Color Calculator
The formula
What the color tells you
The time-derivative of gamma — how quickly the convexity you bought is scheduled to disappear. Day one of a weeklies straddle is a different instrument than day four, and color is the rate of that identity change.
Calculation: Color = ∂Γ/∂t — how gamma decays with the calendar. Enter your inputs and every substitution is shown below the result.
Reading the result
Large negative color means your gamma weapon is melting: the straddle that was going to pay for a move now needs the move immediately. Long-dated positions have mild color; near-expiry ATM ones have violent color.
Rules of thumb: Inside 10 days ATM, color can exceed a full gamma’s worth per day — the convexity half-life is measured in hours
Limitations and best practice
Color explodes as ATM options approach expiry — projections beyond a couple days are wildly linear-biased; re-compute rather than extrapolate, and never size a position on projected gamma.
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
Why is color worse for ATM options?
Does color hurt straddles?
How is color different from charm?
Is color priced anywhere?
Source & methodology
Second-order time Greeks; standard BS differentiation.
How Color works — and what your result really means
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. There are plenty of pages about Color; almost none of them show the working. This one does: the formula, every input, a fully computed example, and a sensitivity analysis calculated live from this engine’s own defaults.
There is a habit that separates people who get useful answers from Options & Derivatives numbers: they decide what question the figure answers before they compute it. Color answers “Color per day (×10,000)?” — and nothing else, which is precisely why the result is trustworthy.
It helps to separate the mechanics from the interpretation. The mechanics are fixed: Color = ∂Γ/∂t — how gamma decays with the calendar. Anyone, anywhere, entering the same inputs will get the same -0.006 /Γ/day. The interpretation is where experience counts: whether -0.006 /Γ/day is good, normal or alarming depends on comparisons covered below, and that is the part most articles about Color never explain.
Every figure in the prose is generated by the engine rather than written beside it — the worked example resolves to color per day (×10,000) = -0.006 /Γ/day on the default inputs, and the sensitivity section ranks the inputs that move the result — Underlying price first, at ≈373.5 % of the headline for a ten-percent error either way in that input. Read the sections in order and you will be able to reproduce every figure by hand.
How Color is computed, line by line
Here is the complete model this tool runs — Color = ∂Γ/∂t — how gamma decays with the calendar — with each input explained below. If a competitor’s page gives you a different answer from the same inputs, this is the text that settles which of you is right.
Underlying price ($) (example value 185) is a measured number in the unit named by the label; the formula does not convert for you. Keep every money input in the same currency; mixing systems quietly corrupts the comparison.
Strike ($) (example value 100) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. If you are unsure what belongs in this field, look at the printed steps: the substitution shows exactly how the engine uses it.
Time to expiry (years) (example value 1) is a quantity rather than a category — precision here is cheap and worth having. Use the value as of today, not as of the last time you looked — time fields drift silently.
Risk-free rate (%) (example value 4) is a measured number in the unit named by the label; the formula does not convert for you. Rates are the most mis-transcribed input on any page like this; copy it from the document rather than retyping from memory.
Implied volatility (%) (example value 26) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Rates are the most mis-transcribed input on any page like this; copy it from the document rather than retyping from memory.
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 Color 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 computed color per day (×10,000) comes out at -0.006 /Γ/day, which the interpretation band labels “Gamma re-sits -0.00000/day from the clock alone — over a week your convexity changes by -19.5% of itself”.
- Color = Γ·(d1·∂d1/∂T + 1/(2T))/365 = -0.000001
- For ATM options color is strongly negative near expiry — convexity evaporates fast
- 7-day projection: 0.0000 → 0.0000
Γ one week from now — 0.000. This is the number experienced users quote when the headline alone would mislead.
Γ now — 0.000. This is the number experienced users quote when the headline alone would mislead.
Weekly gamma drift % — -19.5%. If your inputs change, this is usually the first companion figure to move.
Color/Γ (relative decay) — -0.028 /day. This is the number experienced users quote when the headline alone would mislead.
Keep this worked example open while you enter your own figures: matching the shape of the substitution is the fastest way to spot a unit or convention mistake.
Scenario table: Color at ±10 % and ±20 % of the key input
Read this table as the practical error bar on the headline figure. It answers the question people actually have after seeing a single number: how wrong could this be if the main input is off by ten or twenty percent?
| Underlying price setting | Color per day (×10,000) |
|---|---|
| 80 % of the example value | -0.091 /Γ/day |
| 90 % of the example value | -0.028 /Γ/day |
| example inputs | -0.006 /Γ/day |
| 110 % of the example value | -0.001 /Γ/day |
| 120 % of the example value | -0.000 /Γ/day |
Across 5 settings of Underlying price, the result spans -0.091 /Γ/day to -0.000 /Γ/day. 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 Color 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 color per day (×10,000). For Color the ranking is measured rather than guessed, and it belongs to these defaults: shift the starting point and the order can shift with it.
- Nudge Underlying price by ±10 % and Color lands between -0.028 /Γ/day and -0.001 /Γ/day (sensitivity ≈373.5 %)
- Strike: ten percent up gives -0.022 /Γ/day, ten percent down gives -0.001 /Γ/day — ≈278.2 % of the color per day (×10,000) either way
- Implied volatility +10 % → Color = -0.012 /Γ/day · −10 % → -0.002 /Γ/day (the color per day (×10,000) shifts ≈108.0 %)
- Time to expiry +10 % → Color = -0.008 /Γ/day · −10 % → -0.004 /Γ/day (the color per day (×10,000) shifts ≈29.4 %)
- Risk-free rate: ten percent up gives -0.006 /Γ/day, ten percent down gives -0.006 /Γ/day — ≈4.3 % of the color per day (×10,000) either way
Underlying price is the dominant lever here: ten percent either way moves the result by about 373.5 %, from -0.028 /Γ/day to -0.001 /Γ/day. Measure that input from a document rather than from memory, and treat Strike as the second priority (≈278.2 % per ten percent). The rest of the inputs earn only a rounding-error of attention, and that asymmetry is the practical payoff of measuring rather than asserting.
What a Color of -0.006 /Γ/day means in practice
Nobody acts on a bare figure — they act on a figure with a comparison attached. The default case lands in the “Gamma re-sits -0.00000/day from the clock alone — over a week your convexity changes by -19.5% of itself” band, and bands are deliberately wide because real situations overlap. Before treating the band as fact, note its width: ten percent either way on Underlying price already spans -0.028 /Γ/day to -0.001 /Γ/day. The practical reading rules: read the band as a starting hypothesis, then test it: change the two dominant inputs by ten percent and see whether the verdict survives. Verdicts that survive stress are the ones worth acting on.
In Investing & Markets, Color is one instrument in an orchestra: on its own it is a number, next to Γ one week from now and Γ now it becomes a diagnosis. The tools linked above exist so the headline never has to carry that weight alone.
The errors that quietly break a Color figure
Color explodes as ATM options approach expiry — projections beyond a couple days are wildly linear-biased; re-compute rather than extrapolate, and never size a position on projected gamma. 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 Color begins the moment your own figures replace them.
Attention is also misallocated between fields. Having measured this engine, we can say where it belongs: Underlying price first, everything else second.
Another is comparing across contexts: a Color computed with one set of conventions should never be lined up against a figure computed with another. Check the inputs behind both before ranking them.
Color verification checklist
- Verify each input against its original source document, not memory.
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- Put Underlying price under a magnifier; the sensitivity table above is the reason why.
- Compare the result with one independent method or published benchmark.
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Run the ±10 % stress on the top two levers and check that your conclusion survives both.
Step by step: getting a trustworthy Color out of this tool
The tool does the arithmetic; the routine below is what makes the arithmetic trustworthy. Five steps, a minute total — and afterwards you will know not just what the number is, but which assumption produced it.
Step 1 — start from evidence. The inputs behind Color are underlying price ($), strike ($), time to expiry (years), risk-free rate (%), implied volatility (%), option type. Write them down with their source next to each one; if you cannot name where a figure came from, that is the input most likely to be wrong. The fastest sanity test is to guess the answer first and see how far the calculation disagrees.
Step 2 — compute the version you would not be embarrassed by. If a stranger audited your inputs, which set would you hand over? Enter that set, read the result, and treat everything else as upside. When two sources disagree, it is almost never the arithmetic that differs.
Step 3 — isolate your variables. Change one field, observe, revert. The live sensitivity list does the ranking for the default inputs; verify it against your own, because dominance shifts when the starting point shifts. Half of a good calculation is knowing which input you would hate to be wrong about.
Step 4 — run the scenario trio. Expected, pessimistic, optimistic. The gap between pessimistic and expected is the number to plan against; the optimistic result is useful only as a ceiling. One decimal place more than your data supports is one decimal place of fiction.
Step 5 — write the one-line memo. “Color per day (×10,000) = -0.006 /Γ/day on this date, from these inputs.” That line is the entire deliverable; everything else on this page is how you earned the right to write it. The fastest sanity test is to guess the answer first and see how far the calculation disagrees.
The real-world conversations Color settles
Numbers earn their keep in conversations, and Color is no exception. In Investing & Markets discussions around Options & Derivatives, this figure decides whether an option stays on the table: it converts an opinionated debate into an arithmetic one, and arithmetic is the only referee both sides accept. Rounding early is the quietest way to introduce a permanent error.
Professionals in Options & Derivatives use this style of calculation as a screening filter before spending real money or effort: a quick Color check eliminates weak options in minutes, and the survivors earn the deeper, slower analysis. The input you reach for first is usually the one you measured longest ago.
There is a personal-administration use people overlook: periodic self-checking. Color 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. Half of a good calculation is knowing which input you would hate to be wrong about.
The questions that come up most about Color
What affects Color the most?
The short answer: Underlying price. The longer answer is the sensitivity table on this page, where every numeric input was probed by ten percent and the color per day (×10,000) recalculated — Underlying price moved it furthest, by roughly 373.5 % (-0.028 /Γ/day to -0.001 /Γ/day).
Which matters more: strike or underlying price?
For Color, Underlying price wins the head-to-head (≈373.5 % against ≈278.2 % per ten-percent change). Knowing which input dominates is the difference between careful work and merely slow work.
What is a typical Color?
On the worked example above Color comes out at -0.006 /Γ/day. 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 Color by hand?
Three steps: write the formula (Color = ∂Γ/∂t — how gamma decays with the calendar), 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 Color than any number of calculator runs.
What happens to Color if underlying price changes by 10 %?
On these inputs a ±10 % change in underlying price takes Color to -0.001 /Γ/day against the -0.006 /Γ/day example — around 373.5 % of the headline. The same test on every other field is in the sensitivity section.
Is the Color result of -0.006 /Γ/day good or bad?
Neither, on its own — the label “Gamma re-sits -0.00000/day from the clock alone — over a week your convexity changes by -19.5% of itself” 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 ≈373.5 %.
Can I predict future returns with Color?
No tool predicts; Color computes implications. Use it to ask "if these inputs hold, what follows" — then stress the assumptions.
Does Color 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 Color and should be layered on top before decisions.
Why is color worse for ATM options?
Because their gamma is the highest and depends most on the remaining time window — as the window closes, the most convexity has to go somewhere.
Does color hurt straddles?
It is the mechanism: straddle gamma (the earning asset) decays via color — selling into rising color is how event traders exit.
Do I need an account to use this Color calculator?
No, and no data leaves the tab. The engine runs in the page itself, which is why the worked example, the bands and the sensitivity ranking all respond instantly to your keystrokes.
The vocabulary of Color
- Γ one week from now
- 0.000 for the Color worked case; it sits next to the main result because it carries context the headline leaves out.
- Γ now
- 0.000 in the default Color calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Weekly gamma drift %
- -19.5% in the default Color calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Color per day (×10,000)
- The primary output of this tool: -0.006 /Γ/day for the default inputs, computed exactly from Color = ∂Γ/∂t — how gamma decays with the calendar.
- Worked example
- Every substitution in order, from the example inputs to -0.006 /Γ/day — the audit trail for the headline figure.
- Verdict band
- A named zone on the range of plausible results; the example inputs land in “Gamma re-sits -0.00000/day from the clock alone — over a week your convexity changes by -19.5% of itself”, and your inputs may not.
- Sensitivity (±10 %)
- How far the Color moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Where the Color model comes from
The model is published arithmetic implemented exactly as written: Color = ∂Γ/∂t — how gamma decays with the calendar. Source of record: Second-order time Greeks; standard BS differentiation. Specialist software layers extra coefficients on top of the same algebra; none are hidden here, and that transparency is what makes a disagreement traceable to a specific input instead of a black box.
Nothing here replaces a qualified professional, and nothing here is approximate either — the arithmetic is exact, and the honesty is in the inputs you supply. 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.
Turning this Color into a decision
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
This page was written for people who need one trustworthy number before their next decision, and the promise is that nothing above required trust. Bookmark the tool, re-run it whenever an input moves by more than a few percent, and keep the date with the number.