What Is Volga?

Last reviewed: by .

Volga is the second-order Greek measuring vega convexity: how much vega changes per one-vol-point change in implied volatility. It is identical to vomma - the two names are used interchangeably across the literature. Volga is the structural exposure to vol-of-vol, and the central Greek for trades that bet on the volatility of volatility.

What Is Volga?

Take an option price V(S, sigma, t). Vega is ∂V/∂sigma. Volga (vomma) is ∂²V/∂sigma² - the second derivative with respect to volatility. Equivalently, volga is the rate at which vega changes as IV changes. For a Black-Scholes call:

volga = vega * d1 * d2 / sigma

where d1 and d2 are the standard BSM moneyness terms. Volga is largest at OTM strikes (where d1*d2 is positive and large in magnitude) and smallest at ATM (where d1 is near zero). This is structurally important: an ATM straddle has negligible volga; OTM strangles have substantial volga. Long-strangle = long volga.

Why Does Volga Matter?

Volga vs Vega Convexity

Vega is concave in sigma at OTM strikes - it has a peak somewhere between ATM and deep-OTM, and falls off in both directions. Vega's slope is volga. For a long option position:

Long-strangle = long vega + long volga. As IV rises, the vega rises (positive volga effect), so dollar-for-dollar IV change produces non-linear P&L. This is the asymmetry that vol-of-vol traders harvest.

Worked Example

SPX 30-day OTM put at 4,800 strike with spot at 5,000. BSM calibrated values:

If IV moves from 14% to 17% (+3 vol points):

The volga contribution is the larger component on this OTM put for a moderate vol move. Linear vega-only attribution would understate the realized P&L by 2/3.

How Does Each Pricing Model Treat Volga?

Volga in Trading Applications

Limitations and Caveats

Related Concepts

Vomma · Vanna · Vega · Vol of Vol · Butterfly Arbitrage · Convexity · Greeks · Pricing Model Landscape

References & Further Reading

View live volga across SPY surface ->

This page is part of the Pricing Model Landscape and the canonical reference set on options market structure. Browse all documentation.

Frequently asked questions

What is volga?
Volga is the second-order Greek measuring how vega changes with implied volatility. It is identical to vomma; the two names are used interchangeably across desks.
How is volga calculated?
Volga is the second partial derivative of option price with respect to volatility: d^2 Price / dsigma^2. For a Black-Scholes call, volga has a closed form involving the standard normal density and the d1/d2 terms.
When is volga largest?
Volga is highest for slightly OTM options at moderate maturity, where the option is most sensitive to wing-vol movements. ATM options have lower volga; deep ITM and deep OTM both decay toward zero volga.
How do traders use volga?
Long-volga positions (long straddles, long strangles in moderate tenors) profit when vol of vol rises regardless of spot direction. Dealer books with concentrated volga exposure require active vol-of-vol hedging.
How does volga relate to vol-of-vol?
Volga is the position-level exposure to vol-of-vol; vol-of-vol (nu in SABR, sigma_v in Heston) is the market-level parameter. Volga * (dvol)^2 captures the second-order P&L from vol changes.