Epsilon (Dividend Sensitivity) Calculator
The formula
What the epsilon tells you
The dividend Greek: how option value responds when a company declares, raises, or skips a payout. For calls the dividend is a certain outflow on ex-date; for puts it is the same flow in reverse.
Calculation: Epsilon = ∂V/∂(dividend) — re-price with dividend +10bp of spot; discrete PV-adjusted model. Enter your inputs and every substitution is shown below the result.
Reading the result
If the dividend-adjusted value is materially below the raw Black-Scholes value, the market is right about the payout and your earnings-week call is quietly paying the ex-date tax. Skips and specials flip the whole picture fast.
Rules of thumb: Ex-date call gap ≈ dividend × forward delta; 3+ payouts inside tenor = treat as a yield, not a single deduction
Limitations and best practice
The discrete-PV model used here underestimates sensitivity to surprise dividend cuts on stressed names — those need escrowed-dividend or stochastic-rate trees. Also mind the index vs single-stock convention: SPX handles dividends through the futures basis.
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
Do calls drop exactly by the dividend?
What is an “ex-date gap”?
Are puts better around dividends?
Why does epsilon matter for index options?
Source & methodology
Epsilon per Haug, Complete Guide to Option Pricing; discrete-PV adjustment.
Epsilon (Dividend Sensitivity): the number, the method and the caveats
You are here because you need a specific number, and you want to see how it was produced before you rely on it. Epsilon (Dividend Sensitivity) is the kind of number people argue about from memory. This page ends that argument with arithmetic you can watch happen: enter your figures, get Dividend sensitivity in real time, and see every substitution printed below.
The number itself is the easy part. What takes judgement is knowing which inputs are facts in your situation and which are guesses wearing a decimal point — a distinction this page makes explicit for every field above.
A calculation like this one is worth roughly as much as a careful sentence: it forces several vague considerations into one comparable quantity. Once Epsilon (Dividend Sensitivity) is on the table, the argument can stop being about impressions.
Every figure in the prose is generated by the engine rather than written beside it — the worked example resolves to dividend sensitivity = $-0.98 per declared div on the default inputs, and the sensitivity section ranks the inputs that move the result — Expected dividend before expiry first, at ≈10.0 % of the headline for a ten-percent error either way in that input. Read the sections in order and you will be able to reproduce every figure by hand.
Every input in Epsilon (Dividend Sensitivity), and what it does to the answer
The engine implements a single stated model: Epsilon = ∂V/∂(dividend) — re-price with dividend +10bp of spot; discrete PV-adjusted model. There is no hidden coefficient and no login-gated precision — the formula printed is the formula executed, which is also what makes the result citable.
Underlying price ($) (example value 150) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Use the figure exactly as the source document states it, not a rounded memory of it — an omitted line is the classic silent error.
Strike ($) (example value 105) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. The example value is there to demonstrate the mechanics, not to describe your situation — overwrite it.
Time to expiry (years) (example value 1) is a measured number in the unit named by the label; the formula does not convert for you. Be precise about the boundary (exact date, start of month); time inputs decide the exponent in most formulas.
Risk-free rate (%) (example value 5) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Check the convention first: if the source says “6.5 % per year”, type 6.5 and let the formula do the rest.
Implied volatility (%) (example value 26) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Check the convention first: if the source says “6.5 % per year”, type 6.5 and let the formula do the rest.
Option type (example value Call) is a choice rather than a quantity — pick the option that matches your situation, because the calculation path branches here. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
Expected dividend before expiry ($) (example value 1) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.
Dividends paid before expiry (example value 1) is a plain measured quantity — the unit shown in the label is the unit the formula expects. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
What each “Option type” choice actually does: Call → $-0.98 per declared div · Put → $0.02 per declared div These figures are computed from this engine, not estimated — switch the dropdown above and you will land on exactly these numbers.
The default Epsilon (Dividend Sensitivity) calculation, written out in full
Abstract formulas are hard to trust, so here is the complete substitution using the default inputs, written the way an examiner would want it. Starting figures: Underlying price ($), Strike ($), Time to expiry (years), Risk-free rate (%). Run to the end, the dividend sensitivity resolves to $-0.98 per declared div — A declared $1.00 dividend (×1) moves this premium -$0.98 — calls bleed on ex-date; puts pocket it on the bands this tool uses.
- PV of declared dividends = $1.00 → effective spot $149
- Re-price: dividend-adjusted premium $46.61 vs flat-spot $47.59
- Epsilon (per 0.1% of spot in dividend) = -0.1475
Value ignoring dividends — $47.59 /share. This is the number experienced users quote when the headline alone would mislead.
PV-adjusted value — $46.61 /share. If your inputs change, this is usually the first companion figure to move.
Elasticity to dividend cut (0.1% spot) — -0.147. This is the number experienced users quote when the headline alone would mislead.
Ex-date gap risk (1.5× div) — $1.48 /share. If your inputs change, this is usually the first companion figure to move.
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: Epsilon (Dividend Sensitivity) at ±10 % and ±20 % of the key input
The honest version of any estimate is a corridor, and this one is cheap to produce: Epsilon (Dividend Sensitivity) was recomputed at 5 points along the dominant input, with every other field left untouched.
| Expected dividend before expiry setting | Dividend sensitivity |
|---|---|
| 80 % of the example value | $-0.79 per declared div |
| 90 % of the example value | $-0.89 per declared div |
| example inputs | $-0.98 per declared div |
| 110 % of the example value | $-1.08 per declared div |
| 120 % of the example value | $-1.18 per declared div |
Across 5 settings of Expected dividend before expiry, the result spans $-1.18 per declared div to $-0.79 per declared div. 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 Expected dividend before expiry alone; the substitution steps will follow your figures exactly.
Sensitivity: which inputs change Epsilon (Dividend Sensitivity) the most
Generic advice says “it depends on your inputs”; this section says exactly how much. Each field was perturbed by ±10 % in isolation and the dividend sensitivity recomputed, so the ranking below is measured rather than asserted. It is the fastest honest answer to “what matters most in Epsilon (Dividend Sensitivity)?” — and it is specific to these defaults, because sensitivity moves with the starting point.
- Expected dividend before expiry +10 % → Epsilon (Dividend Sensitivity) = $-1.08 per declared div · −10 % → $-0.89 per declared div (the dividend sensitivity shifts ≈10.0 %)
- Dividends paid before expiry +10 % → Epsilon (Dividend Sensitivity) = $-1.08 per declared div · −10 % → $-0.89 per declared div (the dividend sensitivity shifts ≈10.0 %)
- Underlying price +10 % → Epsilon (Dividend Sensitivity) = $-1.00 per declared div · −10 % → $-0.94 per declared div (the dividend sensitivity shifts ≈4.3 %)
- Strike: ten percent up gives $-0.95 per declared div, ten percent down gives $-1.00 per declared div — ≈3.7 % of the dividend sensitivity either way
- Implied volatility +10 % → Epsilon (Dividend Sensitivity) = $-0.98 per declared div · −10 % → $-0.99 per declared div (the dividend sensitivity shifts ≈0.9 %)
- Time to expiry +10 % → Epsilon (Dividend Sensitivity) = $-0.98 per declared div · −10 % → $-0.99 per declared div (the dividend sensitivity shifts ≈0.4 %)
Expected dividend before expiry is the dominant lever here: ten percent either way moves the result by about 10.0 %, from $-1.08 per declared div to $-0.89 per declared div. That is where a careless figure does the most damage, so check it against a source, and Dividends paid before expiry is effectively tied with it (≈10.0 % for the same nudge), so verify the pair together. The remaining fields can sit at safe defaults without materially changing the answer — knowing which is which is what separates a careful calculation from an anxious one.
Reading the result: bands, zones and thresholds
Nobody acts on a bare figure — they act on a figure with a comparison attached. On the example inputs the band reads “A declared $1.00 dividend (×1) moves this premium -$0.98 — calls bleed on ex-date; puts pocket it”; your own figures place you on a different rung of the same ladder. Before treating the band as fact, note its width: ten percent either way on Expected dividend before expiry already spans $-1.08 per declared div to $-0.89 per declared div. The practical reading rules: compare against your own history before comparing against other people; treat band boundaries as zones, not walls — one point on the wrong side of a threshold rarely changes a real outcome; and when a companion output contradicts the headline, believe the pair.
Placing this figure in context: calculators of this kind differ less in arithmetic than in what they choose to ignore. This one keeps Underlying price ($) explicit so that the omissions are visible rather than hidden in a preset.
The errors that quietly break an Epsilon (Dividend Sensitivity) figure
The discrete-PV model used here underestimates sensitivity to surprise dividend cuts on stressed names — those need escrowed-dividend or stochastic-rate trees. Also mind the index vs single-stock convention: SPX handles dividends through the futures basis. 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.
Confusing a large number with an important one. Epsilon (Dividend Sensitivity) can be dominated by one input whose absolute value looks unimpressive, which is why this page ranks influence separately from magnitude.
Attention is also misallocated between fields. Having measured this engine, we can say where it belongs: Expected dividend before expiry first, everything else second.
The subtlest error is answering the wrong question precisely. Confirm that dividend sensitivity is actually the quantity your decision needs — the arithmetic is flawless either way, which is what makes the mistake invisible.
Before you trust your Epsilon (Dividend Sensitivity): a short checklist
- Re-run the calculation with a ±10 % stress on the two most sensitive inputs.
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Re-verify Expected dividend before expiry against a source document — ten percent of error there moves the headline by ≈10.0 %.
- Verify each input against its original source document, not memory.
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Repeat the ±10 % test on the inputs that matter and see whether the decision — not just the number — still holds.
How to use the Epsilon (Dividend Sensitivity) tool properly
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 Epsilon (Dividend Sensitivity) takes a minute to learn and applies to every input above.
Step 1 — collect, then type. Everything this tool asks for is listed above (underlying price ($), strike ($), time to expiry (years), risk-free rate (%), implied volatility (%), option type and the remaining fields listed above). Pull each figure from something you can point at — paperwork, a dashboard, a label — before touching a field. Guesswork at the input stage cannot be repaired at the interpretation stage. Suspiciously tidy answers deserve the same scrutiny as untidy ones.
Step 2 — start from the case you can defend. Enter pessimistic-but-honest figures first; the optimistic run is a ceiling, not a plan. A conclusion that holds on conservative inputs holds everywhere. When in doubt, prefer the boring input: the interesting one is usually the one you misread.
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. Numbers are cheap to produce and expensive to retract; the extra minute is the cheapest insurance available.
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. Estimates improve most when the worst case is written down in ink.
Step 5 — write the one-line memo. “Dividend sensitivity = $-0.98 per declared div 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. A result worth acting on survives having its two shakiest inputs halved.
The real-world conversations Epsilon (Dividend Sensitivity) settles
Most Options & Derivatives disagreements are arithmetic disagreements in disguise. When Dividend sensitivity of $-0.98 per declared div sits on the table with its working shown, the conversation stops being about who sounds more confident and starts being about which input is wrong. A calculation you cannot explain to somebody else is a calculation you cannot defend.
Used properly this is a five-minute filter that saves weeks. Compute Epsilon (Dividend Sensitivity), reject what fails, and only then bring in the expensive analysis for the survivors. Half of a good calculation is knowing which input you would hate to be wrong about.
Nothing here is stored or transmitted, so the habit of checking is free: open the page, re-enter current figures, compare with the number you saved last time. If the answer changes your behaviour, it deserves a second run with different assumptions.
The questions that come up most about Epsilon (Dividend Sensitivity)
What affects Epsilon (Dividend Sensitivity) the most?
The short answer: Expected dividend before expiry. The longer answer is the sensitivity table on this page, where every numeric input was probed by ten percent and the dividend sensitivity recalculated — Expected dividend before expiry moved it furthest, by roughly 10.0 % ($-1.08 per declared div to $-0.89 per declared div).
Do dividends paid before expiry and expected dividend before expiry matter equally?
Epsilon (Dividend Sensitivity) here is co-driven: Expected dividend before expiry and Dividends paid before expiry produced ≈10.0 % and ≈10.0 % responses, which is a tie for practical purposes. Everything below those two is a rounding error by comparison.
How much does the “Option type” choice change the answer?
The spread is not cosmetic: this choice alone takes Epsilon (Dividend Sensitivity) from $-0.98 per declared div to $0.02 per declared div with every other input frozen, which is more influence than most of the numeric fields on this page can claim.
What is a typical Epsilon (Dividend Sensitivity)?
On the worked example above Epsilon (Dividend Sensitivity) comes out at $-0.98 per declared div. 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 Epsilon (Dividend Sensitivity) by hand?
Epsilon = ∂V/∂(dividend) — re-price with dividend +10bp of spot; discrete PV-adjusted model is the entire method. Work the inputs in that order — PV of declared dividends = $1.00 → effective spot $149 — and you will reach $-0.98 per declared div on the default figures, the same number this tool prints.
What happens to Epsilon (Dividend Sensitivity) if expected dividend before expiry changes by 10 %?
The engine was re-run with that field moved by ten percent while everything else stayed fixed: the dividend sensitivity goes across $-1.08 per declared div to $-0.89 per declared div, a swing of roughly 10.0 % around the $-0.98 per declared div baseline. That ratio is the practical definition of how much this input matters.
Is the Epsilon (Dividend Sensitivity) result of $-0.98 per declared div good or bad?
The tool answers “what”, not “whether”: $-0.98 per declared div carries the verdict “A declared $1.00 dividend (×1) moves this premium -$0.98 — calls bleed on ex-date; puts pocket it” for the default case, which is a starting interpretation rather than a verdict on your situation. Re-run with your own figures and compare the bands.
Does Epsilon (Dividend Sensitivity) account for fees and taxes?
Only what you put in. Fees belong inside Underlying price ($) where they shrink returns before compounding touches them; taxes are outside the scope of a pre-tax Epsilon (Dividend Sensitivity) and should be layered on top before decisions.
Can I predict future returns with Epsilon (Dividend Sensitivity)?
No tool predicts; Epsilon (Dividend Sensitivity) computes implications. Use it to ask "if these inputs hold, what follows" — then stress the assumptions.
Do calls drop exactly by the dividend?
By roughly delta × the dividend — deep ITM calls track almost the full amount; OTM calls barely feel it.
What is an “ex-date gap”?
The scheduled price cut the stock takes on ex-dividend day; it is expected but still mechanically moves option values.
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.
Glossary for Epsilon (Dividend Sensitivity)
- Value ignoring dividends
- $47.59 /share in the default Epsilon (Dividend Sensitivity) calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- PV-adjusted value
- $46.61 /share for the Epsilon (Dividend Sensitivity) worked case; it sits next to the main result because it carries context the headline leaves out.
- Elasticity to dividend cut (0.1% spot)
- -0.147 for the Epsilon (Dividend Sensitivity) worked case; it sits next to the main result because it carries context the headline leaves out.
- Dividend sensitivity
- The primary output of this tool: $-0.98 per declared div for the default inputs, computed exactly from Epsilon = ∂V/∂(dividend) — re-price with dividend +10bp of spot; discrete PV-adjusted model.
- Worked example
- Every substitution in order, from the example inputs to $-0.98 per declared div — the audit trail for the headline figure.
- Verdict band
- A named zone on the range of plausible results; the example inputs land in “A declared $1.00 dividend (×1) moves this premium -$0.98 — calls bleed on ex-date; puts pocket it”, and your inputs may not.
- Sensitivity (±10 %)
- How far the Epsilon (Dividend Sensitivity) 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 Epsilon (Dividend Sensitivity) model comes from
The model is published arithmetic implemented exactly as written: Epsilon = ∂V/∂(dividend) — re-price with dividend +10bp of spot; discrete PV-adjusted model. Source of record: Epsilon per Haug, Complete Guide to Option Pricing; discrete-PV adjustment. 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. What that buys you is reproducibility — two people, two browsers, the same arithmetic, and a printed trail from inputs to result that either of them can audit.
After the number: what to do with it
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
The audience here is people who need one trustworthy number before their next decision. Everything you need to defend the result — formula, substitution, sensitivity, source — is printed above, so the only remaining variable is the honesty of your inputs.