Bond valuation estimates dirty and clean price from discounted cash flows, benchmark rates, credit spread, options, accrued interest, and market inputs.
Bond valuation is the process of estimating a bond’s price by discounting its expected cash flows at rates consistent with their timing, currency, credit risk, liquidity, and embedded options. For a plain fixed-rate bond, those cash flows are coupons and principal; for a risky or option-affected bond, contractual cash flows may not be the best expected-cash-flow assumption.
For a fixed-rate, option-free bond valued with one periodic yield:
Where:
This formula values promised cash flows using one yield. It is most transparent for a standard bullet bond without embedded options.
Consider a three-year bond with face value 100, a 5% annual coupon, and annual payments. If the required yield is 6%:
1Year 1 coupon: 5 / 1.06 = 4.7170
2Year 2 coupon: 5 / 1.06^2 = 4.4500
3Year 3 coupon+face: 105 / 1.06^3 = 88.1600
4Estimated price: 97.3270
The bond is below par because its 5% coupon is lower than the 6% required yield. If the required yield were 5% on a coupon date, the same bond would value at par under these assumptions. If required yield fell below 5%, the value would generally rise above par.
Bond markets often quote a clean price that excludes accrued coupon interest. The amount used for settlement normally reflects the clean price plus accrued interest, subject to market convention and fees:
If a bond is quoted at 97.30 per 100 of face value and accrued interest is 1.25, the full price is 98.55 before transaction charges.
Accrued interest depends on coupon amount, day-count convention, and days in the coupon period. A buyer generally compensates the seller for interest accrued since the last coupon because the buyer receives the next full coupon.
Yield-to-maturity is the single rate that equates the present value of promised cash flows with price. A spot-curve valuation instead applies a discount factor for each cash-flow date:
Spot-curve valuation is useful when curve shape matters. A credit bond may be valued by adding a spread to the relevant benchmark spot rates. The resulting Z-spread is the constant spread that reconciles fixed cash flows with market price.
No curve is neutral. Government, swap, funding, or another benchmark can produce different values, and curve construction introduces interpolation and market-data assumptions.
The simple formula assumes contractual payments arrive in full. A credit-risk valuation may instead use:
Credit spread includes more than expected default loss. Liquidity, uncertainty, structure, technical flows, and options also affect market price. A model value should therefore be compared with current trades, executable quotes, issuer fundamentals, and recovery analysis.
A callable bond may be redeemed when doing so benefits the issuer. Mortgage-backed securities can prepay faster or slower as rates and borrower behavior change. Convertible bonds depend partly on equity value and conversion terms.
For these securities, fixed contractual cash flows are insufficient. Analysts may use a lattice, simulation, or other option model to estimate path-dependent cash flows and option-adjusted spread. The output is model-dependent.
| Measure | Purpose | Main input |
|---|---|---|
| Model value | Estimate economic value under assumptions | Expected cash flows and discount model |
| Market price | Indicate where a trade occurred or may occur | Actual trade, executable quote, or evaluated price |
| Clean price | Quote bond price without accrued interest | Market convention |
| Dirty price | Estimate full settlement price before fees | Clean price plus accrued interest |
| Carrying amount | Report the bond under an accounting framework | Recognition, amortization, impairment, and classification rules |
These numbers can differ without an arithmetic error because they answer different questions.
FINRA’s bond yield and return guide explains price-yield inversion and yield-to-maturity as the discount rate equating price with future cash flows. FINRA’s bond reference guide explains bond quotation, accrued interest, and settlement concepts. The U.S. Treasury publishes its current yield-curve methodology.
This page is educational only. A valuation estimate is not a trade quote or recommendation, and accounting, tax, and legal treatment require current case-specific guidance.