SVQ · Greeks
Volga (vomma)
Also called: vomma, vega convexity, DvegaDvol
Volga, also called vomma, measures how an option's vega changes as implied volatility changes: the convexity of option value in volatility.
Definition
Volga is the second derivative of an option's value with respect to implied volatility. It measures how vega itself changes when volatility moves, so it describes the convexity of an option's price in volatility.
The name is a contraction of "volatility gamma"; vomma is a common synonym.
Intuition
Gamma tells you that a long option gains more from a large spot move than a linear position would. Volga is the same idea for volatility: a long position with positive volga gains more from a large volatility move, in either direction, than its vega alone suggests.
Out-of-the-money options carry the most volga relative to their price, which is one reason wings are priced with extra implied volatility. Practitioner smile models such as vanna–volga pricing in currency options use exactly this sensitivity to explain the smile.
How it's calculated
Volga = ∂²V / ∂σ² = ∂ν / ∂σ
In Black–Scholes, for calls and puts alike:
Volga = ν · d1 · d2 / σ
where ν = S e−qT φ(d1) √T is vega. Volga is near zero at the money (where d1d2 is close to zero for short expiries) and positive in both wings. As with other volatility Greeks, it is quoted per unit of volatility unless the tool states per volatility point.
ΔV ≈ ν · Δσ + ½ · Volga · (Δσ)²
Example: an out-of-the-money option has vega of 0.20 and volga of 0.01, both per volatility point. If implied volatility rises 5 points, vega alone suggests a gain of 5 × 0.20 = 1.00; the volga term adds ½ × 0.01 × 5² = 0.125, for about 1.125. If implied volatility falls 5 points, the loss is about 1.00 − 0.125 = 0.875. That asymmetry in favor of the long position is volga at work.
How to read it
Positive volga on a long-options book means a volatility shock helps more than vega predicts, and a volatility collapse hurts less than vega predicts. Short wing positions are short volga: they lose disproportionately when volatility jumps.
Volga matters most when volatility of volatility is high, around events, and for books concentrated in out-of-the-money strikes.
Common mistakes
- Hedging vega only and assuming the hedge holds through a large volatility move.
- Assuming at-the-money options carry significant volga; it is concentrated in the wings.
- Confusing per-unit and per-point scaling when aggregating across positions.
- Ignoring that model volga changes with the smile assumption.
In Saqrid
SVQ's docked Greek heatmaps include volga with other higher-order sensitivities: vanna, charm, speed, color, zomma and ultima.
Open SVQ.
Go deeper
Saqrid Institute lesson: Hedging & the Greeks II: Rho, Vanna, Charm, Volga. Lesson text is open to read without an account.