What Is Vomma (Volga)?

Last reviewed: May 17, 2026 by Options Analysis Suite Research.

Vomma (also called Volga or vega convexity) is the second derivative of option value with respect to volatility (partial² V / partial sigma²). Equivalently, vomma measures how vega changes when implied volatility moves. In the Black-Scholes model, vomma equals vega × (d₁ × d₂) / sigma. Vomma is the structural exposure traded by butterflies and the analytical signal of vol-of-vol pricing.

What Is Vomma in Options?

Vomma captures the convexity of an option's value as a function of implied volatility. Long options have positive vomma (vega itself increases when IV rises further); short options have negative vomma. Vomma matters operationally because it measures the non-linear part of vol P&L: a vega-only estimate of P&L from a 5-point IV move underestimates the actual move when vomma is large.

Two intuitions. First, vomma is the analog of gamma in the volatility direction - both are second-order convexity measures. Second, vomma scales with vega and with the d₁×d₂ product, meaning it is small for ATM options (where d₁×d₂ is small) and grows in the wings. This is the structural reason butterfly trades have explicit vomma exposure: the wings of the butterfly carry the vomma.

Worked Example

SPY at $500, 60-day OTM call (K=540, about 8% OTM), IV 16%, rate 4%. Black-Scholes inputs:

d₁ = -1.053, d₂ = -1.118, phi(d₁) = 0.229
Vega = 500 × 0.229 × sqrt(60/365) = 46.5 (per share, per unit-vol-change)
Vomma = 46.5 × (-1.053 × -1.118) / 0.16 = 46.5 × 1.177 / 0.16 = 342 (per share, per unit-vol-squared)
Per-1%-IV scaling on vega: divide by 100 = 0.465 per share
Per-1%-IV-squared scaling on vomma: divide by 10000 = 0.0342

Operational reading: an IV move from 16% to 21% (5 vol points up) produces a vega P&L of approximately 5 × 0.465 = $2.33 per share. Plus a vomma P&L of approximately 0.5 × 0.0342 × 5² = $0.43 per share. Total: $2.76 per share - the vomma adds about 18% on top of the linear vega estimate. For a 10-vol-point move, the linear vega estimate is $4.65 and vomma adds roughly $1.71 (about 37%), because the vomma contribution scales as the square of the move size.

How Do Pricing Models Compute Vomma?

Black-Scholes: closed-form vomma vega × (d₁ × d₂) / sigma. Same vomma applies to calls and puts at the same strike (by put-call parity vega is the same; vomma inherits this).
Heston (stochastic volatility): Heston has multiple vol parameters, so "vomma" decomposes: sensitivity to v₀ squared, sensitivity to nu, etc. The aggregate vomma in Heston is computed via Fourier inversion of the second derivative.
SABR: SABR has explicit vol-of-vol structure (nu parameter), so vomma is directly captured. SABR vomma in the Hagan formula has both alpha and nu contributions.
Local volatility (Dupire): vomma computed by re-pricing under bumped surfaces; LV vomma is an artifact of the calibration choice rather than a structural model parameter.
Jump diffusion: vomma includes diffusion-component vomma and jump-component vomma. Bates (Heston + jumps) produces vomma profiles closer to observed market behavior than pure Heston.

Vomma in Trading Strategies

Vomma is the structural exposure of vol-curvature trades:

Long butterfly (sell ATM straddle, buy OTM strangle): long vomma. Profits when realized IV move is larger than expected (vol regime expands).
Short butterfly: short vomma. Profits when IV stays compressed.
Long calendar (sell front, buy back): generally long vomma at long-back-leg.
Long diagonal: mixed vomma profile depending on strikes and expirations.
Long out-of-the-money call or put: long vomma. Wing options carry the bulk of vomma exposure.

Vomma and Vol-of-Vol

The pricing of vomma in the market is the pricing of vol-of-vol. The VVIX index measures implied volatility of VIX itself - it is essentially an aggregate measure of priced vomma in the SPX option chain. When VVIX is elevated (above 110), vomma trades are expensive; when VVIX is compressed (below 80), vomma is cheap. Vol-of-vol regime is one of the structural inputs to vomma valuation.

What Are the Special Cases?

ATM options: vomma near zero. d₁×d₂ approaches zero at the money, killing the vomma magnitude.
OTM options (calls or puts): vomma peaks. Wings carry the convexity exposure.
Deep OTM: vomma falls off again as the option approaches worthlessness.
Long-dated options: vomma scales with vega (which scales with sqrt(T)), so 1-year ATM has larger vomma magnitude than 30-day.

Related Greeks

Vomma is the second derivative in the vol direction. Its sibling cross-derivatives are vanna (cross with spot) and veta (cross with time). The third-order extension is ultima (vomma's sensitivity to vol). Together, vomma, ultima, vanna, and veta describe the second- and third-order vol-direction structure of an option's value.

Related Concepts

Vega · Ultima · Vanna · Veta · Vol of Vol · Volatility Smile · Heston · SABR · All 17 Greeks

References & Further Reading

Hull, J. C. (2022). Options, Futures, and Other Derivatives, 11th ed. Pearson.
Castagna, A. (2010). FX Options and Smile Risk. Wiley. Practitioner reference on vanna, vomma, and volatility-smile hedging.
Gatheral, J. (2006). The Volatility Surface: A Practitioner's Guide. Wiley.

View live SPY IV smile and vomma structure →

This page is part of the 17 Greeks reference covering every options Greek with formula, intuition, worked example, and how each pricing model computes it. Browse the full documentation.

As of the latest snapshot, SPY carries net dealer delta exposure of -$83.87B, net vega exposure of -$988.55M, ATM implied vol of 13.7%. Each Greek is a partial derivative of theoretical option price with respect to a single risk factor (delta vs spot, gamma vs delta, vega vs vol, theta vs time, rho vs rate) holding the others fixed. Reading dealer exposure at the book level (delta, gamma, vega aggregated across the entire chain) is where the chain-level Greeks discussed above translate into the actual hedging flow that moves the underlying in the next session.