FA-61196 / Bond day-count conventions / Open access

Canadian-style semi-annual accrued interest: early-period accrual uses the actual period length · case 01

Accrued interest follows an actual/actual pattern instead of the 365-day basis.

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

ROOT CAUSE

The early branch divides by the coupon period days and pays half a coupon per period.

VERIFIED REPAIR

Accrue c*days/365 in the early part of the period.

Unsuccessful approach: Using 366 in leap years is still not the fixed 365-day basis.

Case contract

Inputs prev and next coupon dates, settlement in [prev, next) and annual rate (semi-annual coupons). c = 100*rate, days = days(prev, settle). If days >= 183 accrued = c/2 - c*days(settle, next)/365, else accrued = c*days/365. Round 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
N = 1
observations = []
def solve(prev, nxt, settle, rate):
    P = datetime.date(*prev)
    Q = datetime.date(*nxt)
    S = datetime.date(*settle)
    days = (S - P).days
    c = 100 * rate
    if days >= 183:
        acc = c / 2 - c * (Q - S).days / 365
    else:
        acc = c / 2 * days / (Q - P).days
    return round(acc, 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression forward accrual basis 1', [[2027, 9, 8], [2028, 3, 8], [2028, 3, 7], 0.0825], 4.091096], ['regression forward accrual basis 2', [[2029, 9, 13], [2030, 3, 13], [2030, 3, 12], 0.05], 2.465753], ['partial repair probe 1', [[2032, 10, 3], [2033, 4, 3], [2032, 10, 16], 0.0825], 0.293836], ['partial repair probe 2', [[2016, 8, 27], [2017, 2, 27], [2016, 11, 15], 0.025], 0.547945], ['boundary control 1', [[2024, 1, 1], [2024, 7, 1], [2024, 1, 1], 0.05], 0.0], ['normal control 1', [[2027, 7, 31], [2028, 1, 31], [2028, 1, 30], 0.05], 2.486301], ['normal control 2', [[2015, 7, 7], [2016, 1, 7], [2016, 1, 6], 0.025], 1.243151], ['normal control 3', [[2019, 3, 22], [2019, 9, 22], [2019, 9, 21], 0.05], 2.486301]], [['regression forward accrual basis 1', [[2022, 1, 16], [2022, 7, 16], [2022, 7, 15], 0.025], 1.232877], ['regression forward accrual basis 2', [[2038, 9, 30], [2039, 3, 30], [2039, 3, 29], 0.025], 1.232877], ['partial repair probe 1', [[2032, 7, 4], [2033, 1, 4], [2032, 8, 12], 0.025], 0.267123], ['partial repair probe 2', [[2040, 5, 31], [2040, 11, 30], [2040, 11, 29], 0.0125], 0.623288], ['boundary control 1', [[2024, 1, 1], [2024, 7, 1], [2024, 1, 1], 0.05], 0.0], ['normal control 1', [[2018, 5, 18], [2018, 11, 18], [2018, 11, 17], 0.0125], 0.621575], ['normal control 2', [[2027, 3, 9], [2027, 9, 9], [2027, 9, 8], 0.025], 1.243151], ['normal control 3', [[2035, 5, 1], [2035, 11, 1], [2035, 10, 31], 0.025], 1.243151]], [['regression forward accrual basis 1', [[2020, 2, 28], [2020, 8, 28], [2020, 8, 26], 0.0125], 0.616438], ['regression forward accrual basis 2', [[2015, 8, 30], [2016, 2, 29], [2016, 2, 28], 0.0375], 1.869863], ['partial repair probe 1', [[2036, 6, 30], [2036, 12, 30], [2036, 12, 29], 0.0825], 4.113699], ['partial repair probe 2', [[2040, 4, 25], [2040, 10, 25], [2040, 10, 23], 0.0825], 4.091096], ['boundary control 1', [[2024, 1, 1], [2024, 7, 1], [2024, 1, 1], 0.05], 0.0], ['normal control 1', [[2034, 5, 18], [2034, 11, 18], [2034, 11, 17], 0.025], 1.243151], ['normal control 2', [[2017, 8, 12], [2018, 2, 12], [2018, 2, 11], 0.05], 2.486301], ['normal control 3', [[2015, 8, 25], [2016, 2, 25], [2016, 2, 24], 0.0825], 4.102397]], [['regression forward accrual basis 1', [[2018, 4, 11], [2018, 10, 11], [2018, 10, 10], 0.0375], 1.869863], ['regression forward accrual basis 2', [[2021, 6, 30], [2021, 12, 30], [2021, 12, 29], 0.0125], 0.623288], ['partial repair probe 1', [[2028, 2, 28], [2028, 8, 28], [2028, 8, 27], 0.0125], 0.619863], ['partial repair probe 2', [[2016, 9, 30], [2017, 3, 30], [2016, 10, 31], 0.025], 0.212329], ['boundary control 1', [[2024, 1, 1], [2024, 7, 1], [2024, 1, 1], 0.05], 0.0], ['normal control 1', [[2015, 7, 11], [2016, 1, 11], [2016, 1, 10], 0.0125], 0.621575], ['normal control 2', [[2020, 3, 18], [2020, 9, 18], [2020, 9, 17], 0.05], 2.486301], ['normal control 3', [[2038, 8, 4], [2039, 2, 4], [2039, 2, 3], 0.05], 2.486301]], [['regression forward accrual basis 1', [[2019, 11, 1], [2020, 5, 1], [2020, 4, 27], 0.0825], 4.023288], ['regression forward accrual basis 2', [[2040, 2, 28], [2040, 8, 28], [2040, 8, 25], 0.0125], 0.613014], ['partial repair probe 1', [[2016, 8, 20], [2017, 2, 20], [2016, 8, 31], 0.05], 0.150685], ['partial repair probe 2', [[2028, 4, 2], [2028, 10, 2], [2028, 10, 1], 0.0125], 0.623288], ['boundary control 1', [[2024, 1, 1], [2024, 7, 1], [2024, 1, 1], 0.05], 0.0], ['normal control 1', [[2021, 5, 9], [2021, 11, 9], [2021, 11, 8], 0.025], 1.243151], ['normal control 2', [[2037, 5, 1], [2037, 11, 1], [2037, 10, 31], 0.025], 1.243151], ['normal control 3', [[2027, 5, 5], [2027, 11, 5], [2027, 11, 4], 0.025], 1.243151]]]
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 forward accrual basis 1	`4.102335`	`4.091096`	Failed
regression forward accrual basis 2	`2.486188`	`2.465753`	Failed
partial repair probe 1	`0.294643`	`0.293836`	Failed
partial repair probe 2	`0.543478`	`0.547945`	Failed
boundary control 1	`0.0`	`0.0`	Passed
normal control 1	`2.486301`	`2.486301`	Passed
normal control 2	`1.243151`	`1.243151`	Passed
normal control 3	`2.486301`	`2.486301`	Passed

SHA-256 / fad35280c46a674af068c7f31f3ba20037dc9129fdeaaf3c3140c74c8f80dd49

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import datetime
N = 1
observations = []
def solve(prev, nxt, settle, rate):
    P = datetime.date(*prev)
    Q = datetime.date(*nxt)
    S = datetime.date(*settle)
    days = (S - P).days
    c = 100 * rate
    if days >= 183:
        acc = c / 2 - c * (Q - S).days / 365
    else:
        acc = c * days / (366 if P.year % 4 == 0 else 365)
    return round(acc, 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression forward accrual basis 1', [[2027, 9, 8], [2028, 3, 8], [2028, 3, 7], 0.0825], 4.091096], ['regression forward accrual basis 2', [[2029, 9, 13], [2030, 3, 13], [2030, 3, 12], 0.05], 2.465753], ['partial repair probe 1', [[2032, 10, 3], [2033, 4, 3], [2032, 10, 16], 0.0825], 0.293836], ['partial repair probe 2', [[2016, 8, 27], [2017, 2, 27], [2016, 11, 15], 0.025], 0.547945], ['boundary control 1', [[2024, 1, 1], [2024, 7, 1], [2024, 1, 1], 0.05], 0.0], ['normal control 1', [[2027, 7, 31], [2028, 1, 31], [2028, 1, 30], 0.05], 2.486301], ['normal control 2', [[2015, 7, 7], [2016, 1, 7], [2016, 1, 6], 0.025], 1.243151], ['normal control 3', [[2019, 3, 22], [2019, 9, 22], [2019, 9, 21], 0.05], 2.486301]], [['regression forward accrual basis 1', [[2022, 1, 16], [2022, 7, 16], [2022, 7, 15], 0.025], 1.232877], ['regression forward accrual basis 2', [[2038, 9, 30], [2039, 3, 30], [2039, 3, 29], 0.025], 1.232877], ['partial repair probe 1', [[2032, 7, 4], [2033, 1, 4], [2032, 8, 12], 0.025], 0.267123], ['partial repair probe 2', [[2040, 5, 31], [2040, 11, 30], [2040, 11, 29], 0.0125], 0.623288], ['boundary control 1', [[2024, 1, 1], [2024, 7, 1], [2024, 1, 1], 0.05], 0.0], ['normal control 1', [[2018, 5, 18], [2018, 11, 18], [2018, 11, 17], 0.0125], 0.621575], ['normal control 2', [[2027, 3, 9], [2027, 9, 9], [2027, 9, 8], 0.025], 1.243151], ['normal control 3', [[2035, 5, 1], [2035, 11, 1], [2035, 10, 31], 0.025], 1.243151]], [['regression forward accrual basis 1', [[2020, 2, 28], [2020, 8, 28], [2020, 8, 26], 0.0125], 0.616438], ['regression forward accrual basis 2', [[2015, 8, 30], [2016, 2, 29], [2016, 2, 28], 0.0375], 1.869863], ['partial repair probe 1', [[2036, 6, 30], [2036, 12, 30], [2036, 12, 29], 0.0825], 4.113699], ['partial repair probe 2', [[2040, 4, 25], [2040, 10, 25], [2040, 10, 23], 0.0825], 4.091096], ['boundary control 1', [[2024, 1, 1], [2024, 7, 1], [2024, 1, 1], 0.05], 0.0], ['normal control 1', [[2034, 5, 18], [2034, 11, 18], [2034, 11, 17], 0.025], 1.243151], ['normal control 2', [[2017, 8, 12], [2018, 2, 12], [2018, 2, 11], 0.05], 2.486301], ['normal control 3', [[2015, 8, 25], [2016, 2, 25], [2016, 2, 24], 0.0825], 4.102397]], [['regression forward accrual basis 1', [[2018, 4, 11], [2018, 10, 11], [2018, 10, 10], 0.0375], 1.869863], ['regression forward accrual basis 2', [[2021, 6, 30], [2021, 12, 30], [2021, 12, 29], 0.0125], 0.623288], ['partial repair probe 1', [[2028, 2, 28], [2028, 8, 28], [2028, 8, 27], 0.0125], 0.619863], ['partial repair probe 2', [[2016, 9, 30], [2017, 3, 30], [2016, 10, 31], 0.025], 0.212329], ['boundary control 1', [[2024, 1, 1], [2024, 7, 1], [2024, 1, 1], 0.05], 0.0], ['normal control 1', [[2015, 7, 11], [2016, 1, 11], [2016, 1, 10], 0.0125], 0.621575], ['normal control 2', [[2020, 3, 18], [2020, 9, 18], [2020, 9, 17], 0.05], 2.486301], ['normal control 3', [[2038, 8, 4], [2039, 2, 4], [2039, 2, 3], 0.05], 2.486301]], [['regression forward accrual basis 1', [[2019, 11, 1], [2020, 5, 1], [2020, 4, 27], 0.0825], 4.023288], ['regression forward accrual basis 2', [[2040, 2, 28], [2040, 8, 28], [2040, 8, 25], 0.0125], 0.613014], ['partial repair probe 1', [[2016, 8, 20], [2017, 2, 20], [2016, 8, 31], 0.05], 0.150685], ['partial repair probe 2', [[2028, 4, 2], [2028, 10, 2], [2028, 10, 1], 0.0125], 0.623288], ['boundary control 1', [[2024, 1, 1], [2024, 7, 1], [2024, 1, 1], 0.05], 0.0], ['normal control 1', [[2021, 5, 9], [2021, 11, 9], [2021, 11, 8], 0.025], 1.243151], ['normal control 2', [[2037, 5, 1], [2037, 11, 1], [2037, 10, 31], 0.025], 1.243151], ['normal control 3', [[2027, 5, 5], [2027, 11, 5], [2027, 11, 4], 0.025], 1.243151]]]
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 forward accrual basis 1	`4.091096`	`4.091096`	Passed
regression forward accrual basis 2	`2.465753`	`2.465753`	Passed
partial repair probe 1	`0.293033`	`0.293836`	Failed
partial repair probe 2	`0.546448`	`0.547945`	Failed
boundary control 1	`0.0`	`0.0`	Passed
normal control 1	`2.486301`	`2.486301`	Passed
normal control 2	`1.243151`	`1.243151`	Passed
normal control 3	`2.486301`	`2.486301`	Passed

SHA-256 / ab43774304bec9f02db69ff0ee295fa19a664fb1e25a8fa31b63d6a5472aec0f

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import datetime
N = 1
observations = []
def solve(prev, nxt, settle, rate):
    P = datetime.date(*prev)
    Q = datetime.date(*nxt)
    S = datetime.date(*settle)
    days = (S - P).days
    c = 100 * rate
    if days >= 183:
        acc = c / 2 - c * (Q - S).days / 365
    else:
        acc = c * days / 365
    return round(acc, 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression forward accrual basis 1', [[2027, 9, 8], [2028, 3, 8], [2028, 3, 7], 0.0825], 4.091096], ['regression forward accrual basis 2', [[2029, 9, 13], [2030, 3, 13], [2030, 3, 12], 0.05], 2.465753], ['partial repair probe 1', [[2032, 10, 3], [2033, 4, 3], [2032, 10, 16], 0.0825], 0.293836], ['partial repair probe 2', [[2016, 8, 27], [2017, 2, 27], [2016, 11, 15], 0.025], 0.547945], ['boundary control 1', [[2024, 1, 1], [2024, 7, 1], [2024, 1, 1], 0.05], 0.0], ['normal control 1', [[2027, 7, 31], [2028, 1, 31], [2028, 1, 30], 0.05], 2.486301], ['normal control 2', [[2015, 7, 7], [2016, 1, 7], [2016, 1, 6], 0.025], 1.243151], ['normal control 3', [[2019, 3, 22], [2019, 9, 22], [2019, 9, 21], 0.05], 2.486301]], [['regression forward accrual basis 1', [[2022, 1, 16], [2022, 7, 16], [2022, 7, 15], 0.025], 1.232877], ['regression forward accrual basis 2', [[2038, 9, 30], [2039, 3, 30], [2039, 3, 29], 0.025], 1.232877], ['partial repair probe 1', [[2032, 7, 4], [2033, 1, 4], [2032, 8, 12], 0.025], 0.267123], ['partial repair probe 2', [[2040, 5, 31], [2040, 11, 30], [2040, 11, 29], 0.0125], 0.623288], ['boundary control 1', [[2024, 1, 1], [2024, 7, 1], [2024, 1, 1], 0.05], 0.0], ['normal control 1', [[2018, 5, 18], [2018, 11, 18], [2018, 11, 17], 0.0125], 0.621575], ['normal control 2', [[2027, 3, 9], [2027, 9, 9], [2027, 9, 8], 0.025], 1.243151], ['normal control 3', [[2035, 5, 1], [2035, 11, 1], [2035, 10, 31], 0.025], 1.243151]], [['regression forward accrual basis 1', [[2020, 2, 28], [2020, 8, 28], [2020, 8, 26], 0.0125], 0.616438], ['regression forward accrual basis 2', [[2015, 8, 30], [2016, 2, 29], [2016, 2, 28], 0.0375], 1.869863], ['partial repair probe 1', [[2036, 6, 30], [2036, 12, 30], [2036, 12, 29], 0.0825], 4.113699], ['partial repair probe 2', [[2040, 4, 25], [2040, 10, 25], [2040, 10, 23], 0.0825], 4.091096], ['boundary control 1', [[2024, 1, 1], [2024, 7, 1], [2024, 1, 1], 0.05], 0.0], ['normal control 1', [[2034, 5, 18], [2034, 11, 18], [2034, 11, 17], 0.025], 1.243151], ['normal control 2', [[2017, 8, 12], [2018, 2, 12], [2018, 2, 11], 0.05], 2.486301], ['normal control 3', [[2015, 8, 25], [2016, 2, 25], [2016, 2, 24], 0.0825], 4.102397]], [['regression forward accrual basis 1', [[2018, 4, 11], [2018, 10, 11], [2018, 10, 10], 0.0375], 1.869863], ['regression forward accrual basis 2', [[2021, 6, 30], [2021, 12, 30], [2021, 12, 29], 0.0125], 0.623288], ['partial repair probe 1', [[2028, 2, 28], [2028, 8, 28], [2028, 8, 27], 0.0125], 0.619863], ['partial repair probe 2', [[2016, 9, 30], [2017, 3, 30], [2016, 10, 31], 0.025], 0.212329], ['boundary control 1', [[2024, 1, 1], [2024, 7, 1], [2024, 1, 1], 0.05], 0.0], ['normal control 1', [[2015, 7, 11], [2016, 1, 11], [2016, 1, 10], 0.0125], 0.621575], ['normal control 2', [[2020, 3, 18], [2020, 9, 18], [2020, 9, 17], 0.05], 2.486301], ['normal control 3', [[2038, 8, 4], [2039, 2, 4], [2039, 2, 3], 0.05], 2.486301]], [['regression forward accrual basis 1', [[2019, 11, 1], [2020, 5, 1], [2020, 4, 27], 0.0825], 4.023288], ['regression forward accrual basis 2', [[2040, 2, 28], [2040, 8, 28], [2040, 8, 25], 0.0125], 0.613014], ['partial repair probe 1', [[2016, 8, 20], [2017, 2, 20], [2016, 8, 31], 0.05], 0.150685], ['partial repair probe 2', [[2028, 4, 2], [2028, 10, 2], [2028, 10, 1], 0.0125], 0.623288], ['boundary control 1', [[2024, 1, 1], [2024, 7, 1], [2024, 1, 1], 0.05], 0.0], ['normal control 1', [[2021, 5, 9], [2021, 11, 9], [2021, 11, 8], 0.025], 1.243151], ['normal control 2', [[2037, 5, 1], [2037, 11, 1], [2037, 10, 31], 0.025], 1.243151], ['normal control 3', [[2027, 5, 5], [2027, 11, 5], [2027, 11, 4], 0.025], 1.243151]]]
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 forward accrual basis 1	`4.091096`	`4.091096`	Passed
regression forward accrual basis 2	`2.465753`	`2.465753`	Passed
partial repair probe 1	`0.293836`	`0.293836`	Passed
partial repair probe 2	`0.547945`	`0.547945`	Passed
boundary control 1	`0.0`	`0.0`	Passed
normal control 1	`2.486301`	`2.486301`	Passed
normal control 2	`1.243151`	`1.243151`	Passed
normal control 3	`2.486301`	`2.486301`	Passed

SHA-256 / a0bf2f05b1e711e5db5ebda6e236d5aa1e7ef44217eec091adac8fe3c66fc6f2

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 2026-09-29T14:46:52.860856+00:00.

Case digest / b3b05db8a0629d8abde3a84a7dd5a7be1c09b33b8ee0cdd158f76bde432679a8