Vomma

What is vomma in options?

Vomma, also called volga, is the second-order option Greek that measures how vega changes as implied volatility changes. It is the second derivative of option value with respect to volatility. When vega is quoted per one percentage point of IV, vomma is quoted per volatility point squared, and the two together give a second-order estimate of the premium change for a volatility move.

Vega gives the slope of the premium response. Vomma gives its curvature. Together they show how a position responds as an IV move grows beyond the first point.

How do you calculate vomma?

In Black-Scholes, raw vomma = raw vega × d1 × d2 / σ, with volatility expressed as a decimal.

Trading displays commonly quote vega per one percentage point of IV. With that convention, use vomma per point squared = vega per point × d1 × d2 / (100 × σ).

For an IV change of h percentage points, calculate:

Premium change = vega per point × h + 0.5 × vomma per point squared × h².

This is the second-order expansion. Reprice the option at the target IV to obtain the full scenario value. Multiply per-share values by the contract multiplier and signed quantity to size the position effect.

Where does vomma turn positive or negative?

For a long Black-Scholes option, vega and σ are positive. The sign therefore comes from d1 × d2.

• When d1 and d2 share a sign, vomma is positive.
• When they have opposite signs, vomma is negative.
• When either term is zero, vomma is zero.

At the forward strike, d1 = σ√T/2 and d2 = −σ√T/2. Their product is negative. This establishes negative vomma for a long option at that strike, including the spot-at-the-money case with zero rates and dividends.

Positive vomma develops beyond the sign boundaries in the wings. It eventually fades toward zero in the distant tails as vega disappears. Shorting the contract reverses the position’s vomma.

Calls and puts with the same strike, expiration, volatility, and other Black-Scholes inputs share the same vega and vomma.

What does positive vomma do to profit and loss?

Take the example above: vega starts at 0.10 per point and ends at 0.16 per point after IV rises ten points.

The starting-vega calculation is 0.10 × 10 = $1.00 per share. Using the average of the two endpoint vegas gives 0.13 × 10 = $1.30 per share. That trapezoidal calculation approximates the area under the changing-vega curve.

The $0.30 difference comes from vega increasing across the move. Positive curvature also adds a positive second-order correction when IV falls: the squared volatility change remains positive, so the correction reduces the loss relative to the starting-vega tangent.

How do traders use vomma?

Compare the IV response of wing options, strangles, and straddles. Price each structure across the same volatility scenarios and compare the resulting premium, vega, and payoff.

Use vanna for volatility-driven delta changes and zomma for volatility-driven gamma changes. Vomma specifically describes the change in vega.

To put dollars on the volatility thesis, compare price, time, and volatility scenarios for the selected contract or structure in the options profit calculator.

Limitations of vomma

• Reprice a large IV move at the target IV. Vomma is a local measure, and the second-order expansion improves on vega alone without replacing the full reprice.
• Add vanna and gamma when spot moves too. Vomma holds spot, time, and rates fixed, and a volatility shock often arrives with a price move.
• Match the units. Vega per point pairs with vomma per point squared and h in percentage points; raw values pair with decimal volatility.
• Sum vomma leg by leg for a spread. The sign changes across the chain: negative at the forward strike, positive in the wings, and fading in the far tails.
• Shock the wings separately. Black-Scholes vomma moves one volatility for each option, while real surfaces shift skew and wings unevenly, so a single IV shock can misstate wing risk.

Bottom line

Vomma shows how much an option’s vega grows or shrinks as implied volatility moves, which matters most for large volatility swings, event scenarios, and wing structures. Quote it in units that match vega, read its sign across the chain, and use the second-order estimate as a check before repricing the full position at the target IV.