Bond Price Calculator
Fast, accurate and free online ceny obligacji calculator tool running directly in your browser.
-
1Enter data
Enter content, paste text or load a file from disk. -
2Click the button
The tool will immediately process your data in the browser. -
3Get the result
Copy the finished text or save the file to your device.
return "Result ready in 0.1s";
}
Bond price calculator
Rate this tool:
Related tools
Other tools you may find usefulBond price calculator - valuation based on coupon, YTM and maturity date
The bond price calculator calculates the current market value of a debt security taking into account the nominal redemption value, fixed coupon, payment frequency and expected yield to maturity YTM. The tool converts the stream of future coupons and the redemption value to today's value, so you can quickly check whether the bond is valued at a discount, at a par or at a premium. Additionally, you will receive the accumulated ACCR coupon, dirty and clean price, as well as approximate duration and convexity metrics.
Run calculator Tools home page
Formulas and theory
Fixed coupon bond pricing model
The bond price is the sum of discounted coupon flows and the nominal value returned on the redemption date. Discounting is carried out using the YTM rate appropriately scaled to the coupon payment frequency.
P = Σt=1..NC/m · 1/(1 + y/m)t+ F · 1/(1 + y/m)N
- Pclean price, without accrued interest,
- Fnominal value of the bond, usually 100 or 1000,
- Cannual coupon amount, i.e. F · k where k is the coupon rate,
- yyield to maturity YTM on an annual basis,
- mnumber of coupons in the year, e.g. 1, 2 or 4,
- Nnumber of remaining coupons to be redeemed.
Clean and dirty price
Between coupon dates, the market price is usually given asclean priceanddirty price. The dirty price includes the coupon accrued from the last payment to the settlement date.
Dirty = Clean + ACCRandACCR = C/m · f
Thefparameter is a fraction of the coupon period calculated according to the day convention, e.g. Actual Actual, Actual 365, 30 360.
Duration and convexity in simple terms
Duration measures the price sensitivity to changes in the YTM rate. Convexity improves this measure for larger rate changes. The tool calculates Macaulay and modified duration as well as approximate convexity from discounted flows.
DurMac= Σ t · PV(CFt) / Pscaled by the number of periods in the year,Durmod= DurMac/ (1 + y/m).
Relationship between coupon and YTM
When the coupon is equal to YTM, the price approaches the face value. If the coupon is less than the YTM, the security trades at a discount. If the coupon exceeds the YTM, the security is trading at a premium.
Input fields and validation
Fields in the calculator
- Denomination Fin currency units,
- Coupon rate kannual percentage,
- YTM yannual percentage,
- Maturity periodin years or dates,
- Coupon frequency m1, 2, 4 or 12,
- Day conventionActual 365, Actual 360, 30 360, Actual Actual,
- Last coupon date i settlement datefor ACCR calculation.
Validation rules
- F, k, y, m non-negative, m from the allowed set,
- Maturity period greater than zero,
- Dates in the correct calendar format,
- For zero-coupon securities k = 0, the formula is simplified to the discount price P = F/(1 + y/m)N.
Calculation examples
Example 1. Fixed coupon, half-year coupon
Data:F = 100, k = 6 percent, y = 7 percent, m = 2, maturity 3 years, N = 6.
Periodic coupon:C/m = 100 · 0.06 / 2 = 3.
Clean price:P = Σ 3/(1 + 0.07/2)t+ 100/(1 + 0.07/2)6≈ 97.65.
Interpretation:A coupon lower than YTM gives a price below the pair, i.e. at a discount.
Example 2. Bonus with a coupon higher than YTM
Data:F = 1000, k = 8 percent, y = 6 percent, m = 2, to maturity 5 years, N = 10.
Clean price:P ≈ 1000 · 1.0889 = 1088.9 approximately from the annuity model and face value discount.
Conclusion:A higher coupon results in a price at a premium to the face value.
Example 3. Zero coupon
Data:F = 100, k = 0 percent, y = 5 percent, m = 1, t = 4 years, N = 4.
Price:P = 100/(1.05)4= 82.27. The investor's entire profit is a discount to the nominal value.
Example 4. ACCR and dirty price
Data:Annual coupon 5%. since F = 100, m = 2, 45 days have passed out of 182 days of the period, clean price = 98.40.
ACCR:C/m = 2.5, f = 45/182 = 0.2473, ACCR = 2.5 · 0.2473 = 0.618.
Dirty:99.018, i.e. the settlement price includes the coupon accrued until the transaction date.
Auxiliary tables
| Parameter | Meaning | Unit | Notes |
|---|---|---|---|
| F | Bond nominal value | currency | Redemption value |
| k | Annual coupon rate | percent | Constant for fixed-coupon securities |
| y | Yield to maturity | percent. | Market discount rate |
| m | Coupon frequency | number | 1, 2, 4, 12 |
| N | Number of coupons to maturity | number | N = m · years to maturity |
| Clean | Price without accrued coupon | currency | Valuation main result |
| ACCR | Accrued coupon | currency | Convention-dependent days |
| Dirty | Price with coupon accrued | currency | Clean + ACCR |
| Dur mod | Duration modified | years | YTM price sensitivity |
| Conv | Convexity | years2 | Curvature correction |
How to use the calculator step by step
- Enter the denomination F and the coupon rate k and select the frequency m.
- Enter the YTM on an annual basis and determine the time remaining until maturity.
- If the quote is between coupons, indicate the last coupon date, settlement date, and day convention.
- ClickCalculateto get clean price, ACCR, dirty price and optional duration and convexity.
- Compare the result to the market price and assess whether the security is attractive relative to alternatives with similar risk.
FAQ
Why does price fall when YTM rises?
A higher YTM means a stronger discounting of future flows, which lowers their today's value and thus the bond price.
What is the difference between a clean price and a dirty price?
The clean price does not include the accrued coupon. The dirty price is the settlement amount of the transaction, i.e. the clean price plus accrued interest from the last coupon payment.
Does the calculator support zero-coupon bonds?
Yes. With k equal to 0, the formula reduces to the simple discount price F divided by the growth factor 1 plus YTM to the power of N.
What day conventions are available?
Actual 365, Actual 360, 30 360 and Actual Actual. The choice affects the length of the period fraction and the amount of ACCR.
Why do I need duration and convexity?
They help estimate the price change with YTM movement. Duration describes a linear sensitivity, convexity introduces a non-linear correction for larger rate changes.
Applications and tips
Comparing securities with different coupons
YTM-based pricing allows you to compare bonds with different coupons and maturities, which helps you choose the most effective security for a given interest rate risk.
Interest Rate Risk Assessment
Duration and convexity indicate how valuations may change following a movement in rates. Long duration means the portfolio is more sensitive to YTM changes.
Summary
The webp.pl bond price calculator converts coupon and redemption flows to current value to provide clean price, ACCR and dirty price and basic measures of interest rate risk. Enter the issue parameters, select the day convention and clickCalculate, and in a few seconds you will know the market value of the security and the impact of the YTM rate on the price. This will make it easier for you to compare emissions, assess the attractiveness of profitability and control the risk in your portfolio.