Bond Conventions And Accrued

Bond conventions and accrued

Accrued interest is not a number. It is a number plus three things: a day-count convention, a coupon schedule, and a settlement date. Drop any one and you still get a plausible answer.

Every figure below is printed by scripts/conventions.py (runs in 0.15 s; QuantLib optional, imported inside quantlib_cross_checks). ✅ Measured means this file produced it on 2026-09-09 with QuantLib 1.43, Python 3.11.3. The worked bond is a 5% semiannual, coupon period 2026-01-15 → 2026-07-15 (181 days), settled 2026-04-30 (105 days in), 1,000,000 face.

The rule: carry (day count, coupon schedule, settlement date) together. ACT/ACT ICMA evaluated from two bare dates is a guess, "30/360" alone does not name a convention, and the screen quotes clean while the wire settles dirty.

1. 🚨 ACT/ACT ICMA without its schedule returns 0.25 and no error

ACT/ACT ICMA (= ISMA = "Bond") is days / (coupon-period days × coupons per year). The denominator is the coupon period, not the year, so two dates are not enough to evaluate it.

✅ Source-verified in QuantLib's own ql/time/daycounters/actualactual.cpp (read 2026-09-09): implementation() dispatches case ISMA: case Bond: if (!schedule.empty()) → ISMA_Impl, else → Old_ISMA_Impl — whose comment says the reference period is taken "equal to (d1,d2)" when unspecified, and which then estimates months = lround(12 * (refPeriodEnd - refPeriodStart) / 365).

✅ Measured on the worked bond:

Why exactly 0.25: the 105-day stub gives lround(12 × 105/365) = 3 months, so it decides this is a quarterly bond and returns one whole quarterly period. ✅ My reference implementation reproduces both numbers to 0.0e+00.

🚨 Where the fallback bites, and where it does not — ✅ measured, and this matters

So the danger is not QuantLib's bond objects — it is your own accrual arithmetic and any curve or rate object you hand the counter to. If you write dc.yearFraction(prev, settle) yourself, pass the schedule: ql.ActualActual(ql.ActualActual.ISMA, schedule). Never use an ACT/ACT ICMA counter as a curve day count — a curve's time axis has no coupon period, so the guess is unavoidable there.

2. 🚨 "30/360" does not name a convention

✅ Source-verified in ql/time/daycounters/thirty360.cpp (read 2026-09-09): six implementations behind nine enum constants — US_Impl (USA), ISMA_Impl (ISMA and BondBasis), EU_Impl (European, EurobondBasis), IT_Impl (Italian), ISDA_Impl (ISDA, German), NASD_Impl (NASD). The rules differ only on the 31st and on the last day of February, which is why they agree on most date pairs and then disagree on yours.

✅ Measured, day counts and the accrued spread on 1,000,000 face at a 5% coupon:

🚨 Thirty360.USA is not Thirty360.BondBasis. ✅ QuantLib 1.43 on the middle row returns USA=180, BondBasis=183, European=182, EurobondBasis=182, Italian=180, German=180, ISMA=183, ISDA=180, NASD=183 — three answers from nine names. My implementation reproduces all five rules exactly.

The rules, from the source:

• US — if both dates are the last of February, dd2 = 30; if d1 is the last of February, dd1 = 30; then dd2 = 30 if dd2 == 31 and dd1 >= 30; then dd1 = 30 if dd1 == 31.
• BondBasis / ISMA — the same without the two February lines. This is the usual US corporate/agency "30/360".
• 30E/360 — min(dd, 30) on both legs. February is untouched, which is why 2026-02-28 stays 28 and the count is 182.
• 30E/360 ISDA — last day of the month → 30 on both legs, except an end date that is the termination date and falls in February. It needs the maturity to be evaluated at all.
• Italian — European, plus a February date after the 27th → 30.
• ✅ NASD is algebraically identical to BondBasis: it maps dd2 = 1; mm2++ where BondBasis leaves 31, and 30(m+1) + 1 = 30m + 31.

3. The same bond, every convention — ✅ measured

✅ QuantLib's FixedRateBond.accruedAmount agrees with the reference implementation on all five counters to |diff| < 1e-14. Note ACT/ACT ISDA and ACT/365F coincide on this period — they are different conventions that happen to agree inside a single non-leap year, which is exactly how a mismatch survives testing.

ACT/ACT ISDA is not ACT/ACT ICMA. ISDA splits the interval at each year end and divides each piece by that year's own length (365 or 366); ICMA divides by the coupon period. They are used for different instruments — ICMA for bonds, ISDA for swap legs — and swapping them is a silent 119.20 per 1,000,000 here and larger across a leap year.

4. Clean, dirty, and what actually settles

✅ At a clean price of 98.500: dirty = 98.500 + 1.450276 = 99.950276, and the cash on 1,000,000 face is 999,502.76, of which 14,502.76 is accrued.

• Clean (flat) is what screens, indices and most APIs quote.
• Dirty (full, invoice) is what settles. dirty = clean + accrued.
• 🚨 A P&L or return series built from clean prices alone drops the coupon accrual. Over a year on a 5% bond that is 5 points of return that never appears.
• Total return = clean change + accrual + coupons received + reinvestment. Index vendors do this for you; a yfinance-style price series does not.

5. Settlement lag moves the cash at an unchanged price

✅ Measured on the same bond, same clean price, business-day settlement:

One day of settlement is 138.12 per 1,000,000 — the same order as the entire 30/360 argument in §2. T+2 lands on Monday 2026-05-04 and picks up the weekend, which is why the step from T+1 to T+2 is three days of accrual, not one.

✅ Source-verified at eCFR 17 CFR 240.15c6-1(a) (fetched 2026-09-09): a broker-dealer may not contract for settlement "later than the first business day after the date of the contract" — T+1 — and the rule excepts "an exempted security, a government security, a municipal security, commercial paper, bankers' acceptances, or commercial bills". 🚨 So Treasuries are outside the rule entirely; their T+1 is market convention, not 15c6-1, and new issues priced after 16:30 ET get T+2 under 15c6-1(c). Calendars, holidays and business-day conventions live in ../../../fin-core/skills/us-market-rules/SKILL.md.

6. What the script gives you

scripts/conventions.py — standard library only at import; QuantLib inside one function.

Where this sits

• ../ex-dividend-and-rebate-interest/SKILL.md — when accrued goes negative. Gilts trade ex-dividend seven business days before the coupon, and a QuantLib sign convention makes that window silently disappear.
• ../yield-measures-and-bill-quotes/SKILL.md — price → yield, once the accrued is right.
• ../duration-convexity-and-dv01/SKILL.md — the risk numbers this arithmetic feeds.
• ../../../fin-models/skills/term-structure-models/SKILL.md — the curve side: one discount factor is a different zero rate under every day count and compounding (measured there, −17.68 bp). Bootstrapping, Nelson-Siegel and the short-rate closed forms live there, not here.
• ../../../fin-libraries/skills/lib-quantlib/SKILL.md — 🚨 Settings.instance().evaluationDate is a global and a stale one gives NPV exactly 0.0; ql.Date is day-first.
• ../../../fin-core/skills/us-market-rules/SKILL.md — trading calendars, holidays and the settlement rules §5 only does the arithmetic for.