FA-60906 / Bond day-count conventions / Open access

ICMA regular-period accrued with ex-coupon: the per-day coupon is rounded before multiplying by days · case 01

Accrued interest differs in the last decimals for long accrual periods.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Rounding is applied to the daily coupon rate instead of the final accrued amount.

THE FAILURE

Rounding is applied to the daily coupon rate instead of the final accrued amount.

Unsuccessful approach: Rounding the daily rate to 8 decimals shrinks but does not remove the drift.

Case contract

Inputs prev, nxt, settle ([y,m,d]), annual rate, frequency and ex-coupon days. Settlement outside [prev, nxt] returns "settlement outside period"; settlement on nxt returns 0.0. If the settlement is within ex-coupon days of nxt (days to nxt <= exdays), accrued is negative: -coupon*days(settle,nxt)/days(prev,nxt). Otherwise accrued = coupon*days(prev,settle)/days(prev,nxt). coupon=100*rate/freq; round the final value to 6 decimals.

Why this case matters

Bond accrual and pricing systems depend on exact day-count arithmetic; a single-day error changes settlement cash.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import datetime
from fractions import Fraction
N = 1
observations = []
def solve(prev, nxt, settle, rate, freq, exdays):
    P = datetime.date(*prev)
    Q = datetime.date(*nxt)
    S = datetime.date(*settle)
    if not (P <= S <= Q):
        return 'settlement outside period'
    if S == Q:
        return 0.0
    period = (Q - P).days
    coupon = 100 * rate / freq
    if (Q - S).days <= exdays:
        return round(-coupon * (Q - S).days / period, 6)
    days = (S - P).days
    return round(round(coupon / period, 6) * days, 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression daily rate rounding stage 1', [[2019, 7, 31], [2020, 1, 31], [2019, 11, 17], 0.0625, 2, 5], 1.851223], ['regression daily rate rounding stage 2', [[2060, 6, 3], [2061, 6, 3], [2060, 12, 24], 0.02, 1, 0], 1.117808], ['partial repair probe 1', [[2030, 9, 16], [2030, 12, 16], [2030, 12, 11], 0.02, 4, 0], 0.472527], ['partial repair probe 2', [[2049, 3, 10], [2049, 9, 10], [2049, 5, 17], 0.0625, 2, 3], 1.154891], ['boundary control 1', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 16], 0.05, 2, 7], 'settlement outside period'], ['boundary control 2', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 8], 0.05, 2, 7], -0.096154], ['normal control 1', [[2042, 11, 16], [2043, 5, 16], [2043, 5, 14], 0.02, 2, 5], -0.01105], ['normal control 2', [[2027, 1, 25], [2027, 7, 25], [2027, 7, 25], 0.0625, 2, 0], 0.0]], [['regression daily rate rounding stage 1', [[2050, 11, 30], [2050, 12, 30], [2050, 12, 18], 0.04125, 12, 7], 0.20625], ['regression daily rate rounding stage 2', [[2030, 5, 27], [2031, 5, 27], [2030, 12, 17], 0.0275, 1, 0], 1.536986], ['partial repair probe 1', [[2003, 7, 29], [2004, 1, 29], [2003, 12, 3], 0.0625, 2, 3], 2.156929], ['partial repair probe 2', [[2035, 12, 26], [2036, 12, 26], [2036, 12, 16], 0.07, 1, 0], 6.808743], ['boundary control 1', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 8], 0.05, 2, 7], -0.096154], ['boundary control 2', [[2024, 1, 15], [2024, 7, 15], [2024, 1, 15], 0.05, 2, 7], 0.0], ['normal control 1', [[2038, 2, 5], [2038, 5, 5], [2038, 5, 3], 0.02, 4, 7], -0.011236], ['normal control 2', [[2032, 2, 27], [2032, 3, 27], [2032, 2, 27], 0.0275, 12, 0], 0.0]], [['regression daily rate rounding stage 1', [[2003, 1, 22], [2003, 4, 22], [2003, 3, 31], 0.05, 4, 0], 0.944444], ['regression daily rate rounding stage 2', [[2034, 9, 16], [2034, 12, 16], [2034, 11, 25], 0.0625, 4, 0], 1.201923], ['partial repair probe 1', [[2006, 5, 15], [2006, 11, 15], [2006, 7, 16], 0.02, 2, 10], 0.336957], ['partial repair probe 2', [[2033, 4, 30], [2033, 7, 30], [2033, 7, 27], 0.035, 4, 0], 0.846154], ['boundary control 1', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 16], 0.05, 2, 7], 'settlement outside period'], ['boundary control 2', [[2024, 1, 15], [2024, 7, 15], [2024, 1, 15], 0.05, 2, 7], 0.0], ['normal control 1', [[2039, 6, 30], [2039, 9, 30], [2039, 6, 30], 0.035, 4, 7], 0.0], ['normal control 2', [[2041, 9, 27], [2042, 3, 27], [2041, 9, 27], 0.05, 2, 7], 0.0]], [['regression daily rate rounding stage 1', [[2050, 9, 30], [2051, 9, 30], [2051, 2, 13], 0.07, 1, 10], 2.608219], ['regression daily rate rounding stage 2', [[2028, 7, 30], [2029, 1, 30], [2028, 9, 6], 0.0125, 2, 7], 0.129076], ['partial repair probe 1', [[2027, 11, 15], [2028, 5, 15], [2028, 5, 13], 0.04125, 2, 0], 2.039835], ['partial repair probe 2', [[2000, 8, 24], [2001, 8, 24], [2001, 8, 20], 0.02, 1, 0], 1.978082], ['boundary control 1', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 15], 0.05, 2, 7], 0.0], ['boundary control 2', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 8], 0.05, 2, 7], -0.096154], ['normal control 1', [[2032, 12, 2], [2033, 1, 2], [2033, 1, 2], 0.0275, 12, 10], 0.0], ['normal control 2', [[2041, 9, 30], [2042, 9, 30], [2041, 9, 30], 0.02, 1, 0], 0.0]], [['regression daily rate rounding stage 1', [[2021, 12, 4], [2022, 3, 4], [2022, 2, 26], 0.02, 4, 0], 0.466667], ['regression daily rate rounding stage 2', [[2015, 5, 19], [2015, 11, 19], [2015, 11, 11], 0.02, 2, 7], 0.956522], ['partial repair probe 1', [[2042, 9, 20], [2042, 12, 20], [2042, 11, 10], 0.0125, 4, 0], 0.175137], ['partial repair probe 2', [[2033, 12, 31], [2034, 12, 31], [2034, 12, 22], 0.02, 1, 0], 1.950685], ['boundary control 1', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 16], 0.05, 2, 7], 'settlement outside period'], ['boundary control 2', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 8], 0.05, 2, 7], -0.096154], ['normal control 1', [[2039, 1, 31], [2039, 7, 31], [2039, 2, 16], 0.07, 2, 5], 0.309392], ['normal control 2', [[2051, 11, 14], [2051, 12, 14], [2051, 12, 10], 0.0275, 12, 5], -0.030556]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
regression daily rate rounding stage 1	`1.851256`	`1.851223`	Failed
regression daily rate rounding stage 2	`1.117716`	`1.117808`	Failed
partial repair probe 1	`0.47257`	`0.472527`	Failed
partial repair probe 2	`1.154912`	`1.154891`	Failed
boundary control 1	`settlement outside period`	`settlement outside period`	Passed
boundary control 2	`-0.096154`	`-0.096154`	Passed
normal control 1	`-0.01105`	`-0.01105`	Passed
normal control 2	`0.0`	`0.0`	Passed

SHA-256 / 6e0f42f48f78ce4887c39980066f27a145303df0162818b500fed9ccc6456445

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import datetime
from fractions import Fraction
N = 1
observations = []
def solve(prev, nxt, settle, rate, freq, exdays):
    P = datetime.date(*prev)
    Q = datetime.date(*nxt)
    S = datetime.date(*settle)
    if not (P <= S <= Q):
        return 'settlement outside period'
    if S == Q:
        return 0.0
    period = (Q - P).days
    coupon = 100 * rate / freq
    if (Q - S).days <= exdays:
        return round(-coupon * (Q - S).days / period, 6)
    days = (S - P).days
    return round(round(coupon / period, 8) * days, 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression daily rate rounding stage 1', [[2019, 7, 31], [2020, 1, 31], [2019, 11, 17], 0.0625, 2, 5], 1.851223], ['regression daily rate rounding stage 2', [[2060, 6, 3], [2061, 6, 3], [2060, 12, 24], 0.02, 1, 0], 1.117808], ['partial repair probe 1', [[2030, 9, 16], [2030, 12, 16], [2030, 12, 11], 0.02, 4, 0], 0.472527], ['partial repair probe 2', [[2049, 3, 10], [2049, 9, 10], [2049, 5, 17], 0.0625, 2, 3], 1.154891], ['boundary control 1', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 16], 0.05, 2, 7], 'settlement outside period'], ['boundary control 2', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 8], 0.05, 2, 7], -0.096154], ['normal control 1', [[2042, 11, 16], [2043, 5, 16], [2043, 5, 14], 0.02, 2, 5], -0.01105], ['normal control 2', [[2027, 1, 25], [2027, 7, 25], [2027, 7, 25], 0.0625, 2, 0], 0.0]], [['regression daily rate rounding stage 1', [[2050, 11, 30], [2050, 12, 30], [2050, 12, 18], 0.04125, 12, 7], 0.20625], ['regression daily rate rounding stage 2', [[2030, 5, 27], [2031, 5, 27], [2030, 12, 17], 0.0275, 1, 0], 1.536986], ['partial repair probe 1', [[2003, 7, 29], [2004, 1, 29], [2003, 12, 3], 0.0625, 2, 3], 2.156929], ['partial repair probe 2', [[2035, 12, 26], [2036, 12, 26], [2036, 12, 16], 0.07, 1, 0], 6.808743], ['boundary control 1', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 8], 0.05, 2, 7], -0.096154], ['boundary control 2', [[2024, 1, 15], [2024, 7, 15], [2024, 1, 15], 0.05, 2, 7], 0.0], ['normal control 1', [[2038, 2, 5], [2038, 5, 5], [2038, 5, 3], 0.02, 4, 7], -0.011236], ['normal control 2', [[2032, 2, 27], [2032, 3, 27], [2032, 2, 27], 0.0275, 12, 0], 0.0]], [['regression daily rate rounding stage 1', [[2003, 1, 22], [2003, 4, 22], [2003, 3, 31], 0.05, 4, 0], 0.944444], ['regression daily rate rounding stage 2', [[2034, 9, 16], [2034, 12, 16], [2034, 11, 25], 0.0625, 4, 0], 1.201923], ['partial repair probe 1', [[2006, 5, 15], [2006, 11, 15], [2006, 7, 16], 0.02, 2, 10], 0.336957], ['partial repair probe 2', [[2033, 4, 30], [2033, 7, 30], [2033, 7, 27], 0.035, 4, 0], 0.846154], ['boundary control 1', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 16], 0.05, 2, 7], 'settlement outside period'], ['boundary control 2', [[2024, 1, 15], [2024, 7, 15], [2024, 1, 15], 0.05, 2, 7], 0.0], ['normal control 1', [[2039, 6, 30], [2039, 9, 30], [2039, 6, 30], 0.035, 4, 7], 0.0], ['normal control 2', [[2041, 9, 27], [2042, 3, 27], [2041, 9, 27], 0.05, 2, 7], 0.0]], [['regression daily rate rounding stage 1', [[2050, 9, 30], [2051, 9, 30], [2051, 2, 13], 0.07, 1, 10], 2.608219], ['regression daily rate rounding stage 2', [[2028, 7, 30], [2029, 1, 30], [2028, 9, 6], 0.0125, 2, 7], 0.129076], ['partial repair probe 1', [[2027, 11, 15], [2028, 5, 15], [2028, 5, 13], 0.04125, 2, 0], 2.039835], ['partial repair probe 2', [[2000, 8, 24], [2001, 8, 24], [2001, 8, 20], 0.02, 1, 0], 1.978082], ['boundary control 1', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 15], 0.05, 2, 7], 0.0], ['boundary control 2', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 8], 0.05, 2, 7], -0.096154], ['normal control 1', [[2032, 12, 2], [2033, 1, 2], [2033, 1, 2], 0.0275, 12, 10], 0.0], ['normal control 2', [[2041, 9, 30], [2042, 9, 30], [2041, 9, 30], 0.02, 1, 0], 0.0]], [['regression daily rate rounding stage 1', [[2021, 12, 4], [2022, 3, 4], [2022, 2, 26], 0.02, 4, 0], 0.466667], ['regression daily rate rounding stage 2', [[2015, 5, 19], [2015, 11, 19], [2015, 11, 11], 0.02, 2, 7], 0.956522], ['partial repair probe 1', [[2042, 9, 20], [2042, 12, 20], [2042, 11, 10], 0.0125, 4, 0], 0.175137], ['partial repair probe 2', [[2033, 12, 31], [2034, 12, 31], [2034, 12, 22], 0.02, 1, 0], 1.950685], ['boundary control 1', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 16], 0.05, 2, 7], 'settlement outside period'], ['boundary control 2', [[2024, 1, 15], [2024, 7, 15], [2024, 7, 8], 0.05, 2, 7], -0.096154], ['normal control 1', [[2039, 1, 31], [2039, 7, 31], [2039, 2, 16], 0.07, 2, 5], 0.309392], ['normal control 2', [[2051, 11, 14], [2051, 12, 14], [2051, 12, 10], 0.0275, 12, 5], -0.030556]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
regression daily rate rounding stage 1	`1.851223`	`1.851223`	Passed
regression daily rate rounding stage 2	`1.117808`	`1.117808`	Passed
partial repair probe 1	`0.472528`	`0.472527`	Failed
partial repair probe 2	`1.154892`	`1.154891`	Failed
boundary control 1	`settlement outside period`	`settlement outside period`	Passed
boundary control 2	`-0.096154`	`-0.096154`	Passed
normal control 1	`-0.01105`	`-0.01105`	Passed
normal control 2	`0.0`	`0.0`	Passed

SHA-256 / 2f04b8d49eebc9f2493c59ea5bd4685e976b26076437774303ac211f95664ba5

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Verification & scope

A deterministic toy contract stated explicitly in the contract field; no claim of conformance to any published convention text. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:46:49.973271+00:00.

Case digest / 5e918db5d75946f654d71bca97a66ec993a10ce6d0eafa5169ce3b2de26a4674