Zomma (∂³V/∂S³)

Q: What is Zomma in options trading?

Zomma is the third derivative of an option's value with respect to the underlying price (∂³V/∂S³). It tells you how fast gamma itself is changing as spot moves. If gamma is the rate of change of delta, zomma is the rate of change of gamma — sometimes called the 'gamma of gamma'. It is essential for dynamic hedging of large, gamma-concentrated positions.

Q: Why does Zomma matter for hedging?

When hedging a portfolio with significant gamma, traders re-hedge delta as spot moves. Zomma tells them how quickly gamma will change during that move. High zomma means gamma shifts rapidly, so hedges go stale faster and need more frequent adjustment. Market makers with large at-the-money positions monitor zomma to anticipate how their gamma profile will evolve intraday.

Q: How do I get Zomma from the FlashAlpha API?

Call GET /v1/pricing/greeks with spot, strike, dte, sigma, type, and optional r and q parameters. The response includes a third_order object containing the zomma field. The endpoint is available on the Free tier.

Q: Why does Zomma matter for trading?

Zomma is a third-order Greek — the cross between gamma and vol. It tells you how your convexity itself evolves when vol changes. For books with large wing exposure, zomma is a significant P&L driver during vol regime shifts; for retail ATM traders, it's background noise.

Q: When is Zomma good versus bad for a trader?

Long zomma is good for tail-risk hedges and long-vol wing positions — convexity grows into stress. Short zomma is bad for wing sellers in vol rallies — hedging shrinks right when they need it most. ATM books have minimal zomma exposure; other Greeks dominate.

Third-order Greek measuring how gamma changes with the underlying price — the "gamma of gamma".

Definition

The third partial derivative of option value with respect to the underlying spot price. Zomma quantifies how rapidly gamma changes as spot moves, making it essential for dynamic hedging of portfolios with concentrated gamma exposure.

Formula

Zomma = ∂Γ/∂S = -(Γ / S) × [ (d₁ / (σ√t)) + 2 ]

Where Γ is gamma, d₁ is the standard Black-Scholes d₁ term, σ is implied volatility, t is time to expiry, and S is spot price. Zomma is typically a very small number and is quoted per unit move in the underlying.

Inputs

spot price strike price time to expiry implied vol

API Field

third_order.zomma

Interpretation

Positive zomma: gamma is increasing as spot rises. The option is becoming more convex — delta will accelerate faster on further up-moves.
Negative zomma: gamma is decreasing as spot rises. The option's convexity is flattening — delta acceleration is slowing.
Near ATM: zomma is near zero at the money (gamma peaks there). Zomma is most significant for OTM options approaching the strike.
Dynamic hedging: high absolute zomma means gamma is unstable — re-hedging intervals must be tightened to avoid delta slippage.

Why Zomma Matters

Gamma tells you how much delta will change for a unit move in spot. But gamma itself is not constant — it peaks at the money and falls off as the option moves into or out of the money. Zomma measures this curvature of gamma. For a market maker hedging a large book, zomma determines how quickly their gamma hedge becomes stale after a spot move.

Consider a portfolio that is long gamma near the current spot. As price moves away, gamma declines (zomma is the rate of that decline). If zomma is large, the hedge deteriorates rapidly, forcing more frequent and costly re-hedging. Conversely, if zomma is low, the gamma profile is stable and hedges last longer.

Zomma is particularly relevant around major option expirations when gamma is highly concentrated at a few strikes. A small spot move can shift the gamma profile dramatically, and zomma is the metric that quantifies that instability.

Get Zomma via API

Endpoint

GET /v1/pricing/greeks

Tier

Free

Parameters

spot (required) — underlying price
strike (required) — option strike price
dte (required) — days to expiration
sigma (required) — implied volatility (decimal)
type (required) — call or put
r (optional) — risk-free rate (default 0.05)
q (optional) — dividend yield (default 0.0)

Response field

{
  "third_order": {
    "zomma": 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"

import requests
r = requests.get(
    "https://lab.flashalpha.com/v1/pricing/greeks",
    params={"spot": 550, "strike": 560, "dte": 30, "sigma": 0.18, "type": "call"},
    headers={"X-Api-Key": "YOUR_KEY"}
)
print(f"Zomma: {r.json()['third_order']['zomma']:.8f}")

const params = new URLSearchParams({
  spot: 550, strike: 560, dte: 30, sigma: 0.18, type: "call"
});
const r = await fetch(
  `https://lab.flashalpha.com/v1/pricing/greeks?${params}`,
  { headers: { "X-Api-Key": "YOUR_KEY" } }
);
const d = await r.json();
console.log(`Zomma: ${d.third_order.zomma}`);

Why Zomma Matters for Trading

TL;DR

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

Long zomma

Gamma grows when vol grows
Convex in joint vol-price spikes
Valuable in stress regimes
Multi-variable tail hedge

Good for: long-vol tail hedges

Short zomma

Gamma shrinks when vol grows
Hedging drops off in shocks
Short-wing book failure mode
Vol-regime trap

Bad for: short-wing books in vol rally

ATM (zomma ≈ 0)

Near-ATM zomma is tiny
Retail-accessible regime
Standard gamma/vega trade
Negligible zomma exposure

Flat

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.