Bond Price Yield Duration Convexity Calculator

Purpose and model boundary

This model prices a synthetic fixed-rate bullet bond from an entered nominal annual yield or solves a nominal annual yield from an observed dirty price. It also measures current yield, Macaulay and modified duration, discrete convexity, dollar duration, and DV01. It is a transparent coupon-date valuation and local interest-rate-risk model, not an executable quote, accounting valuation, recommendation, or complete security model.

Inputs and units

The solve route selects direct price from yield or a guarded yield-from-price bisection. Coupon frequency is annual, semiannual, or quarterly. Face value and redemption value are positive user-currency amounts and may differ. The coupon rate and market yield are annual fractions; maturity is a whole number of years. In yield-from-price mode, the observed dirty price and the upper yield-search bracket become active. In price-from-yield mode those two fields are ignored, and changing them does not change an output.

Settlement is exactly on a coupon date, so accrued interest is zero and clean price equals dirty price in this model. The entered yield is nominal annual yield compounded at the coupon frequency.

Governing relationships

Let m be payments per year, T maturity in whole years, N = m × T total periods, F coupon face value, R redemption value, and c annual coupon rate. The periodic coupon and period-k cash flow are:

C = F × c / m

CF_k = C + R when k = N, and CF_k = C otherwise.

For nominal annual yield y, price and each present value are:

PV_k = CF_k / (1 + y/m)^k

P(y) = sum(PV_k), k = 1...N

The yield-from-price route searches 0 <= y <= y_max. Price is evaluated at both bracket ends and the workbook performs 40 monotonic bisection iterations, keeping the half whose price brackets the observed dirty price. The reported yield is the final bracket midpoint.

With cash-flow time t_k = k/m, the risk measures are:

D_Mac = sum(t_k × PV_k) / P

D_Mod = D_Mac / (1 + y/m)

Convexity = sum[k(k+1) × PV_k / (1 + y/m)^2] / (P × m^2)

Current yield = F × c / P

Dollar duration = P × D_Mod

DV01 = Dollar duration × 0.0001

Calculation sequence

1. Validate the route, coupon frequency, common bond terms, and only the inputs active for the selected route.
2. Convert frequency to m, calculate N and the level periodic coupon, and populate at most 120 contractual periods.
3. In price mode, use the entered market yield. In yield mode, verify that the observed price lies between the zero-yield undiscounted cash flow and the price at the entered search maximum, then run 40 bisection iterations.
4. Discount every active coupon and redemption cash flow at the active periodic yield and sum price.
5. Calculate current yield, duration, convexity, dollar duration, DV01, total coupon cash flow, and total periods.
6. Build the price-across-yield chart from ten workbook-calculated scenarios between zero and the active chart maximum.
7. Apply the derived-range gate and then the zero-coupon CHECK rule.

Outputs and interpretation

Bond price is the present value of coupons and redemption. Yield to maturity is either the entered yield or the bisection solution. Macaulay duration is the present-value-weighted average cash-flow time; modified duration translates it into first-order price sensitivity. Convexity is the workbook's discrete second-order sensitivity. Dollar duration and DV01 express local price exposure in user currency, with DV01 corresponding to one basis point. Current yield considers annual coupon cash flow only and is not yield to maturity.

The chart shows the workbook-computed inverse price/yield relationship. It is scenario evidence, not a live market curve or a forecast.

Validation and status logic

The workbook evaluates status in this order:

For yield-from-price, the observed price must not exceed the undiscounted cash-flow total and must not be below the price at y_max. The solved price must match the observation within 1e-8 × max(1, observed price). Input and derived failures take precedence over the zero-coupon check.

Assumptions and limitations

• Coupons are level, redemption occurs with the final coupon, and maturity times frequency is an integer.
• Yield is nonnegative and uses the selected coupon frequency as its compounding frequency.
• There is no accrued interest, irregular coupon, day-count convention, business-day calendar, call, put, default, recovery, inflation, credit spread, tax, or reinvestment model.
• Duration, DV01, and convexity are local parallel-yield measures. They do not replace key-rate or full-revaluation scenarios.
• All terms and chart values are synthetic user data, not licensed market observations.

Restrictions and non-computing states

Face and redemption values must be from 0.01 through 1,000,000,000; coupon rate from 0 through 1; maturity from 1 through 30 whole years; and direct market yield from 0 through 5. Yield mode additionally requires observed dirty price from 0.000001 through 31,000,000,000 and a search maximum from 0.01 through 5. The schedule supports no more than 120 quarterly periods. A price outside the nonnegative-yield bracket prevents a result instead of producing a negative or unbounded yield.

Errors and warnings

This calculator can refuse an unknown option, missing active field, or number outside its allowed range before calculation. Workbook NOT VALID distinguishes active-input failure from a failed price/yield bracket or derived result. Workbook CHECK identifies a valid zero-coupon calculation whose current yield is necessarily zero. A connection or calculation-service failure is not a bond-model status and must not be interpreted as a zero value.

The model follows the general coupon, current-yield, yield-to-maturity, price/yield, and duration relationships described in FINRA's Bond Yield and Return. Instrument and interest-rate-risk context follows Investor.gov's Bonds or Fixed Income Products. The workbook independently implements the equations and embeds no security prices, issuer data, or copyrighted table.