Lags, schedules, and the MLK payment — From Zero to the Curve

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Worked examples

Read the claim, then run it and check the machine agrees. One at a time — nothing here is taken on trust.

Example 1 of 3 Spot is not today

example.py

import QuantLib as ql

usgov = ql.UnitedStates(ql.UnitedStates.GovernmentBond)
trade = ql.Date(9, 7, 2026)   # a Thursday
print("trade:", trade.ISO())
print("T+1:  ", usgov.advance(trade, 1, ql.Days).ISO())
print("T+2:  ", usgov.advance(trade, 2, ql.Days).ISO(), "  <- spot crosses the weekend")

Two business days from a Thursday is Monday — the weekend doesn't count. Every date in the trade hangs off this one: deal a "2-year swap" on Thursday and its cash flows anchor to Monday the 13th, not to the trade date. (And per lesson 2.1's challenge: had this been early April, the count could have skipped a Good Friday too — with SIFMA deciding whether it counts.)

Example 2 of 3 Backward generation leaves the stub in front

example.py

import QuantLib as ql

usgov = ql.UnitedStates(ql.UnitedStates.GovernmentBond)
spot = ql.Date(13, 7, 2026)
termination = spot + ql.Period(18, ql.Months)

sched = ql.Schedule(spot, termination, ql.Period(1, ql.Years), usgov,
                    ql.ModifiedFollowing, ql.ModifiedFollowing,
                    ql.DateGeneration.Backward, False)
dates = list(sched)
print("accrual dates: ", [d.ISO() for d in dates])
print("period lengths:", [b - a for a, b in zip(dates, dates[1:])], "days")

Backward means: stand at 13 January 2028 and step a year at a time — 13 January 2027... and the leftover 184-day piece lands against spot, at the front. Forward generation would have produced a short back stub instead — same trade description, different cash flow dates, which is why the generation rule is part of market convention (Backward is standard) and not a free choice.

Example 3 of 3 The payment that found a holiday

example.py

import QuantLib as ql

usgov = ql.UnitedStates(ql.UnitedStates.GovernmentBond)
accrual_end = ql.Date(13, 1, 2028)   # a Thursday
print("accrual ends:      ", accrual_end.ISO())
print("+1 business day:   ", usgov.advance(accrual_end, 1, ql.Days).ISO())
print("+2 business days:  ", usgov.advance(accrual_end, 2, ql.Days).ISO())
print("Mon 17 Jan 2028 open?", usgov.isBusinessDay(ql.Date(17, 1, 2028)))

One business day is Friday the 14th. The second should be Monday the 17th — but that's Martin Luther King Day, so the count slides to Tuesday the 18th. A trade dealt in July 2026 has its final cash flow date decided by a January 2028 holiday. Nobody's mental arithmetic catches this; advance on the right calendar does, every time.

Check the concept

One question at a time. Unsure? Revisit the lecture, then answer.

Question 1 of 4

Why does a SOFR OIS pay 2 business days AFTER each accrual period ends, rather than on the end date?

tradition inherited from LIBOR the final overnight fixing isn't known until the period ends — the compounded coupon can't even be computed on the end date to give the payer extra float because of the weekend

The challenge

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