Vomma (also called volga) is a second‑order option Greek that measures how an option’s vega changes as implied volatility (σ) changes. In plain terms, vomma tells you the sensitivity (and convexity) of vega with respect to volatility: how much more (or less) sensitive an option’s price becomes to volatility after volatility itself moves.
Key takeaways
– Vomma = ∂(vega)/∂σ = ∂^2V/∂σ^2. It is a second‑order derivative (a “second‑order Greek”).
– A positive vomma means vega increases when volatility rises (vega is convex in σ); a negative vomma means vega falls as volatility rises.
– Traders with long option positions typically prefer positive vomma; sellers often prefer negative vomma.
– Vomma is model dependent (usually reported under Black‑Scholes assumptions) and should be used alongside vega, delta, gamma, vanna, and scenario analysis.
Understanding vomma (intuition)
– Vega measures the first‑order change in option value for a 1 percentage‑point change in implied volatility.
– Vomma measures the rate at which that vega itself changes when implied volatility changes. In other words: vega’s curvature with respect to volatility.
– If vomma is large and positive, a rise in volatility will increase vega, boosting the option’s sensitivity to further volatility moves (risk compounds). If vomma is negative, a rise in volatility can reduce vega.
Mathematical definition (Black‑Scholes context)
– By definition:
vomma = ∂ν/∂σ = ∂^2V/∂σ^2
where ν (nu) denotes vega and V denotes the option value.
– Under Black‑Scholes, a convenient closed form is:
vomma = vega * (d1 * d2) / σ
where
d1 = [ln(S/K) + (r + σ^2/2) t] / (σ √t)
d2 = d1 − σ √t
vega = S φ(d1) √t
φ(d1) = standard normal density at d1
S = underlying price, K = strike, r = risk‑free rate, σ = implied volatility, t = time to expiry
– This form makes it easy to compute vomma once you have vega and the d1/d2 terms.
Numerical example
Assume S = K = 100, σ = 20% (0.20), t = 0.5 years, r ≈ 0.
– d1 = (0 + 0.5*(0.20)^2 * 0.5) / (0.20*√0.5) ≈ 0.0707
– d2 = d1 − σ√t ≈ −0.0707
– φ(d1) ≈ 0.398 × (slightly less) ≈ 0.398
– vega ≈ S * φ(d1) * √t ≈ 100 * 0.398 * 0.707 ≈ 28.1
– vomma ≈ vega * (d1*d2) / σ ≈ 28.1 * (0.0707 * −0.0707) / 0.20 ≈ −0.70
Interpretation: in this (near‑ATM, short‑dated) example vomma is slightly negative — a small rise in implied volatility would slightly reduce vega.
Practical steps for traders (how to use vomma)
1. Get reliable Greeks:
• Use your broker’s option analytics, a Greeks calculator, or build a small Black‑Scholes implementation to report vega and vomma (and other Greeks).
2. Interpret sign and magnitude:
• Positive vomma: vega will grow if volatility rises (beneficial for long‑vol positions).
• Negative vomma: vega will shrink if volatility rises (can be beneficial for short‑vol positions).
• Look at the magnitude relative to position size to assess sensitivity.
3. Combine vomma with vega and other Greeks:
• Vomma only describes vega’s curvature. Also check vega (how big the immediate exposure is), vanna (sensitivity of option value to simultaneous moves in spot and vol), delta, and gamma.
4. Construct or select trades intentionally:
• Long options or long straddles/strangles often exhibit positive vomma exposure; they benefit if volatility rises and vega increases.
• Calendar spreads and some complex spreads can produce particular vomma profiles—monitor both near‑term and longer‑term vomma.
5. Manage exposure:
• If you want to limit implied‑volatility convexity risk, adjust position size or add offsetting instruments to get a desired vomma exposure (e.g., reduce long wings or add short options in strikes that offset vomma).
• Use vega‑ and vomma‑neutral approaches if your objective is to be insensitive to volatility and its convexity.
6. Scenario and stress testing:
• Run scenario analysis: simulate changes in implied vol (±10% etc.) and observe option/P&L changes. Because vomma governs curvature, include non‑linear moves in volatility in scenarios.
7. Rebalance as market conditions change:
• Vomma, like vega and delta, changes as time passes and as S and σ move. Recompute and rebalance periodically, especially as expiry approaches.
8. Use position limits and hedging:
• Because vomma can amplify volatility exposure, use position limits, stop rules, and hedges. Consider options with different expiries to manage term structure of vomma.
Common trading implications and strategies
– Long volatility strategies (long straddles/strangles, long puts/calls):
• Tend to have positive vomma; they gain not only from an increase in implied volatility but from the amplification of vega as volatility rises.
– Short volatility strategies:
• Benefit if volatility falls and/or if vomma is negative so that vega falls as volatility rises slightly (but beware of large adverse vol spikes).
– Calendar (time) spreads:
• Can have complex vomma profiles because different expiries have different vega and vomma; useful to trade term structure of vol.
– Hedging:
• If you are long vega but worried about volatility‑convexity risk, you can add short vomma exposure via structured spreads to flatten second‑order exposure.
Limitations and caveats
– Model dependence: Vomma values typically come from Black‑Scholes or other analytic models, so they inherit model assumptions (lognormal returns, constant volatility between recalculations, no jumps). Real markets deviate (skew, kurtosis, jumps).
– Implied vs realized volatility: Vomma deals with the sensitivity of implied volatility exposure. Realized volatility moves can differ and can cause model mispricing.
– Liquidity and discrete strikes: You cannot trade continuous σ exposure; options exist at discrete strikes and expiries, and transaction costs matter.
– Small magnitudes: For many practical positions vomma can be small relative to vega and gamma; always check absolute exposures.
– Correlations with other Greeks: Changes in underlying price S change d1/d2 and therefore vega and vomma; do not treat vomma in isolation.
Checklist for implementing vomma‑aware trades
– Compute current vega and vomma for candidate options or portfolios.
– Decide desired vomma posture: net positive, net negative, or neutral.
– Size positions so vomma‑driven P&L fits portfolio risk limits.
– Complement vomma view with scenario tests (price moves, volatility moves, skew changes).
– Monitor and rebalance frequently (vomma decays/change with time).
– Track realized vs implied volatility outcomes and adjust assumptions as required.
Conclusion
Vomma is a useful second‑order Greek that helps traders understand how volatility sensitivity (vega) itself will change as market volatility changes. It is most useful when used with vega, delta/gamma, and other second‑order Greeks, and when applied with careful scenario analysis and risk management. Because vomma is model‑dependent and often small relative to first‑order Greeks, treat it as part of a broader toolkit rather than as a standalone signal.
Source
– Investopedia, “Vomma” — (used as the primary source for definitions and basic interpretation).