Fixed-Income Model Validation: Prove the Calculation and Its Limits

Write the supported question before testing answers

The parent tools' stated scope is regular noncallable fixed-coupon bullet bonds valued at a coupon date. Years are integers from one through thirty, and coupon frequency is one, two or four per year. Yield is annual nominal, compounded at that same frequency. Accrued interest, settlement day counts, default, calls and reinvestment simulation are excluded. A review should preserve these conditions before deciding which calculations count as valid examples.

Federal Reserve model-risk guidance distinguishes sound construction from appropriate use and emphasizes objective challenge. Those banking principles offer a useful analogy for educational review, not a claim that this calculator receives regulatory approval or falls under every aspect of the guidance. The practical question is whether a result's label is broader than its method. A correct noncallable price cannot validate a claim about a callable or inflation-linked bond.

Inspect the payment schedule independently

For face amount F, annual coupon rate c, frequency m and years T, the schedule has m * T payments. Each coupon is F * c / m; the final payment adds F once. On a coupon-date valuation immediately after the current coupon, the first future payment arrives one full period later. This convention prevents an accidental immediate coupon from inflating value or a missing final coupon from reducing it.

The schedule review should use a direct list of amounts and period numbers rather than the same helper that generated the reported value. Count payments, sum coupons and confirm that principal appears exactly once. Check the unit perimeter as well: a price per 100 of face is not a full position value. A scaling mistake can pass a percentage-return test while producing a materially incorrect currency result.

Review the FinancialJS present-value mapping

The parent dependency is FinancialJS 0.2.4, the financial package. Its pv documentation defines a per-period rate, number of periods, periodic payment, terminal value and payment timing. For the stated bond convention, these map to y / m, m * T, F * c / m, F and end-of-period payments. An annual percentage entered by a reader must first be converted to its decimal annual rate before frequency conversion.

The library uses a cash-flow sign convention: positive future receipts imply a negative present-value cash outflow. A displayed positive asset price can therefore be expressed as -pv(y / m, m * T, F * c / m, F, 0). The sign change is intentional, not a correction to an erroneous negative bond price. Preserve the distinction between investor outflow and positive asset value throughout the surrounding calculations.

Reproduce a numerical case without the library

Take hypothetical face USD 1,000, annual coupon 4%, annual nominal yield 6%, semiannual payments and two years remaining at a coupon date. There are four future periods, the coupon is USD 20 and the periodic yield is 3%. Direct discounting gives 20 / 1.03 + 20 / 1.03^2 + 20 / 1.03^3 + 1,020 / 1.03^4 = USD 962.829016, rounded to six decimals.

Independently, the annuity-plus-principal expression is 20 * (1 - 1.03^(-4)) / 0.03 + 1,000 * 1.03^(-4), giving the same value. This comparison does not invoke the dependency. It checks the expected result that an implementation should reproduce; it does not claim that the runtime has been tested. Preserve full working precision and state the display tolerance so that rounding is not mistaken for a failed calculation.

Use invariants to expose mapping errors

At zero yield, the same schedule has value USD 1,000 plus four USD 20 coupons, or USD 1,080. A formula using division by yield needs a proper zero-rate treatment rather than an undefined numerical result. For a regular coupon-date bullet, setting coupon rate equal to yield under matching compounding should give par. These checks target different failure modes and are more informative together than repeated tests of one typical input.

Scaling face amount scales all payments and present value proportionally. Increasing yield reduces value for positive fixed payments within the valid discounting domain. The necessary denominator condition is 1 + y / m > 0; any stricter documented input limits still apply. Negative yield is not automatically a mathematical error, but values outside the accepted domain should not silently produce a plausible-looking result through clipping or an undocumented fallback.

Test sensitivities without recycling the answer

A duration check can compare an analytical result with central differences from independently repriced upward and downward yield changes. Use annual decimal yield changes consistently, even though discounting occurs per coupon period. Record bump size and inspect stability at another sensible step. A missing frequency conversion or basis-point conversion can produce a clean-looking sensitivity that is wrong by a large, systematic factor across every example.

Convexity checks similarly need explicit units and full-precision prices. Do not round each intermediate present value to cents before estimating a small derivative, because that can overwhelm the signal being measured. When an approximation differs from exact repricing under a larger shock, retain the residual rather than forcing agreement. The discrepancy may reflect expected curvature or may reveal a coding error; its interpretation requires the calculation's stated purpose and assumptions.

Record what passing evidence actually establishes

A validation record should identify the model version, dependency version, input fixture, expected result, independent method, tolerance and observed result when execution is performed. Keep unresolved exceptions and unsupported instruments visible. A library upgrade or change in payment mapping should trigger review of affected evidence. Reusing an old passing result without its version and assumptions weakens the very reproducibility that the test was intended to establish.

Arithmetic agreement supports a claim about calculation correctness under specified inputs. It does not establish executable market value, successful strategy performance, suitability for a person or operational readiness. Those require different evidence and are outside this guide's purpose. A useful final statement names both the checks completed and the claims deliberately withheld. That makes a narrow calculator trustworthy as an educational instrument without presenting it as a broader investment or production system.

Primary references

1. FinancialJS: pv Function Documentation
2. Federal Reserve: Supervisory Guidance on Model Risk Management