FA-61221 / Bond day-count conventions / Open access

Irregular final coupon amount: the extension beyond q1 is measured against the first notional period · case 01

Long final coupons are misstated when consecutive notional periods have different lengths.

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

ROOT CAUSE

The extension fraction divides by days(prev, q1) instead of days(q1, q2).

VERIFIED REPAIR

Divide the extension by the length of the second notional period.

Unsuccessful approach: Dividing by the whole irregular period mixes the regular and extension parts.

Case contract

Inputs the last regular coupon date prev, maturity (prev < maturity <= prev + 2 periods), months per period and annual rate. Quasi dates are prev shifted forward k*months with the prev day clamped to month length. c = 100*rate/freq. Short final period (maturity <= q1): c*days(prev,mat)/days(prev,q1). Long final period: c*(1 + days(q1,mat)/days(q1,q2)). 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
from fractions import Fraction
N = 1
observations = []
def solve(prev, maturity, months, rate):
    def mlen(y, m):
        if m == 2:
            return 29 if (y % 4 == 0 and y % 100 != 0) or y % 400 == 0 else 28
        return 30 if m in (4, 6, 9, 11) else 31
    P = datetime.date(*prev)
    M = datetime.date(*maturity)
    freq = 12 // months
    def fwd(k):
        t = P.year * 12 + P.month - 1 + k * months
        y, m = t // 12, t % 12 + 1
        return datetime.date(y, m, min(P.day, mlen(y, m)))
    c = 100 * Fraction(str(rate)) / freq
    q1 = fwd(1)
    if M <= q1:
        frac = Fraction((M - P).days, (q1 - P).days)
    else:
        q2 = fwd(2)
        frac = 1 + Fraction((M - q1).days, (q1 - P).days)
    return round(float(c * frac), 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression long stub extension denominator 1', [[2015, 5, 30], [2017, 1, 1], 12, 0.05], 7.958904], ['regression long stub extension denominator 2', [[2017, 7, 31], [2017, 9, 30], 1, 0.045], 0.75], ['partial repair probe 1', [[2033, 2, 28], [2034, 11, 6], 12, 0.03], 5.063014], ['partial repair probe 2', [[2017, 11, 30], [2019, 10, 26], 12, 0.045], 8.568493], ['boundary control 1', [[2024, 1, 31], [2024, 4, 30], 6, 0.05], 1.236264], ['boundary control 2', [[2024, 1, 31], [2024, 7, 31], 6, 0.05], 2.5], ['normal control 1', [[2042, 3, 31], [2042, 7, 7], 6, 0.0725], 1.941257], ['normal control 2', [[2014, 4, 7], [2014, 10, 7], 6, 0.045], 2.25]], [['regression long stub extension denominator 1', [[2016, 10, 30], [2017, 8, 24], 6, 0.045], 3.67623], ['regression long stub extension denominator 2', [[2045, 9, 30], [2046, 9, 30], 6, 0.05], 5.0], ['partial repair probe 1', [[2023, 9, 30], [2024, 3, 27], 3, 0.045], 2.212912], ['partial repair probe 2', [[2034, 7, 4], [2034, 10, 5], 3, 0.045], 1.137228], ['boundary control 1', [[2024, 1, 31], [2024, 4, 30], 6, 0.05], 1.236264], ['boundary control 2', [[2024, 1, 31], [2024, 7, 31], 6, 0.05], 2.5], ['normal control 1', [[2013, 4, 3], [2013, 11, 23], 12, 0.03], 1.923288], ['normal control 2', [[2018, 6, 30], [2018, 9, 30], 3, 0.05], 1.25]], [['regression long stub extension denominator 1', [[2019, 2, 28], [2019, 8, 29], 6, 0.05], 2.513587], ['regression long stub extension denominator 2', [[2017, 12, 1], [2018, 3, 30], 3, 0.03], 0.986413], ['partial repair probe 1', [[2039, 6, 30], [2040, 3, 13], 6, 0.05], 3.510929], ['partial repair probe 2', [[2013, 10, 29], [2014, 12, 28], 12, 0.03], 3.493151], ['boundary control 1', [[2024, 1, 31], [2024, 4, 30], 6, 0.05], 1.236264], ['boundary control 2', [[2024, 1, 31], [2024, 7, 31], 6, 0.05], 2.5], ['normal control 1', [[2026, 7, 31], [2026, 8, 27], 1, 0.0725], 0.52621], ['normal control 2', [[2018, 7, 21], [2018, 8, 3], 6, 0.03], 0.105978]], [['regression long stub extension denominator 1', [[2020, 9, 7], [2021, 7, 20], 6, 0.0725], 6.284647], ['regression long stub extension denominator 2', [[2034, 11, 18], [2035, 11, 10], 6, 0.03], 2.934783], ['partial repair probe 1', [[2005, 6, 30], [2007, 6, 30], 12, 0.045], 9.0], ['partial repair probe 2', [[2037, 5, 26], [2038, 8, 20], 12, 0.03], 3.706849], ['boundary control 1', [[2024, 1, 31], [2024, 4, 30], 6, 0.05], 1.236264], ['boundary control 2', [[2024, 1, 31], [2024, 7, 31], 6, 0.05], 2.5], ['normal control 1', [[2014, 4, 29], [2014, 5, 3], 1, 0.0725], 0.080556], ['normal control 2', [[2006, 1, 11], [2006, 7, 11], 6, 0.03], 1.5]], [['regression long stub extension denominator 1', [[2009, 2, 28], [2009, 4, 5], 1, 0.05], 0.524194], ['regression long stub extension denominator 2', [[2005, 11, 30], [2006, 1, 5], 1, 0.03], 0.298387], ['partial repair probe 1', [[2023, 4, 28], [2024, 1, 14], 6, 0.05], 3.565574], ['partial repair probe 2', [[2023, 6, 20], [2024, 6, 20], 6, 0.045], 4.5], ['boundary control 1', [[2024, 1, 31], [2024, 4, 30], 6, 0.05], 1.236264], ['boundary control 2', [[2024, 1, 31], [2024, 7, 31], 6, 0.05], 2.5], ['normal control 1', [[2042, 12, 1], [2043, 3, 10], 12, 0.03], 0.813699], ['normal control 2', [[2030, 6, 29], [2030, 8, 27], 3, 0.03], 0.480978]]]
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 long stub extension denominator 1	`7.95082`	`7.958904`	Failed
regression long stub extension denominator 2	`0.737903`	`0.75`	Failed
partial repair probe 1	`5.063014`	`5.063014`	Passed
partial repair probe 2	`8.568493`	`8.568493`	Passed
boundary control 1	`1.236264`	`1.236264`	Passed
boundary control 2	`2.5`	`2.5`	Passed
normal control 1	`1.941257`	`1.941257`	Passed
normal control 2	`2.25`	`2.25`	Passed

SHA-256 / d2e5c02a33dee78ea70833ef35f0ebdfea7b980a29bde6560c928b4d4cc118f9

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, maturity, months, rate):
    def mlen(y, m):
        if m == 2:
            return 29 if (y % 4 == 0 and y % 100 != 0) or y % 400 == 0 else 28
        return 30 if m in (4, 6, 9, 11) else 31
    P = datetime.date(*prev)
    M = datetime.date(*maturity)
    freq = 12 // months
    def fwd(k):
        t = P.year * 12 + P.month - 1 + k * months
        y, m = t // 12, t % 12 + 1
        return datetime.date(y, m, min(P.day, mlen(y, m)))
    c = 100 * Fraction(str(rate)) / freq
    q1 = fwd(1)
    if M <= q1:
        frac = Fraction((M - P).days, (q1 - P).days)
    else:
        q2 = fwd(2)
        frac = 1 + Fraction((M - q1).days, (M - P).days)
    return round(float(c * frac), 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression long stub extension denominator 1', [[2015, 5, 30], [2017, 1, 1], 12, 0.05], 7.958904], ['regression long stub extension denominator 2', [[2017, 7, 31], [2017, 9, 30], 1, 0.045], 0.75], ['partial repair probe 1', [[2033, 2, 28], [2034, 11, 6], 12, 0.03], 5.063014], ['partial repair probe 2', [[2017, 11, 30], [2019, 10, 26], 12, 0.045], 8.568493], ['boundary control 1', [[2024, 1, 31], [2024, 4, 30], 6, 0.05], 1.236264], ['boundary control 2', [[2024, 1, 31], [2024, 7, 31], 6, 0.05], 2.5], ['normal control 1', [[2042, 3, 31], [2042, 7, 7], 6, 0.0725], 1.941257], ['normal control 2', [[2014, 4, 7], [2014, 10, 7], 6, 0.045], 2.25]], [['regression long stub extension denominator 1', [[2016, 10, 30], [2017, 8, 24], 6, 0.045], 3.67623], ['regression long stub extension denominator 2', [[2045, 9, 30], [2046, 9, 30], 6, 0.05], 5.0], ['partial repair probe 1', [[2023, 9, 30], [2024, 3, 27], 3, 0.045], 2.212912], ['partial repair probe 2', [[2034, 7, 4], [2034, 10, 5], 3, 0.045], 1.137228], ['boundary control 1', [[2024, 1, 31], [2024, 4, 30], 6, 0.05], 1.236264], ['boundary control 2', [[2024, 1, 31], [2024, 7, 31], 6, 0.05], 2.5], ['normal control 1', [[2013, 4, 3], [2013, 11, 23], 12, 0.03], 1.923288], ['normal control 2', [[2018, 6, 30], [2018, 9, 30], 3, 0.05], 1.25]], [['regression long stub extension denominator 1', [[2019, 2, 28], [2019, 8, 29], 6, 0.05], 2.513587], ['regression long stub extension denominator 2', [[2017, 12, 1], [2018, 3, 30], 3, 0.03], 0.986413], ['partial repair probe 1', [[2039, 6, 30], [2040, 3, 13], 6, 0.05], 3.510929], ['partial repair probe 2', [[2013, 10, 29], [2014, 12, 28], 12, 0.03], 3.493151], ['boundary control 1', [[2024, 1, 31], [2024, 4, 30], 6, 0.05], 1.236264], ['boundary control 2', [[2024, 1, 31], [2024, 7, 31], 6, 0.05], 2.5], ['normal control 1', [[2026, 7, 31], [2026, 8, 27], 1, 0.0725], 0.52621], ['normal control 2', [[2018, 7, 21], [2018, 8, 3], 6, 0.03], 0.105978]], [['regression long stub extension denominator 1', [[2020, 9, 7], [2021, 7, 20], 6, 0.0725], 6.284647], ['regression long stub extension denominator 2', [[2034, 11, 18], [2035, 11, 10], 6, 0.03], 2.934783], ['partial repair probe 1', [[2005, 6, 30], [2007, 6, 30], 12, 0.045], 9.0], ['partial repair probe 2', [[2037, 5, 26], [2038, 8, 20], 12, 0.03], 3.706849], ['boundary control 1', [[2024, 1, 31], [2024, 4, 30], 6, 0.05], 1.236264], ['boundary control 2', [[2024, 1, 31], [2024, 7, 31], 6, 0.05], 2.5], ['normal control 1', [[2014, 4, 29], [2014, 5, 3], 1, 0.0725], 0.080556], ['normal control 2', [[2006, 1, 11], [2006, 7, 11], 6, 0.03], 1.5]], [['regression long stub extension denominator 1', [[2009, 2, 28], [2009, 4, 5], 1, 0.05], 0.524194], ['regression long stub extension denominator 2', [[2005, 11, 30], [2006, 1, 5], 1, 0.03], 0.298387], ['partial repair probe 1', [[2023, 4, 28], [2024, 1, 14], 6, 0.05], 3.565574], ['partial repair probe 2', [[2023, 6, 20], [2024, 6, 20], 6, 0.045], 4.5], ['boundary control 1', [[2024, 1, 31], [2024, 4, 30], 6, 0.05], 1.236264], ['boundary control 2', [[2024, 1, 31], [2024, 7, 31], 6, 0.05], 2.5], ['normal control 1', [[2042, 12, 1], [2043, 3, 10], 12, 0.03], 0.813699], ['normal control 2', [[2030, 6, 29], [2030, 8, 27], 3, 0.03], 0.480978]]]
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 long stub extension denominator 1	`6.85567`	`7.958904`	Failed
regression long stub extension denominator 2	`0.559426`	`0.75`	Failed
partial repair probe 1	`4.222403`	`5.063014`	Failed
partial repair probe 2	`6.636691`	`8.568493`	Failed
boundary control 1	`1.236264`	`1.236264`	Passed
boundary control 2	`2.5`	`2.5`	Passed
normal control 1	`1.941257`	`1.941257`	Passed
normal control 2	`2.25`	`2.25`	Passed

SHA-256 / c9d71f236290460fd4e13edbab68557b1b4cff33da1a0dc3547f582db3c3922d

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import datetime
from fractions import Fraction
N = 1
observations = []
def solve(prev, maturity, months, rate):
    def mlen(y, m):
        if m == 2:
            return 29 if (y % 4 == 0 and y % 100 != 0) or y % 400 == 0 else 28
        return 30 if m in (4, 6, 9, 11) else 31
    P = datetime.date(*prev)
    M = datetime.date(*maturity)
    freq = 12 // months
    def fwd(k):
        t = P.year * 12 + P.month - 1 + k * months
        y, m = t // 12, t % 12 + 1
        return datetime.date(y, m, min(P.day, mlen(y, m)))
    c = 100 * Fraction(str(rate)) / freq
    q1 = fwd(1)
    if M <= q1:
        frac = Fraction((M - P).days, (q1 - P).days)
    else:
        q2 = fwd(2)
        frac = 1 + Fraction((M - q1).days, (q2 - q1).days)
    return round(float(c * frac), 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression long stub extension denominator 1', [[2015, 5, 30], [2017, 1, 1], 12, 0.05], 7.958904], ['regression long stub extension denominator 2', [[2017, 7, 31], [2017, 9, 30], 1, 0.045], 0.75], ['partial repair probe 1', [[2033, 2, 28], [2034, 11, 6], 12, 0.03], 5.063014], ['partial repair probe 2', [[2017, 11, 30], [2019, 10, 26], 12, 0.045], 8.568493], ['boundary control 1', [[2024, 1, 31], [2024, 4, 30], 6, 0.05], 1.236264], ['boundary control 2', [[2024, 1, 31], [2024, 7, 31], 6, 0.05], 2.5], ['normal control 1', [[2042, 3, 31], [2042, 7, 7], 6, 0.0725], 1.941257], ['normal control 2', [[2014, 4, 7], [2014, 10, 7], 6, 0.045], 2.25]], [['regression long stub extension denominator 1', [[2016, 10, 30], [2017, 8, 24], 6, 0.045], 3.67623], ['regression long stub extension denominator 2', [[2045, 9, 30], [2046, 9, 30], 6, 0.05], 5.0], ['partial repair probe 1', [[2023, 9, 30], [2024, 3, 27], 3, 0.045], 2.212912], ['partial repair probe 2', [[2034, 7, 4], [2034, 10, 5], 3, 0.045], 1.137228], ['boundary control 1', [[2024, 1, 31], [2024, 4, 30], 6, 0.05], 1.236264], ['boundary control 2', [[2024, 1, 31], [2024, 7, 31], 6, 0.05], 2.5], ['normal control 1', [[2013, 4, 3], [2013, 11, 23], 12, 0.03], 1.923288], ['normal control 2', [[2018, 6, 30], [2018, 9, 30], 3, 0.05], 1.25]], [['regression long stub extension denominator 1', [[2019, 2, 28], [2019, 8, 29], 6, 0.05], 2.513587], ['regression long stub extension denominator 2', [[2017, 12, 1], [2018, 3, 30], 3, 0.03], 0.986413], ['partial repair probe 1', [[2039, 6, 30], [2040, 3, 13], 6, 0.05], 3.510929], ['partial repair probe 2', [[2013, 10, 29], [2014, 12, 28], 12, 0.03], 3.493151], ['boundary control 1', [[2024, 1, 31], [2024, 4, 30], 6, 0.05], 1.236264], ['boundary control 2', [[2024, 1, 31], [2024, 7, 31], 6, 0.05], 2.5], ['normal control 1', [[2026, 7, 31], [2026, 8, 27], 1, 0.0725], 0.52621], ['normal control 2', [[2018, 7, 21], [2018, 8, 3], 6, 0.03], 0.105978]], [['regression long stub extension denominator 1', [[2020, 9, 7], [2021, 7, 20], 6, 0.0725], 6.284647], ['regression long stub extension denominator 2', [[2034, 11, 18], [2035, 11, 10], 6, 0.03], 2.934783], ['partial repair probe 1', [[2005, 6, 30], [2007, 6, 30], 12, 0.045], 9.0], ['partial repair probe 2', [[2037, 5, 26], [2038, 8, 20], 12, 0.03], 3.706849], ['boundary control 1', [[2024, 1, 31], [2024, 4, 30], 6, 0.05], 1.236264], ['boundary control 2', [[2024, 1, 31], [2024, 7, 31], 6, 0.05], 2.5], ['normal control 1', [[2014, 4, 29], [2014, 5, 3], 1, 0.0725], 0.080556], ['normal control 2', [[2006, 1, 11], [2006, 7, 11], 6, 0.03], 1.5]], [['regression long stub extension denominator 1', [[2009, 2, 28], [2009, 4, 5], 1, 0.05], 0.524194], ['regression long stub extension denominator 2', [[2005, 11, 30], [2006, 1, 5], 1, 0.03], 0.298387], ['partial repair probe 1', [[2023, 4, 28], [2024, 1, 14], 6, 0.05], 3.565574], ['partial repair probe 2', [[2023, 6, 20], [2024, 6, 20], 6, 0.045], 4.5], ['boundary control 1', [[2024, 1, 31], [2024, 4, 30], 6, 0.05], 1.236264], ['boundary control 2', [[2024, 1, 31], [2024, 7, 31], 6, 0.05], 2.5], ['normal control 1', [[2042, 12, 1], [2043, 3, 10], 12, 0.03], 0.813699], ['normal control 2', [[2030, 6, 29], [2030, 8, 27], 3, 0.03], 0.480978]]]
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 long stub extension denominator 1	`7.958904`	`7.958904`	Passed
regression long stub extension denominator 2	`0.75`	`0.75`	Passed
partial repair probe 1	`5.063014`	`5.063014`	Passed
partial repair probe 2	`8.568493`	`8.568493`	Passed
boundary control 1	`1.236264`	`1.236264`	Passed
boundary control 2	`2.5`	`2.5`	Passed
normal control 1	`1.941257`	`1.941257`	Passed
normal control 2	`2.25`	`2.25`	Passed

SHA-256 / 8f2df7963fea6a07f8f6a26e94888b004daeba053dcc3603cfbb69ee57d1040e

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 2026-09-29T14:46:53.136774+00:00.

Case digest / fd1ed0f15569c60fa4ace03a432f70e87d861c8ee395b9e3764a5469210b87d4