Ex Dividend And Rebate Interest

Ex-dividend and rebate interest

A gilt bought inside its ex-dividend window does not receive the coupon that is about to be paid, so accrued interest is NEGATIVE. Most fixed-income code has no branch for this. The code that does can have the sign backwards and never fail.

Every figure below is printed by scripts/ex_dividend.py (runs in 0.15 s; QuantLib optional). ✅ Measured means this file produced it on 2026-09-09 with QuantLib 1.43, Python 3.11.3. The worked bond is a 4% gilt, coupons 7 Jun / 7 Dec, maturity 2035-06-07, y = 4.20%, and the coupon in question is 2026-12-07 (a Monday), whose ex-dividend date is 2026-11-26.

The rule: inside the window AI = (t/s − 1)·d1, which is negative — and QuantLib's exCouponPeriod counts days BACK from the coupon, so it takes Period(7, Days) and never Period(-7, Days).

1. ✅ The rule, from the source

✅ UK DMO, "Formulae for Calculating Gilt Prices from Yields", 4th edition, 18 December 2024, Note 5 (read 2026-09-09): the ex-dividend date for all gilts is currently the date seven business days before the dividend date.

✅ Section Three (1)(i), the accrued-interest formula, verbatim in structure:

AI = (t/s)     * d1     if the settlement date occurs on or before the ex-dividend date
AI = (t/s - 1) * d1     if the settlement date occurs after the ex-dividend date

with t = calendar days from the previous quasi-coupon date to settlement, s = calendar days in the full quasi-coupon period, d1 = the next dividend per £100 nominal. The − 1 is the whole thing: it subtracts one full coupon.

🔴 The 3½% War Loan ten-business-day exception is dead. It was in the 3rd edition (16 March 2005). ✅ The stock was redeemed in full at par on 2015-03-09 (announced 2014-12-03), and the 4th edition says seven business days for all gilts, with no exception. A model that recites the War Loan carve-out is quoting a 2005 document about a security that no longer exists.

⚠️ US Treasuries and USD corporates have no ex-dividend period — accrued runs straight through the coupon date — which is exactly why a US-shaped bond library has no code path for this and a US-trained prior does not expect one.

2. ✅ What the window does to accrued, dirty and clean

✅ Measured, per £100 nominal, on 1,000,000 nominal:

• ✅ Accrued falls +1.879781 → −0.109290, a drop of 1.989071 — exactly one coupon (2.00) minus one day of accrual.
• ✅ The DIRTY price drops −1.986321; the CLEAN price moves +0.002750. That is the whole point of quoting clean: the clean price is continuous across the ex-dividend date and the dirty price is not. A model that watches dirty prices sees a 2-point crash that never happened.
• ✅ In the DMO price formula the same fact appears as d1 = 0 — the next quasi-coupon cash flow simply is not receivable by the buyer.

3. 🚨 ql.Period(-7, ql.Days) is accepted and does the opposite

✅ Source-verified in QuantLib's ql/cashflows/fixedratecoupon.cpp (FixedRateLeg::operator Leg(), read 2026-09-09):

if (exCouponPeriod_ != Period())
{
    exCouponDate = exCouponCalendar_.advance(paymentDate,
                                             -exCouponPeriod_,
                                             exCouponAdjustment_,
                                             exCouponEndOfMonth_);
}

exCouponPeriod is already a look-BACK, so QuantLib negates it. Passing a negative period double-negates into a forward advance. ✅ Measured on the 2026-12-07 coupon:

✅ Accrued per 100 across the window, and the error on 1,000,000 nominal:

🚨 The Period(-7) column is character-for-character the no-ex-coupon column, on every date. You wrote the ex-dividend handling, it compiled, it ran, and it did nothing. The error is exactly one coupon — 2.000000 per 100, 20,000 on 1,000,000 nominal — on every settlement date in the window, and it does not shrink with the size of the window.

How to catch it in one line: after building the bond, assert the ex-coupon date is before the coupon date.

c = ql.as_coupon(bond.cashflows()[i])
assert c.exCouponDate() < c.date(), "exCouponPeriod sign is wrong"

4. ⚠️ The boundary is one day wide

✅ Measured: on the ex-dividend date itself (2026-11-26) QuantLib with Period(7, Days) is already ex (−0.120219) while the DMO formula is still cum (+1.879781). QuantLib's rule is exCouponDate <= settlement → ex; the DMO's is "settlement after the ex-dividend date".

⚠️ They reconcile through the settlement lag, not through the arithmetic. The DMO formula is written in settlement dates; "trades ex-dividend" is a trade-date idea. With gilts settling T+1, a trade on the ex-dividend date settles the next business day and is therefore ex under both. If you feed QuantLib settlement dates, Period(7, Days) goes ex one settlement day earlier than the DMO formula; Period(6, Days) reproduces the DMO boundary exactly (measured: it matches the DMO column on all seven dates above). Decide which date type your pipeline carries and write the assertion for it.

5. ✅ The DMO price formula, checked against QuantLib

gilt_price_from_yield implements DMO Section One for conventional gilts (n ≥ 1):

P = v^(r/s) [ d1 + d2 v + (c/f) v^2 (1 - v^(n-1)) / (1 - v) + 100 v^n ],   v = 1/(1 + y/f)

✅ Against ql.BondFunctions.cleanPrice on the same bond at y = 4.20%, over all seven settlement dates: worst |diff| = 4.3e-14 on both clean and dirty. Two independent implementations of the same pricer, so neither is confirming itself.

🚨 But only with paymentConvention = Unadjusted. ✅ The DMO states cash flows falling on non-business days are not adjusted ("not 'bumped'"). QuantLib's usual ql.Following moves the 2030-12-07 and 2031-06-07 coupons off their weekends and shifts the clean price by −0.000947 per 100 = −9.47 per 1,000,000. Small, but it is a systematic sign-consistent error that never appears as a failure — and it is the reason a "QuantLib does not match the DMO" investigation usually ends in the wrong place.

6. What the script gives you

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

Where this sits

• ../bond-conventions-and-accrued/SKILL.md — ordinary (positive) accrued, the day-count choice, clean vs dirty, and 🚨 ActualActual(ISMA) without a schedule returning 0.25.
• ../yield-measures-and-bill-quotes/SKILL.md — solving the DMO price formula the other way, and the quotes that are not yields at all.
• ../duration-convexity-and-dv01/SKILL.md — the risk of a bond whose next cash flow is zero.
• ../../../fin-libraries/skills/lib-quantlib/SKILL.md — 🚨 Settings.instance().evaluationDate is a global; every accruedAmount call above sets it first. ql.Date is day-first, which is its own way to get 2026-12-07 wrong.
• ../../../fin-core/skills/us-market-rules/SKILL.md — the settlement-lag and calendar side of §4.
• ../../../fin-models/skills/term-structure-models/SKILL.md — curve construction; the index-linked gilt formulae in the same DMO document (8-month and 3-month indexation lags) belong with inflation modelling, not here.