Vomma

Core Description

• Vomma (often called volga) is the second-order volatility Greek that tells you how vega changes when implied volatility (IV) changes, so it helps you assess whether your volatility exposure is stable or accelerating.
• It becomes most relevant when markets shift volatility regimes, such as around earnings, central bank meetings, or macro shocks, because a vega hedge that looked neutral can drift quickly after an IV move.
• Used correctly, Vomma supports scenario tests (e.g., IV up or down by a few volatility points), improves volatility-risk reporting, and reduces the chance of treating vega as a constant when it is not.

Definition and Background

What Vomma Means in Options Pricing

Vomma measures the sensitivity of an option’s vega to changes in implied volatility (IV). In plain language, if vega answers "How much does the option price change if IV moves a little?", then Vomma answers "How much does that vega number itself change when IV moves?"

A quick comparison helps anchor the idea:

Why Traders Started Caring About Vomma

Options risk management historically expanded in layers as markets and models evolved:

• Early options practice emphasized delta hedging because underlying price moves were the dominant day-to-day risk.
• As traders learned that delta changes when price moves, gamma became essential to describe nonlinearity in price risk.
• With the mainstream adoption of the Black–Scholes framework, vega became the standard way to quantify exposure to implied volatility.
• Over time, desks noticed that volatility itself can change regimes (quiet markets vs. stressed markets). When IV shifts, vega is not constant, and that "vega curvature" is what Vomma captures.

As a result, Vomma became common in institutional risk systems because it explains a frequent real-world problem: a vega hedge can break after IV moves, not because the hedge was wrong at inception, but because the underlying vega changed.

When Vomma Tends to Matter Most

While the exact level depends on model inputs and the volatility surface, Vomma is often more relevant when:

• Options are near the money (ATM), where vega is typically most responsive.
• There is meaningful time to expiry, where volatility exposure has room to evolve.
• The market is near an event that can shift IV quickly (earnings, CPI releases, rate decisions).

Calculation Methods and Applications

The Core Calculation (Concept First)

Formally, Vomma is the derivative of vega with respect to volatility, equivalently the second derivative of the option value with respect to volatility. This is standard in options textbooks and is commonly presented under Black–Scholes as:

\[\text{Vomma}=\frac{\partial \text{Vega}}{\partial \sigma}=\frac{\partial^2 V}{\partial \sigma^2}\]

A widely used Black–Scholes expression is:

\[\text{Vomma}=\text{Vega}\cdot\frac{d_1 d_2}{\sigma}\]

with

\[d_1=\frac{\ln(S/K)+(r+\tfrac12\sigma^2) T}{\sigma\sqrt{T}},\quad d_2=d_1-\sigma\sqrt{T}\]

where the inputs follow the usual Black–Scholes conventions: spot price \(S\), strike \(K\), time to expiry \(T\), risk-free rate \(r\), and volatility \(\sigma\).

A Practical "Desk-Friendly" Way to Estimate Vomma

Many investors do not compute \(d_1\) and \(d_2\) manually. A common practical approach is a finite-difference estimate:

1. Compute vega at current IV (your platform often provides it).
2. Shift IV up by a small amount (e.g., + 1 volatility point) and recompute vega.
3. Approximate Vomma as the change in vega divided by the IV change.

This approach is intuitive for risk teams because it aligns with scenario testing: you are directly measuring how vega drifts when IV moves.

How Vomma Is Used in Real Portfolios

1) Stress-testing volatility exposure

If you only monitor vega, you implicitly assume the relationship between price and IV is roughly linear over the shock size. Vomma indicates how quickly that linear approximation deteriorates.

A simple workflow used in risk reports:

• Choose IV shocks such as \(\pm 1\), \(\pm 3\), or \(\pm 5\) volatility points.
• Reprice the options (or recompute Greeks) under each shock.
• Compare the new vega to the old vega to see whether the hedge ratio changes materially.

2) Explaining "hedge slippage"

A vega-neutral book at 9:30 a.m. can become meaningfully vega-long or vega-short by noon if IV moved and Vomma is large. In that sense, Vomma is often discussed as vega convexity, meaning it indicates whether your volatility exposure accelerates when volatility moves.

3) Strategy comparison beyond first-order Greeks

Two strategies can share similar vega today but behave very differently after an IV jump. Vomma helps distinguish them, especially for:

• Long straddles vs. spreads
• Concentrated near-ATM positions vs. diversified strikes
• Books that are "vega-flat" but still sensitive to volatility-of-volatility

Comparison, Advantages, and Common Misconceptions

Vomma vs. Nearby Greeks (and Naming Confusion)

Vomma is often used interchangeably with volga in practitioner conversations. However, naming conventions can vary across desks and analytics platforms, so confirm definitions when comparing reports.

Advantages of Monitoring Vomma

• Captures second-order volatility risk: You can see when vega exposure is likely to drift after IV moves.
• Improves scenario realism: Stress tests become more accurate when IV shocks are not assumed linear.
• Supports better hedging discipline: Helps set thresholds for when a vega hedge should be rebalanced.

Limitations and Trade-offs

• Model dependence: The computed Vomma depends on the pricing model and the volatility inputs.
• Input sensitivity: Small marking differences in IV (and time-to-expiry granularity) can create noisy Vomma readings, especially for very short-dated options.
• Surface dynamics are ignored in a single-number Greek: Real markets involve skew, term structure shifts, and discrete repricing around events. Vomma is helpful, but it is not a complete volatility-surface risk map.

Common Misconceptions (and How to Avoid Them)

"High IV automatically means high Vomma"

Not necessarily. Vomma is about how vega changes as IV changes, not the absolute level of IV.

"Vega is stable, so hedging vega once is enough"

If Vomma is meaningful, vega can drift quickly after an IV move. Hedging once and walking away can be risky in event-driven markets. Options also involve material risks, including volatility risk and potential losses, and hedging does not eliminate these risks.

"Vomma is a trading signal"

Vomma describes sensitivity, not direction. A high-Vomma position can experience larger-than-expected hedge drift, but it does not predict whether IV will rise or fall.

"Ignore the sign; only magnitude matters"

Sign can matter in scenario analysis because it indicates whether vega tends to expand or shrink as IV rises. Risk teams typically retain sign information when running shocks.

Practical Guide

A Simple Checklist for Using Vomma in Risk Monitoring

Step 1: Start with vega, then ask if it is stable

• Record position vega and portfolio vega.
• Check whether positions are clustered around ATM and event dates, as these areas often have higher sensitivity to IV changes.

Step 2: Add Vomma to your daily report

• Track both Vega and Vomma side by side.
• Flag positions where Vomma is large relative to vega, because those positions may cause hedge ratios to drift quickly.

Step 3: Run IV shock scenarios that match your holding period

• If you actively manage intraday, shocks might be smaller (e.g., 1 to 2 vol points).
• If you hold through events, shocks might be larger (e.g., 3 to 5 vol points or more depending on the product and historical behavior).

Step 4: Set re-hedge triggers instead of re-hedging constantly

Over-trading is a real cost. One practical approach is to define a threshold such as:

• "Rebalance only when vega changes by more than X% under a 1 to 3 vol point move", where X reflects internal risk tolerance and transaction costs.

Case Study (Hypothetical Example, Not Investment Advice)

Assume a trader holds a near-ATM option position ahead of a scheduled earnings release. The risk system shows:

• Current vega: $12,000 per 1 vol point
• Current Vomma: $2,400 per 1 vol point

Interpretation: if IV rises by 2 volatility points, the position’s vega may increase by roughly:

• Vega change \(\approx 2 \times \) 2,400 = $4,800$ per vol point

So vega could drift from $12,000 to about $16,800 per vol point, meaning the original vega hedge is no longer sized correctly.

Why it matters operationally:

• If the desk hedged vega to near zero in the morning and IV jumps, the book may become meaningfully net vega again, requiring a re-hedge under potentially worse liquidity and wider spreads.

What this teaches:

• Vomma does not predict the IV jump.
• Vomma quantifies how quickly your vega exposure can change if the IV jump happens.

A Real-World Reference Point (Data-Based, Non-Predictive)

Event risk is a common setting where traders pay more attention to volatility risk. For example, the Cboe Volatility Index (VIX), often described as a market "fear gauge" for S&P 500 implied volatility, has historically experienced sharp spikes during stress episodes, including during the 2008 and 2020 market turmoil (source: Cboe historical information and widely cited market records). These regime shifts illustrate the environment where second-order volatility effects can become more relevant, because hedges calibrated in calm conditions may behave differently when volatility accelerates.

This reference is not a forecast and does not imply any specific future market move. It is provided as context for why desks monitor convexity measures such as Vomma.

Resources for Learning and Improvement

Books and References (Conceptual + Practical)

• Options pricing textbooks that derive Greeks under Black–Scholes and discuss second-order sensitivities, including vega and Vomma.
• Volatility-focused trading and risk texts that connect Greeks to volatility surfaces (smile, skew, and term structure).

Exchange and Clearinghouse Education

• Exchange education portals that explain implied volatility, option Greeks, and risk disclosures in practical terms.
• Clearinghouse materials on margin, stress testing, and how risk sensitivities are used operationally.

Practice Tools (What to Look For)

When choosing a platform or workflow, prioritize tools that:

• Show Vega and Vomma / Volga consistently with clear units (per 1 vol point).
• Allow IV shock analysis (scenario grids) and portfolio aggregation on a single volatility surface snapshot.
• Provide time-stamped snapshots so you can avoid mixing Greeks from different IV marks.

FAQs

What is Vomma in simple terms?

Vomma indicates how vega changes when implied volatility changes. It is a second-order Greek focused on the stability of volatility exposure.

How is Vomma different from Vega?

Vega estimates how the option price changes for a small IV move. Vomma estimates how the vega value itself changes after that IV move.

When should I pay the most attention to Vomma?

Vomma tends to matter more when IV can move quickly, such as around earnings, major macro releases, or broader volatility regime shifts, especially for near-ATM options with meaningful time to expiry.

Is high Vomma good or bad?

Neither by itself. High Vomma indicates vega exposure is more nonlinear, which can increase hedge drift and can make scenario testing more important.

Does Vomma help with hedging?

It can support hedging discipline. If Vomma is large, a vega hedge can become stale after an IV move. Monitoring Vomma can help identify when hedge ratios may need review or rebalancing. Hedging does not guarantee risk elimination, and losses remain possible.

Is Vomma the same as Volga?

Often yes in practice, but naming conventions differ. Confirm the definition and units used by your analytics system.

Can Vomma be negative? What would that imply?

Yes, depending on moneyness, maturity, and model specifics. Negative Vomma suggests vega decreases as IV rises in that local region, which can reduce volatility exposure as IV increases.

Why might Vomma look noisy on very short-dated options?

Near expiry, small changes in time and IV marking can produce large relative swings in computed Greeks. Bid-ask effects and discrete volatility marking can dominate the signal.

How do risk teams use Vomma in reporting?

They often report Vomma alongside delta, gamma, and vega to flag nonlinear volatility exposure and run IV shock scenarios to estimate hedge drift and P&L curvature.

Does Vomma fully capture volatility-surface risk?

No. It is a local sensitivity to IV moves and does not fully represent skew shifts, term-structure changes, jumps, or liquidity constraints. It is typically used alongside surface-aware scenarios.

Conclusion

Vomma is the second-order volatility Greek that measures how vega changes when implied volatility moves, highlighting that volatility exposure is not fixed. Its practical value is in supporting scenario analysis, explaining vega hedge drift, and reducing the chance of treating vega as constant across volatility regimes. Used alongside vega, and complemented by volatility-surface scenarios, Vomma provides a structured way to assess how volatility risk can evolve nonlinearly when markets transition between calm and stressed conditions.