Zomma Calculator
The formula
What the zomma tells you
Bridges vol and convexity: how much gamma you gain or lose as the vol regime shifts. In a crisis it decides whether your hedges get sharper exactly when you need them to — or duller.
Calculation: Zomma = ∂Γ/∂σ — gamma’s sensitivity to implied vol. Enter your inputs and every substitution is shown below the result.
Reading the result
OTM options gain gamma when vol rises (positive zomma) — the tail hedge strengthens as the tail event threatens; that convexity-on-demand is why tail hedging survives its long droughts.
Rules of thumb: Zomma effects matter when vol moves 10+ points; below that gamma re-sits barely register
Limitations and best practice
Zomma is third-order and noisy from market data — it needs a full surface re-fit to estimate honestly from quotes. Treat single-number zomma as model-based bookkeeping, not observation.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Is zomma related to volga?
Who needs zomma?
Why do my OTM puts gain gamma in a crash?
Can zomma be negative?
Source & methodology
Jaubert et al., Advanced Greeks (2011).
Zomma: what this tool answers
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. Searchers land on a Zomma page for three reasons — to plan, to compare options, and to check that somebody else’s arithmetic is honest. This tool serves all three, and everything after the calculator explains the model instead of hiding it.
Most confusion about Zomma comes from mixing up the input you control with the input you merely observe. The formula treats them identically, but your decisions should not: one deserves measurement, the other deserves a defensible estimate.
It helps to separate the mechanics from the interpretation. The mechanics are fixed: Zomma = ∂Γ/∂σ — gamma’s sensitivity to implied vol. Anyone, anywhere, entering the same inputs will get the same 0.000 /Γ/vol-pt. The interpretation is where experience counts: whether 0.000 /Γ/vol-pt is good, normal or alarming depends on comparisons covered below, and that is the part most articles about Zomma never explain.
Nothing below is stock text pasted around a number: the worked example computes zomma per 1% vol (×1,000) = 0.000 /Γ/vol-pt from this tool’s own defaults, and the sensitivity section ranks the inputs that move the result — Underlying price first, at ≈820.4 % of the headline for a ten-percent error either way in that input. Work down the page and by the end you could re-derive the result in a spreadsheet from memory.
Every input in Zomma, and what it does to the answer
One formula, published in full: Zomma = ∂Γ/∂σ — gamma’s sensitivity to implied vol. Anything you can read, you can reproduce in a spreadsheet, and that reproducibility is the whole point of printing it rather than hiding it behind a button.
Underlying price ($) (example value 235) is a measured number in the unit named by the label; the formula does not convert for you. If your source quotes a figure before and after some deduction, decide which one the formula wants and be consistent for every field.
Strike ($) (example value 107) is a quantity rather than a category — precision here is cheap and worth having. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.
Time to expiry (years) (example value 1) is a measured number in the unit named by the label; the formula does not convert for you. Be precise about the boundary (exact date, start of month); time inputs decide the exponent in most formulas.
Risk-free rate (%) (example value 5) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Enter it exactly as your document states it — quoted annual, monthly and effective rates are three different numbers.
Implied volatility (%) (example value 26) is a quantity rather than a category — precision here is cheap and worth having. Enter it exactly as your document states it — quoted annual, monthly and effective rates are three different numbers.
Option type (example value Call) is a choice rather than a quantity — pick the option that matches your situation, because the calculation path branches here. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
A fully worked Zomma example
The tool prints its own working; this is the same arithmetic on the example values, reproduced so you can follow it by hand. Starting figures: Underlying price ($), Strike ($), Time to expiry (years), Risk-free rate (%). The endpoint of that chain is 0.000 /Γ/vol-pt of zomma per 1% vol (×1,000), sitting in the “A 5-pt vol move changes gamma 353.2% — vol regimes re-price convexity, not just premium” band.
- Zomma = Γ·(d1·d2 − 1)/(σ·100) = 0.000000
- Sign of zomma: rising vol can thicken or thin your convexity depending on moneyness
- +5pt scenario: gamma 0.0000 → 0.0000
Γ after +5 vol pts — 0.000. Read next to the headline, this is the figure that shows the shape of the trade-off.
Γ after −5 vol pts — 0.000. This is the number experienced users quote when the headline alone would mislead.
Current gamma — 0.000. This is the number experienced users quote when the headline alone would mislead.
Zomma/Γ — 0.706 /pt. If your inputs change, this is usually the first companion figure to move.
Overwrite any input above and every line of this example updates with it — the substitution is live, not a screenshot of somebody else’s numbers.
Scenario table: Zomma at ±10 % and ±20 % of the key input
The honest version of any estimate is a corridor, and this one is cheap to produce: Zomma was recomputed at 5 points along the dominant input, with every other field left untouched.
| Underlying price setting | Zomma per 1% vol (×1,000) |
|---|---|
| 80 % of the example value | 0.019 /Γ/vol-pt |
| 90 % of the example value | 0.002 /Γ/vol-pt |
| example inputs | 0.000 /Γ/vol-pt |
| 110 % of the example value | 0.000 /Γ/vol-pt |
| 120 % of the example value | 0.000 /Γ/vol-pt |
Across 5 settings of Underlying price, the result spans 0.000 /Γ/vol-pt to 0.019 /Γ/vol-pt. A decision that only works at one row of this table is a decision waiting for an input to move. Reproduce it in the form above by editing Underlying price alone; the substitution steps will follow your figures exactly.
Sensitivity: which inputs change Zomma the most
Nobody should have to guess which input matters. The engine was re-run once per field below — ten percent up, ten percent down, everything else frozen — and the results ranked by how far they moved the zomma per 1% vol (×1,000). Read it as a map of where Zomma is fragile — drawn for the example inputs, which is the map you want when deciding what to measure carefully.
- Underlying price +10 % → Zomma = 0.000 /Γ/vol-pt · −10 % → 0.002 /Γ/vol-pt (the zomma per 1% vol (×1,000) shifts ≈820.4 %)
- Strike: ten percent up gives 0.002 /Γ/vol-pt, ten percent down gives 0.000 /Γ/vol-pt — ≈588.2 % of the zomma per 1% vol (×1,000) either way
- Nudge Implied volatility by ±10 % and Zomma lands between 0.000 /Γ/vol-pt and 0.001 /Γ/vol-pt (sensitivity ≈262.4 %)
- Time to expiry: ten percent up gives 0.001 /Γ/vol-pt, ten percent down gives 0.000 /Γ/vol-pt — ≈98.9 % of the zomma per 1% vol (×1,000) either way
- Risk-free rate +10 % → Zomma = 0.000 /Γ/vol-pt · −10 % → 0.000 /Γ/vol-pt (the zomma per 1% vol (×1,000) shifts ≈5.0 %)
Underlying price is the dominant lever here: ten percent either way moves the result by about 820.4 %, from 0.000 /Γ/vol-pt to 0.002 /Γ/vol-pt. Measure that input from a document rather than from memory, and treat Strike as the second priority (≈588.2 % per ten percent). Everything below that can stay approximate, which is a licence to stop chasing data that would not change the decision.
What a Zomma of 0.000 /Γ/vol-pt means in practice
The value above only becomes useful the moment you know what it is being measured against. The verdict attached to the default calculation — “A 5-pt vol move changes gamma 353.2% — vol regimes re-price convexity, not just premium” — is one band on a ladder your own figure may sit somewhere else on. Before treating the band as fact, note its width: ten percent either way on Underlying price already spans 0.000 /Γ/vol-pt to 0.002 /Γ/vol-pt. The practical reading rules: ask what would have to change to move you one band. If the answer is “a small, plausible input difference”, the band itself is not the finding — the uncertainty is.
Related measures answer related questions, and the distinctions matter: Zomma is the quantity, Zomma per 1% vol (×1,000) is this tool’s reading of it, and the decision that follows belongs to neither of them separately.
The errors that quietly break a Zomma figure
Zomma is third-order and noisy from market data — it needs a full surface re-fit to estimate honestly from quotes. Treat single-number zomma as model-based bookkeeping, not observation. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Treating the example inputs as a recommendation. They are a demonstration of the mechanism — a decision-grade Zomma begins the moment your own figures replace them.
This model has its own particular trap: Underlying price carries ≈820.4 % of the response per ten percent of error, so effort spent elsewhere is largely decorative.
A final trap is presentation: reporting Zomma to more decimal places than the inputs support. The tool prints what the arithmetic gives; you should quote only what your least precise field justifies.
A quick check for any Zomma figure
- Confirm the example values are plausible for your own situation before replacing them.
- Note the date and the inputs beside the number so the figure can be audited later.
- Put Underlying price under a magnifier; the sensitivity table above is the reason why.
- Recompute once with the dominant input deliberately set low, and see whether the decision changes.
- Re-run the calculation with a ±10 % stress on the two most sensitive inputs.
- Run the ±10 % stress on the top two levers and check that your conclusion survives both.
A routine for decision-grade Zomma
Using a calculator well sounds trivial, but the difference between a decision-grade figure and a throwaway one lives entirely in the routine. The routine for Zomma takes a minute to learn and applies to every input above.
Step 1 — gather before you type. Zomma depends on underlying price ($), strike ($), time to expiry (years), risk-free rate (%), implied volatility (%), option type. Collect them from a source document — a statement, a report, an invoice, a log — rather than from memory, because recalled inputs are the single largest cause of wrong results. A result worth acting on survives having its two shakiest inputs halved.
Step 2 — baseline before exploration. Get one defensible Zomma per 1% vol (×1,000) on screen before you start nudging numbers. Without a baseline, every variation looks interesting and none of them means anything. Re-running a number costs seconds; retracting a decision costs considerably more.
Step 3 — measure what deserves measuring. The ranked levers above tell you where a careful figure pays off. Everything else can stay approximate, which is a licence to stop hunting for data you do not need. Most surprises in numbers are surprises about inputs, not about formulas.
Step 4 — compute a corridor, not a point. Three runs — worst, likely, best — turn Zomma from a snapshot into a range. Plan against the pessimistic end and treat the optimistic end as the upside story. The inputs are the part of the work that nobody else can do for you.
Step 5 — schedule the next run. In Investing & Markets the inputs drift quietly. Put a reminder a quarter out, re-enter the same fields, and read the change rather than the level. Rounding early is the quietest way to introduce a permanent error.
Who actually uses Zomma — and when
In Options & Derivatives the figure computed here is usually the first one somebody asks to see. Having it — with the formula behind it — changes your position in the conversation from participant to reference. The point of transparency is that a reader can disagree with a specific line rather than with you.
The audience for this page is people who need one trustworthy number before their next decision. In professional Options & Derivatives practice the pattern is always the same — screen with Zomma, then invest slow analysis only in whatever survives the screen. Note the assumption you are least sure about; that is where the real risk lives.
There is a personal-administration use people overlook: periodic self-checking. Zomma quietly drifts as life changes — rates move, bodies change, costs compound — and re-running it a few times a year catches drift while correction is still cheap. The point of transparency is that a reader can disagree with a specific line rather than with you.
People also ask about Zomma
What affects Zomma the most?
Measured on this engine, Underlying price is the dominant lever: moving it ±10 % shifts the zomma per 1% vol (×1,000) across 0.000 /Γ/vol-pt to 0.002 /Γ/vol-pt — about 820.4 % of the headline, with Strike next at ≈588.2 %. The ranked list in the sensitivity section is computed live, not asserted from a template.
Which matters more: strike or underlying price?
Underlying price, by a factor of about 1.4. Concretely: ten percent on Underlying price is worth ≈820.4 % of Zomma, the same nudge on Strike only ≈588.2 %. That ranking is re-computed for each page from that page’s own defaults.
What is a typical Zomma?
On the worked example above Zomma comes out at 0.000 /Γ/vol-pt. Treat that as one point on a distribution rather than a norm: the bands, the companion outputs and the sensitivity ranking tell you how wide the plausible range really is.
How do I calculate Zomma by hand?
Three steps: write the formula (Zomma = ∂Γ/∂σ — gamma’s sensitivity to implied vol), insert your values, and simplify. The worked example section shows exactly that chain for the default inputs; replicating it once on paper teaches you more about Zomma than any number of calculator runs.
What happens to Zomma if underlying price changes by 10 %?
On these inputs a ±10 % change in underlying price takes Zomma to 0.000 /Γ/vol-pt against the 0.000 /Γ/vol-pt example — around 820.4 % of the headline. The same test on every other field is in the sensitivity section.
Is the Zomma result of 0.000 /Γ/vol-pt good or bad?
Neither, on its own — the label “A 5-pt vol move changes gamma 353.2% — vol regimes re-price convexity, not just premium” is the band this figure falls in for the example inputs, and your own inputs will place you elsewhere on the same ladder. Judge the number against your history and your alternatives, and remember that a ten-percent error in Underlying price alone moves it by ≈820.4 %.
How do I calculate Zomma manually?
Write down the inputs, then follow the printed steps in order — Zomma = ∂Γ/∂σ — gamma’s sensitivity to implied vol. A spreadsheet replicates it with two or three cells. The manual route is worth doing once to build intuition; after that the calculator saves time and eliminates transcription slips.
Does Zomma account for fees and taxes?
Only what you put in. Fees belong inside Underlying price ($) where they shrink returns before compounding touches them; taxes are outside the scope of a pre-tax Zomma and should be layered on top before decisions.
Is zomma related to volga?
Both live on the vol axis: volga curves vega; zomma curves gamma (∂Γ/∂σ = d1d2·Γ/σ in closed form).
Who needs zomma?
Gamma scalpers and tail-hedgers — anyone whose P&L depends on gamma actually being there when the regime flips.
Can this tool see the numbers I type?
It cannot. There is no submission step: the calculation happens in your browser and the result disappears when you close the page. Treat the fields above as a scratchpad rather than a form.
The vocabulary of Zomma
- Γ after +5 vol pts
- 0.000 for the Zomma worked case; it sits next to the main result because it carries context the headline leaves out.
- Γ after −5 vol pts
- 0.000 for the Zomma worked case; it sits next to the main result because it carries context the headline leaves out.
- Current gamma
- 0.000 on the example inputs — a companion figure printed beside the headline of Zomma so that no result is read in isolation.
- Zomma per 1% vol (×1,000)
- The primary output of this tool: 0.000 /Γ/vol-pt for the default inputs, computed exactly from Zomma = ∂Γ/∂σ — gamma’s sensitivity to implied vol.
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- The interpretation attached to a result (“A 5-pt vol move changes gamma 353.2% — vol regimes re-price convexity, not just premium” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Zomma moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
The provenance of this Zomma calculation
Everything above runs on one stated formula, applied without hidden coefficients: Zomma = ∂Γ/∂σ — gamma’s sensitivity to implied vol. Source of record: Jaubert et al., Advanced Greeks (2011). Where a professional version of this calculation differs, it differs in inputs and jurisdiction-specific coefficients, not in the algebra — which is why re-checking your inputs beats hunting for a second calculator.
Treat the output as a precise answer to the question you typed: exact arithmetic, transparent formula, published source, no hidden rounding. The sensitivity table above is part of that promise rather than a bonus: it lets you see how much of the result depends on how carefully you measured.
Next steps after the calculation
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
Whoever you are (people who need one trustworthy number before their next decision), the next step is the same: replace the example inputs with your own, note the date, and re-run whenever a figure moves. In Investing & Markets, a dated figure is a trend, and an undated one is a rumour.