Bond Valuation, Clean/Dirty Price & Convexity Curve Calculator
The formula
The Inverse Relationship Between Bond Prices and Interest Rates
When interest rates in the economy rise, newly issued bonds offer higher coupon payments, making existing bonds with lower coupons less valuable. Consequently, existing bond prices must fall until their yield equals the new market rate. The longer a bond’s maturity, the more volatile its price response (measured by Modified Duration).
Frequently asked questions
What is the difference between Clean and Dirty bond prices?
Source & methodology
Fabozzi FJ. The Handbook of Fixed Income Securities (9th ed., McGraw-Hill); SIFMA Bond Pricing Conventions.
Bond Valuation, Clean/Dirty Price & Convexity Curve: the number, the method and the caveats
Budgets fail on the numbers nobody wrote down — this tool forces every one of them into the open. There are plenty of pages about Bond Valuation, Clean/Dirty Price & Convexity Curve; 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.
Most confusion about Bond Valuation, Clean/Dirty Price & Convexity Curve 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.
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.
Every figure in the prose is generated by the engine rather than written beside it — the worked example resolves to clean bond price = $1,055.08 on the default inputs, and the sensitivity section ranks the inputs that move the result — Par / Face value of bond first, at ≈10.0 % of the headline for a ten-percent error either way in that input. Work down the page and by the end you could re-derive the result in a spreadsheet from memory.
The Bond Valuation, Clean/Dirty Price & Convexity Curve formula, explained
Here is the complete model this tool runs — Price = Σ [ C / (1+y)^t ] + [ Par / (1+y)^n ] | Dirty = Clean + Accrued Interest — with each input explained below. If a competitor’s page gives you a different answer from the same inputs, this is the text that settles which of you is right.
Par / Face value of bond ($) (example value $1,000.00) is a currency figure — enter the total exactly as your document states it, fees included. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.
Annual coupon interest rate (%) (example value 6) 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.
Market Yield to Maturity — YTM (%) (example value 5) 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.
Years to maturity (example value 10) is a quantity rather than a category — precision here is cheap and worth having. Be precise about the boundary (exact date, start of month); time inputs decide the exponent in most formulas.
Coupon payment frequency (example value Semiannual (2x per year — US Treasury & Corporate standard)) is a branching choice rather than a figure you measure; the per-option effects are computed below. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.
Days since last coupon payment (example value 45) is a measured number in the unit named by the label; the formula does not convert for you. Use the value as of today, not as of the last time you looked — time fields drift silently.
What each “Coupon payment frequency” choice actually does: Semiannual (2x per year — US Treasury & Corporate standard) → $1,055.08 · Annual (1x per year — Eurobond standard) → $1,054.58 · Quarterly → $1,055.34 — each value above is the model’s own output for that option, so the choice can be made on evidence rather than on what a category feels like it means.
A fully worked Bond Valuation, Clean/Dirty Price & Convexity Curve example
Abstract formulas are hard to trust, so here is the complete substitution using the default inputs, written the way an examiner would want it. Starting figures: Par / Face value of bond ($), Annual coupon interest rate (%), Market Yield to Maturity — YTM (%), Years to maturity. The endpoint of that chain is $1,055.08 of clean bond price, sitting in the “Trading at a Premium (YTM < Coupon) (105.51% of par).” band.
- Periodic Coupon = ($1000 × 5.5%) ÷ 2 = $27.50 per period
- Total Coupon Periods = 10 years × 2 = 20 periods
- PV of Coupons = $432.78 | PV of Principal ($1000) = $622.30
- Clean Price = PV(Coupons) + PV(Par) = $1,055.08
- Accrued Interest = (45 ÷ 182.5) × $27.50 = $6.78
- Dirty Invoice Price = Clean ($1,055.08) + Accrued ($6.78) = $1,061.86
Dirty (Invoice) Price — $1,061.86. Compare it against the main result of $1,055.08 before drawing conclusions.
Modified Duration — 7.71. Compare it against the main result of $1,055.08 before drawing conclusions.
Macaulay Duration — 7.89. Read next to the headline, this is the figure that shows the shape of the trade-off.
Annual Coupon Income — $55. If your inputs change, this is usually the first companion figure to move.
Current Yield — 5.21%. Compare it against the main result of $1,055.08 before drawing conclusions.
Re-running with your own figures is instant; re-running by hand once is the best way to know the tool is telling you the truth.
The Bond Valuation, Clean/Dirty Price & Convexity Curve corridor: your result across a realistic band
Single-point answers invite false confidence, so the same engine was run across a band around the input that matters most here. Each row is a full recalculation of Bond Valuation, Clean/Dirty Price & Convexity Curve, not an interpolation.
| Par / Face value of bond setting | Clean Bond Price |
|---|---|
| 80 % of the example value | $844.06 |
| 90 % of the example value | $949.57 |
| example inputs | $1,055.08 |
| 110 % of the example value | $1,160.59 |
| 120 % of the example value | $1,266.10 |
That spread — $844.06 at the low end, $1,266.10 at the high — is what a careful read of Bond Valuation, Clean/Dirty Price & Convexity Curve looks like: a band you can state out loud, with the reason for each edge. Reproduce it in the form above by editing Par / Face value of bond alone; the substitution steps will follow your figures exactly.
Sensitivity: which inputs change Bond Valuation, Clean/Dirty Price & Convexity Curve the most
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 clean bond price was recalculated from scratch. For Bond Valuation, Clean/Dirty Price & Convexity Curve the ranking is measured rather than guessed, and it belongs to these defaults: shift the starting point and the order can shift with it.
- Par / Face value of bond: ten percent up gives $1,160.59, ten percent down gives $949.57 — ≈10.0 % of the clean bond price either way
- Nudge Annual coupon interest rate by ±10 % and Bond Valuation, Clean/Dirty Price & Convexity Curve lands between $1,011.80 and $1,098.36 (sensitivity ≈4.1 %)
- Nudge Market Yield to Maturity — YTM by ±10 % and Bond Valuation, Clean/Dirty Price & Convexity Curve lands between $1,016.92 and $1,095.00 (sensitivity ≈3.8 %)
- Years to maturity +10 % → Bond Valuation, Clean/Dirty Price & Convexity Curve = $1,059.29 · −10 % → $1,050.67 (the clean bond price shifts ≈0.4 %)
Par / Face value of bond is the dominant lever here: ten percent either way moves the result by about 10.0 %, from $949.57 to $1,160.59. Measure that input from a document rather than from memory, and treat Annual coupon interest rate as the second priority (≈4.1 % per ten percent). Everything below that can stay approximate, which is a licence to stop chasing data that would not change the decision.
Interpreting the Bond Valuation, Clean/Dirty Price & Convexity Curve verdict
Nobody acts on a bare figure — they act on a figure with a comparison attached. The default case lands in the “Trading at a Premium (YTM < Coupon) (105.51% of par).” band, and bands are deliberately wide because real situations overlap. How much of that band is luck? On Par / Face value of bond alone ten percent either way covers $949.57 to $1,160.59. 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.
Where Bond Valuation, Clean/Dirty Price & Convexity Curve sits next to similar measures: this tool answers “how much is the Bond Valuation, Clean/Dirty Price & Convexity Curve”, while the related calculators answer “what do I do about it”. Reading the result alone tends to over-weight a single snapshot; pairing it with the companion tools above turns the number into a decision.
Why Bond Valuation, Clean/Dirty Price & Convexity Curve results go wrong — and how to prevent it
Stopping at the first plausible answer. If the result surprises you, the productive question is which input would have to be wrong for the surprise to disappear — then go check that input.
Stopping at the first plausible answer. If the result surprises you, the productive question is which input would have to be wrong for the surprise to disappear — then go check that input.
Attention is also misallocated between fields. Having measured this engine, we can say where it belongs: Par / Face value of bond first, everything else second.
Another is comparing across contexts: a Bond Valuation, Clean/Dirty Price & Convexity Curve 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.
A quick check for any Bond Valuation, Clean/Dirty Price & Convexity Curve figure
- Note the date and the inputs beside the number so the figure can be audited later.
- Compare the result with one independent method or published benchmark.
- Re-verify Par / Face value of bond against a source document — ten percent of error there moves the headline by ≈10.0 %.
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Confirm the example values are plausible for your own situation before replacing them.
- Confirm the answer against one independent method or published benchmark for Bond Valuation, Clean/Dirty Price & Convexity Curve.
Five steps from raw inputs to a figure you can defend
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 — one document, one pass. Open the statement, label or record that holds par / face value of bond ($), annual coupon interest rate (%), market yield to maturity — ytm (%), years to maturity, coupon payment frequency, days since last coupon payment and transcribe straight into the form. Transcription from a single source removes the mismatch errors that appear when figures are assembled from three different places. The point of transparency is that a reader can disagree with a specific line rather than with you.
Step 2 — baseline before exploration. Get one defensible Clean Bond Price on screen before you start nudging numbers. Without a baseline, every variation looks interesting and none of them means anything. One decimal place more than your data supports is one decimal place of fiction.
Step 3 — change one input at a time. Nudge a single field by ten percent, watch the headline and its companions move, then undo it. Two or three fields will dominate — the sensitivity table above already ranks them for this engine. Re-running a number costs seconds; retracting a decision costs considerably more.
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. Write the figure down before moving on; memory flatters whichever number you saw last.
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. Write the figure down before moving on; memory flatters whichever number you saw last.
Who actually uses Bond Valuation, Clean/Dirty Price & Convexity Curve — and when
Numbers earn their keep in conversations, and Bond Valuation, Clean/Dirty Price & Convexity Curve is no exception. In Investing & Markets discussions around Fixed Income, 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. Precision is a promise you make about your data; make sure your inputs can keep it.
Used properly this is a five-minute filter that saves weeks. Compute Bond Valuation, Clean/Dirty Price & Convexity Curve, reject what fails, and only then bring in the expensive analysis for the survivors. Comparisons are cheap: run the identical calculation for the alternative and look at the gap.
Re-running this page costs nothing and catches the slow drifts that never announce themselves. In Investing & Markets the expensive mistakes are rarely sudden; they are small changes in Par / Face value of bond ($) that nobody recalculated for a year. Suspiciously tidy answers deserve the same scrutiny as untidy ones.
Quick answers: what searchers ask about Bond Valuation, Clean/Dirty Price & Convexity Curve
What affects Bond Valuation, Clean/Dirty Price & Convexity Curve the most?
Bond Valuation, Clean/Dirty Price & Convexity Curve is driven above all by Par / Face value of bond. Perturbing only that field by ten percent either way produced $1,160.59 against the $1,055.08 baseline — a ≈10.0 % response, while Annual coupon interest rate manages ≈4.1 %.
Which matters more: annual coupon interest rate or par / face value of bond?
By the numbers, Par / Face value of bond: a ten-percent change in it moves the result ≈10.0 %, versus ≈4.1 % for Annual coupon interest rate. Spend your measuring effort in that order — precision on the weaker lever buys almost nothing.
How much does the “Coupon payment frequency” choice change the answer?
The spread is not cosmetic: this choice alone takes Bond Valuation, Clean/Dirty Price & Convexity Curve from $1,054.58 to $1,055.34 with every other input frozen, which is more influence than most of the numeric fields on this page can claim.
What is a typical Bond Valuation, Clean/Dirty Price & Convexity Curve?
There is no honest universal average for Bond Valuation, Clean/Dirty Price & Convexity Curve, but there is a reference point: the defaults on this page produce $1,055.08 (Trading at a Premium (YTM < Coupon) (105.51% of par).). Replace the inputs with your own and compare — that comparison is the useful meaning of “typical”.
How do I calculate Bond Valuation, Clean/Dirty Price & Convexity Curve by hand?
Price = Σ [ C / (1+y)^t ] + [ Par / (1+y)^n ] | Dirty = Clean + Accrued Interest is the entire method. Work the inputs in that order — Periodic Coupon = ($1000 × 5.5%) ÷ 2 = $27.50 per period — and you will reach $1,055.08 on the default figures, the same number this tool prints.
What happens to Bond Valuation, Clean/Dirty Price & Convexity Curve if par / face value of bond changes by 10 %?
The engine was re-run with that field moved by ten percent while everything else stayed fixed: the clean bond price goes across $949.57 to $1,160.59, a swing of roughly 10.0 % around the $1,055.08 baseline. That ratio is the practical definition of how much this input matters.
Is the Bond Valuation, Clean/Dirty Price & Convexity Curve result of $1,055.08 good or bad?
Good and bad are comparisons, so the honest test is three questions: where does your own Bond Valuation, Clean/Dirty Price & Convexity Curve sit against the $1,055.08 reference above, how far would a plausible input error move it (≈10.0 % per ten percent on Par / Face value of bond), and what does the alternative option compute to?
What affects Bond Valuation, Clean/Dirty Price & Convexity Curve the most?
Sensitivity depends on where you start, but the inputs Par / Face value of bond ($) and Annual coupon interest rate (%) typically move Bond Valuation, Clean/Dirty Price & Convexity Curve 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.
Does Bond Valuation, Clean/Dirty Price & Convexity Curve account for fees and taxes?
Only what you put in. Fees belong inside Par / Face value of bond ($) where they shrink returns before compounding touches them; taxes are outside the scope of a pre-tax Bond Valuation, Clean/Dirty Price & Convexity Curve and should be layered on top before decisions.
What is the difference between Clean and Dirty bond prices?
The Clean Price is the standard headline quote that excludes accrued interest. The Dirty Price (Invoice Price) is what you actually pay the seller, which includes the interest accrued between the last coupon date and settlement.
Does this Bond Valuation, Clean/Dirty Price & Convexity Curve tool store my numbers?
No. The entire calculation runs in your browser session; nothing entered above is transmitted or saved, which is the correct behaviour for sensitive Investing & Markets figures and the reason you can re-run this page as often as you like.
What the labels on this page mean
- Dirty (Invoice) Price
- $1,061.86 in the default Bond Valuation, Clean/Dirty Price & Convexity Curve calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Modified Duration
- 7.71 in the default Bond Valuation, Clean/Dirty Price & Convexity Curve calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Macaulay Duration
- 7.89 on the example inputs — a companion figure printed beside the headline of Bond Valuation, Clean/Dirty Price & Convexity Curve so that no result is read in isolation.
- Clean Bond Price
- The primary output of this tool: $1,055.08 for the default inputs, computed exactly from Price = Σ [ C / (1+y)^t ] + [ Par / (1+y)^n ] | Dirty = Clean + Accrued Interest.
- 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 (“Trading at a Premium (YTM < Coupon) (105.51% of par).” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Bond Valuation, Clean/Dirty Price & Convexity Curve 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: Price = Σ [ C / (1+y)^t ] + [ Par / (1+y)^n ] | Dirty = Clean + Accrued Interest. Source of record: Fabozzi FJ. The Handbook of Fixed Income Securities (9th ed., McGraw-Hill); SIFMA Bond Pricing Conventions. 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.
This page is an estimation aid, not professional advice. The design rule is simple: two people entering identical figures must get identical answers. The design constraint was set by usefulness rather than by comfort: an estimate you can interrogate beats an answer you have to trust.
After the number: what to do with it
Get one independent quote and reconcile it against this calculation; unexplained gaps are where hidden costs live.
The audience here is planners sizing a spend before committing money. 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.