Charm Calculator

The formula

What the charm (delta bleed) tells you

How the option’s delta changes purely from the passage of time — the “delta decay” that quietly re-hedges a position every day even when markets are flat. Second-order, but second-order costs money.

Calculation: Charm = ∂Δ/∂t = −φ(d1)·∂d1/∂T per calendar day (closed form). Enter your inputs and every substitution is shown below the result.

See also: Vanna Calculator

Reading the result

For a delta-hedged book, charm is the daily rebalancing P&L you did not trade for: OTM calls lose delta (charm drains the position), while ITM calls gain it as they harden toward the binary.

Rules of thumb: Meaningful charm starts inside 10% of life; on 0DTE it dominates intraday delta behavior

Limitations and best practice

Charm is conflated with two other “delta over time” definitions (∂Δ/∂t vs the funding-adjusted decay); always ask which convention the desk uses before quoting numbers. It is never a standalone signal — pair it with gamma on flat days.

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

Source & methodology

Standard second-order Greeks (Jaubert et al. taxonomy).

Charm: 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. Searchers land on a Charm 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.

The useful way to hold Charm is as a ratio with a story attached: Charm = ∂Δ/∂t = −φ(d1)·∂d1/∂T per calendar day (closed form) says how the parts combine, and the 0.015 /Δ/day figure above is simply that sentence written in numbers. Everything that follows unpacks one clause of the sentence at a time.

What makes Charm worth calculating is not precision but position: it tells you which side of a threshold you are on, and by how much. A rough figure that settles the direction beats an elaborate one that never commits.

Every figure in the prose is generated by the engine rather than written beside it — the worked example resolves to charm per day (×1,000) = 0.015 /Δ/day on the default inputs, and the sensitivity section ranks the inputs that move the result — Underlying price first, at ≈453.6 % 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 Charm, and what it does to the answer

Here is the complete model this tool runs — Charm = ∂Δ/∂t = −φ(d1)·∂d1/∂T per calendar day (closed form) — 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 175) 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 109) is a quantity rather than a category — precision here is cheap and worth having. 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 numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Use the value as of today, not as of the last time you looked — time fields drift silently.

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. 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 22) 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 categorical input — the option you choose decides which numbers the formula uses. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.

See also: Volga Calculator

The default Charm 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 (%). The computed charm per day (×1,000) comes out at 0.015 /Δ/day, which the interpretation band labels “Delta drifts 0.00001/day with the clock alone — over a week, 0.0001 of unhedged delta creep; rebalance or eat the drift”.

1. Charm = −φ(d1)·∂d1/∂T ÷ 365 = 0.000015 delta per day
2. Positive charm: delta grows without any spot move (calls) — the hedge size itself moves on time
3. At-the-money charm is largest; expiry-week delta walks toward 0/1 daily

Weekly delta drift (×1,000) — 0.102. Read next to the headline, this is the figure that shows the shape of the trade-off.

Drift over 1% of life (×1,000) — 0.027. This is the number experienced users quote when the headline alone would mislead.

Current delta — 0.999. Compare it against the main result of 0.015 /Δ/day before drawing conclusions.

Delta-days to re-hedge 0.05 — 3,428 days. Compare it against the main result of 0.015 /Δ/day before drawing conclusions.

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.

The Charm corridor: your result across a realistic band

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?

Across 5 settings of Underlying price, the result spans 0.000 /Δ/day to 0.279 /Δ/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.

The levers behind Charm, ranked by effect

This list was computed for this specific engine just now: each numeric input was nudged ±10 % while every other field held its example value, and the charm per day (×1,000) was recalculated from scratch. For Charm 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 Charm lands between 0.002 /Δ/day and 0.081 /Δ/day (sensitivity ≈453.6 %)
• Nudge Strike by ±10 % and Charm lands between 0.002 /Δ/day and 0.070 /Δ/day (sensitivity ≈381.3 %)
• Implied volatility +10 % → Charm = 0.032 /Δ/day · −10 % → 0.005 /Δ/day (the charm per day (×1,000) shifts ≈118.9 %)
• Time to expiry +10 % → Charm = 0.019 /Δ/day · −10 % → 0.010 /Δ/day (the charm per day (×1,000) shifts ≈30.6 %)
• Risk-free rate: ten percent up gives 0.014 /Δ/day, ten percent down gives 0.015 /Δ/day — ≈5.6 % of the charm per day (×1,000) either way

Underlying price is the dominant lever here: ten percent either way moves the result by about 453.6 %, from 0.002 /Δ/day to 0.081 /Δ/day. Measure that input from a document rather than from memory, and treat Strike as the second priority (≈381.3 % per ten percent). Everything below that can stay approximate, which is a licence to stop chasing data that would not change the decision.

Reading the result: bands, zones and thresholds

The value above only becomes useful the moment you know what it is being measured against. On the example inputs the band reads “Delta drifts 0.00001/day with the clock alone — over a week, 0.0001 of unhedged delta creep; rebalance or eat the drift”; your own figures place you on a different rung of the same ladder. The sensitivity list shows how far a modest input error moves you along that ladder: for Underlying price, ±10 % covers 0.002 /Δ/day to 0.081 /Δ/day. 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.

Set Charm beside its neighbours and it usually plays a specific role: this figure establishes the size of something, and the neighbouring tools establish whether that size is acceptable. Skipping the first step makes the second one arbitrary.

See also: Speed Calculator

The errors that quietly break a Charm figure

Charm is conflated with two other “delta over time” definitions (∂Δ/∂t vs the funding-adjusted decay); always ask which convention the desk uses before quoting numbers. It is never a standalone signal — pair it with gamma on flat days. 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.

Chasing precision in Strike ($) while Underlying price ($) is still a guess. The sensitivity ranking above shows exactly where the accuracy budget should go.

This model has its own particular trap: Underlying price carries ≈453.6 % of the response per ten percent of error, so effort spent elsewhere is largely decorative.

The subtlest error is answering the wrong question precisely. Confirm that charm per day (×1,000) is actually the quantity your decision needs — the arithmetic is flawless either way, which is what makes the mistake invisible.

Before you trust your Charm: a short checklist

• Recompute once with the dominant input deliberately set low, and see whether the decision changes.
• Confirm the example values are plausible for your own situation before replacing them.
• Check Underlying price before anything else: it is the measured dominant input, ≈453.6 % of Charm per ten percent.
• Verify each input against its original source document, not memory.
• Check that every field the formula needs actually arrived from a document, not from recollection.
• Repeat the ±10 % test on the inputs that matter and see whether the decision — not just the number — still holds.

Step by step: getting a trustworthy Charm out of this tool

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 Charm 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). 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. If the answer changes your behaviour, it deserves a second run with different assumptions.

Step 2 — enter the conservative case first. Resist the flattering scenario. Type the inputs you would defend in front of a sceptical reader, read the Charm per day (×1,000) (0.015 /Δ/day for the example values), and note the verdict band. Note the assumption you are least sure about; that is where the real risk lives.

Step 3 — play with the inputs on purpose. Ten percent up, ten percent down, one field at a time. Within a few minutes you will know this calculation better than most people who quote its results. If a result feels obviously right, that is the moment to check the inputs hardest.

Step 4 — compute a corridor, not a point. Three runs — worst, likely, best — turn Charm from a snapshot into a range. Plan against the pessimistic end and treat the optimistic end as the upside story. When in doubt, prefer the boring input: the interesting one is usually the one you misread.

Step 5 — save the story with the figure. A number without its inputs and its date is unusable within a quarter. Record 0.015 /Δ/day, the assumptions behind it, and today’s date; your future self will be auditing a stranger’s arithmetic. Precision is a promise you make about your data; make sure your inputs can keep it.

See also: Color Calculator

From calculation to decision: where Charm earns its keep

Investing & Markets arguments end at arithmetic or they do not end. Charm is the arithmetic: 0.015 /Δ/day on the example inputs, reproducible by anyone who types the same numbers. If the answer changes your behaviour, it deserves a second run with different assumptions.

Professionals in Options & Derivatives use this style of calculation as a screening filter before spending real money or effort: a quick Charm check eliminates weak options in minutes, and the survivors earn the deeper, slower analysis. Repeating a calculation with the same numbers proves only that the arithmetic is reliable — which is worth knowing.

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. Write the figure down before moving on; memory flatters whichever number you saw last.

Quick answers: what searchers ask about Charm

What affects Charm the most?

Measured on this engine, Underlying price is the dominant lever: moving it ±10 % shifts the charm per day (×1,000) across 0.002 /Δ/day to 0.081 /Δ/day — about 453.6 % of the headline, with Strike next at ≈381.3 %. The ranked list in the sensitivity section is computed live, not asserted from a template.

Which matters more: strike or underlying price?

For Charm, Underlying price wins the head-to-head (≈453.6 % against ≈381.3 % per ten-percent change). Knowing which input dominates is the difference between careful work and merely slow work.

What is a typical Charm?

With the example inputs on this page the result is 0.015 /Δ/day, labelled “Delta drifts 0.00001/day with the clock alone — over a week, 0.0001 of unhedged delta creep; rebalance or eat the drift”. “Typical” varies with situation, which is why every result here ships with its verdict band and its sensitivity list: they turn one figure into a range you can locate yourself inside.

How do I calculate Charm by hand?

Charm = ∂Δ/∂t = −φ(d1)·∂d1/∂T per calendar day (closed form) is the entire method. Work the inputs in that order — Charm = −φ(d1)·∂d1/∂T ÷ 365 = 0.000015 delta per day — and you will reach 0.015 /Δ/day on the default figures, the same number this tool prints.

What happens to Charm if underlying price changes by 10 %?

The engine was re-run with that field moved by ten percent while everything else stayed fixed: the charm per day (×1,000) goes across 0.002 /Δ/day to 0.081 /Δ/day, a swing of roughly 453.6 % around the 0.015 /Δ/day baseline. That ratio is the practical definition of how much this input matters.

Is the Charm result of 0.015 /Δ/day good or bad?

Good and bad are comparisons, so the honest test is three questions: where does your own Charm sit against the 0.015 /Δ/day reference above, how far would a plausible input error move it (≈453.6 % per ten percent on Underlying price), and what does the alternative option compute to?

What affects Charm the most?

Sensitivity depends on where you start, but the inputs Underlying price ($) and Strike ($) typically move Charm further than the rest because they enter the formula multiplicatively. If you can only measure two things well, measure those and hold the others at conservative defaults.

Is Charm accurate?

The arithmetic is exact: Charm = ∂Δ/∂t = −φ(d1)·∂d1/∂T per calendar day (closed form) is evaluated with full floating-point precision and every substitution is printed in the worked example. What limits accuracy is input quality and the model’s assumptions, so treat the 0.015 /Δ/day result as the correct answer to the question you typed — and check the assumptions section before acting on it.

Is charm the same as theta?

No — theta is value decay; charm is exposure drift. Both come from the clock, they measure different books.

Why does an OTM call’s delta fall in flat markets?

Charm: as expiry nears with no move, the odds of reaching the strike shrink; the position deflates without trades.

Do I need an account to use this Charm 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.

Glossary for Charm

Weekly delta drift (×1,000)

0.102 for the Charm worked case; it sits next to the main result because it carries context the headline leaves out.

Drift over 1% of life (×1,000)

0.027 for the Charm worked case; it sits next to the main result because it carries context the headline leaves out.

Current delta

0.999 on the example inputs — a companion figure printed beside the headline of Charm so that no result is read in isolation.

Charm per day (×1,000)

The primary output of this tool: 0.015 /Δ/day for the default inputs, computed exactly from Charm = ∂Δ/∂t = −φ(d1)·∂d1/∂T per calendar day (closed form).

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 plain-language label — here “Delta drifts 0.00001/day with the clock alone — over a week, 0.0001 of unhedged delta creep; rebalance or eat the drift” — mapping the computed figure onto experience-based ranges for Investing & Markets.

Sensitivity (±10 %)

How far the Charm moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.

Methodology, sources and limits

The model is published arithmetic implemented exactly as written: Charm = ∂Δ/∂t = −φ(d1)·∂d1/∂T per calendar day (closed form). Source of record: Standard second-order Greeks (Jaubert et al. taxonomy). 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.

This page is an estimation aid, not professional advice. The design rule is simple: two people entering identical figures must get identical answers. 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.

Turning this Charm into a decision

Save the number together with its inputs and today’s date; a Charm figure without context is unusable the moment an input changes.

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.

See also: Zomma Calculator