the classic vol-rally trade.
- What it measures
- ∂Γ/∂σ — how gamma changes when IV changes.
- What it signals
- How much your convexity grows or shrinks in vol shocks.
- Why we measure it
- Vol doesn't just change vega. It also changes gamma — i.e. how your book rehedges. Zomma captures that.
- Who uses it
- Vol quants, market makers, structured-product desks.
How to read Zomma
- Gamma grows when vol grows
- Convex in joint vol-price spikes
- Valuable in stress regimes
- Multi-variable tail hedge
- Gamma shrinks when vol grows
- Hedging drops off in shocks
- Short-wing book failure mode
- Vol-regime trap
- Near-ATM zomma is tiny
- Retail-accessible regime
- Standard gamma/vega trade
- Negligible zomma exposure
Rules of thumb
- Wing-specific Greek. Zomma lives out of the money. ATM zomma is too small to matter.
- Pair with vomma. Both are wing convexity measures. Together they describe the out-of-the-money vol topology.
- Event-sensitive. Major vol regime shifts produce zomma P&L even when spot barely moves.
- Not retail-managed directly. Managed through strike/DTE selection rather than hedged directly.
- Structured-products bread and butter. Variance swaps and wing-hedged books care deeply about zomma.
Related Concepts
The second derivative of option value with respect to spot — the rate of change of delta that zomma itself measures the curvature of.
First-order sensitivity to spot. Delta is the foundation that gamma and zomma build upon.
Aggregate dealer gamma across the chain. Zomma determines how quickly GEX profiles shift as spot moves.
How gamma changes with implied vol — the vol-axis sibling of zomma.
Live for 6,000+ US symbols. One API call, sub-200ms.
Stop scraping chains and coding Black—Scholes from scratch. FlashAlpha computes GEX, DEX, VEX, CHEX, 15 BSM Greeks, SVI surfaces, max pain, VRP and more — fresh every 30s, cached at the edge. Free tier, no credit card, no rate-limit games.