FA-61066 / Bond day-count conventions / Open access

Irregular first coupon accrued by quasi-coupon periods: the annual coupon is applied to each quasi-period fraction · case 01

Accrued interest is freq times too large.

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

ROOT CAUSE

The periodic coupon omits division by the payment frequency.

THE FAILURE

The periodic coupon omits division by the payment frequency.

Unsuccessful approach: Dividing by the number of quasi periods confuses irregular period count with frequency.

Case contract

Inputs issue, first coupon and settlement [y,m,d], annual rate and months per period. Settlement must lie in [issue, first] else return "settlement outside first period". Quasi-coupon dates are generated back from the first coupon in steps of months (day clamped to month length) until one is on or before issue. For each quasi period [start, end), accrued days are those in [max(start, issue), min(end, settle)) and are divided by that quasi period length. Accrued = 100*rate/freq*sum, rounded 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(issue, first, settle, rate, months):
    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
    I = datetime.date(*issue)
    Fc = datetime.date(*first)
    S = datetime.date(*settle)
    if not (I <= S <= Fc):
        return 'settlement outside first period'
    freq = 12 // months
    def back(k):
        t = Fc.year * 12 + Fc.month - 1 - k * months
        y, m = t // 12, t % 12 + 1
        return datetime.date(y, m, min(Fc.day, mlen(y, m)))
    q = [Fc]
    k = 1
    while q[-1] > I:
        q.append(back(k))
        k += 1
    frac = Fraction(0)
    for j in range(len(q) - 1):
        end, start = q[j], q[j + 1]
        lo = max(start, I)
        hi = min(end, S)
        if hi > lo:
            frac += Fraction((hi - lo).days, (end - start).days)
    return round(float(100 * Fraction(str(rate)) * frac), 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression coupon per quasi period 1', [[2005, 9, 29], [2005, 10, 31], [2005, 9, 30], 0.02, 3], 0.005435], ['regression coupon per quasi period 2', [[2041, 9, 29], [2042, 3, 31], [2041, 10, 18], 0.05, 6], 0.260914], ['partial repair probe 1', [[2030, 8, 6], [2031, 11, 1], [2031, 4, 19], 0.0675, 12], 4.734247], ['partial repair probe 2', [[2031, 8, 7], [2033, 2, 28], [2031, 10, 22], 0.02, 12], 0.416438], ['boundary control 1', [[2024, 1, 10], [2024, 9, 15], [2024, 9, 16], 0.05, 6], 'settlement outside first period'], ['normal control 1', [[2035, 2, 3], [2035, 5, 4], [2035, 2, 3], 0.045, 3], 0.0], ['normal control 2', [[2019, 11, 10], [2020, 3, 3], [2019, 11, 7], 0.045, 6], 'settlement outside first period'], ['normal control 3', [[2007, 12, 27], [2008, 1, 1], [2007, 12, 27], 0.05, 1], 0.0]], [['regression coupon per quasi period 1', [[2040, 8, 29], [2040, 9, 6], [2040, 8, 31], 0.03, 3], 0.016304], ['regression coupon per quasi period 2', [[2030, 7, 25], [2030, 9, 15], [2030, 9, 15], 0.05, 3], 0.706522], ['partial repair probe 1', [[2015, 7, 5], [2018, 1, 31], [2017, 9, 10], 0.02, 12], 4.367123], ['partial repair probe 2', [[2023, 11, 5], [2025, 4, 30], [2025, 4, 30], 0.03, 12], 4.45082], ['boundary control 1', [[2024, 1, 10], [2024, 9, 15], [2024, 9, 16], 0.05, 6], 'settlement outside first period'], ['normal control 1', [[2038, 1, 19], [2038, 3, 31], [2038, 1, 19], 0.03, 6], 0.0], ['normal control 2', [[2012, 6, 22], [2012, 7, 20], [2012, 6, 22], 0.0675, 1], 0.0], ['normal control 3', [[2000, 6, 21], [2001, 1, 22], [2000, 12, 7], 0.02, 12], 0.923497]], [['regression coupon per quasi period 1', [[2003, 9, 19], [2003, 9, 30], [2003, 9, 22], 0.03, 1], 0.024194], ['regression coupon per quasi period 2', [[2014, 12, 1], [2014, 12, 28], [2014, 12, 27], 0.03, 1], 0.216667], ['partial repair probe 1', [[2034, 4, 21], [2035, 9, 1], [2035, 6, 28], 0.05, 12], 5.931507], ['partial repair probe 2', [[2007, 7, 11], [2008, 11, 28], [2008, 1, 9], 0.0675, 12], 3.363631], ['boundary control 1', [[2024, 1, 10], [2024, 9, 15], [2024, 9, 16], 0.05, 6], 'settlement outside first period'], ['normal control 1', [[2001, 12, 2], [2003, 4, 13], [2001, 12, 2], 0.05, 12], 0.0], ['normal control 2', [[2012, 10, 11], [2014, 5, 30], [2012, 10, 8], 0.05, 12], 'settlement outside first period'], ['normal control 3', [[2009, 2, 26], [2009, 11, 12], [2009, 2, 26], 0.05, 3], 0.0]], [['regression coupon per quasi period 1', [[2029, 8, 10], [2029, 9, 30], [2029, 9, 30], 0.0675, 1], 0.925403], ['regression coupon per quasi period 2', [[2014, 9, 3], [2014, 11, 30], [2014, 9, 15], 0.045, 1], 0.145161], ['partial repair probe 1', [[2003, 6, 28], [2006, 2, 11], [2005, 1, 15], 0.0675, 12], 10.468488], ['partial repair probe 2', [[2014, 1, 8], [2016, 8, 1], [2014, 9, 23], 0.0675, 12], 4.771233], ['boundary control 1', [[2024, 1, 10], [2024, 9, 15], [2024, 9, 16], 0.05, 6], 'settlement outside first period'], ['normal control 1', [[2020, 3, 5], [2021, 2, 28], [2020, 6, 30], 0.03, 12], 0.959016], ['normal control 2', [[2007, 2, 26], [2007, 12, 16], [2007, 2, 23], 0.05, 12], 'settlement outside first period'], ['normal control 3', [[2003, 4, 30], [2003, 7, 31], [2003, 5, 22], 0.05, 12], 0.30137]], [['regression coupon per quasi period 1', [[2034, 6, 17], [2034, 7, 16], [2034, 6, 27], 0.045, 1], 0.125], ['regression coupon per quasi period 2', [[2010, 7, 5], [2010, 8, 1], [2010, 7, 14], 0.03, 6], 0.074586], ['partial repair probe 1', [[2032, 8, 31], [2034, 4, 30], [2032, 12, 30], 0.03, 12], 0.994521], ['partial repair probe 2', [[2026, 2, 25], [2027, 4, 30], [2027, 2, 11], 0.045, 12], 4.327397], ['boundary control 1', [[2024, 1, 10], [2024, 9, 15], [2024, 9, 16], 0.05, 6], 'settlement outside first period'], ['normal control 1', [[2029, 1, 21], [2029, 5, 29], [2029, 1, 21], 0.02, 6], 0.0], ['normal control 2', [[2019, 5, 3], [2019, 7, 29], [2019, 4, 30], 0.08, 3], 'settlement outside first period'], ['normal control 3', [[2001, 12, 9], [2002, 5, 1], [2001, 12, 6], 0.08, 6], 'settlement outside first period']]]
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 coupon per quasi period 1	`0.021739`	`0.005435`	Failed
regression coupon per quasi period 2	`0.521828`	`0.260914`	Failed
partial repair probe 1	`4.734247`	`4.734247`	Passed
partial repair probe 2	`0.416438`	`0.416438`	Passed
boundary control 1	`settlement outside first period`	`settlement outside first period`	Passed
normal control 1	`0.0`	`0.0`	Passed
normal control 2	`settlement outside first period`	`settlement outside first period`	Passed
normal control 3	`0.0`	`0.0`	Passed

SHA-256 / a7b4bd5f79c40fcfa5d61c8403f9172262ab48f81a60403a41ab67ac6eb45f8f

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(issue, first, settle, rate, months):
    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
    I = datetime.date(*issue)
    Fc = datetime.date(*first)
    S = datetime.date(*settle)
    if not (I <= S <= Fc):
        return 'settlement outside first period'
    freq = 12 // months
    def back(k):
        t = Fc.year * 12 + Fc.month - 1 - k * months
        y, m = t // 12, t % 12 + 1
        return datetime.date(y, m, min(Fc.day, mlen(y, m)))
    q = [Fc]
    k = 1
    while q[-1] > I:
        q.append(back(k))
        k += 1
    frac = Fraction(0)
    for j in range(len(q) - 1):
        end, start = q[j], q[j + 1]
        lo = max(start, I)
        hi = min(end, S)
        if hi > lo:
            frac += Fraction((hi - lo).days, (end - start).days)
    return round(float(100 * Fraction(str(rate)) / (len(q) - 1) * frac), 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression coupon per quasi period 1', [[2005, 9, 29], [2005, 10, 31], [2005, 9, 30], 0.02, 3], 0.005435], ['regression coupon per quasi period 2', [[2041, 9, 29], [2042, 3, 31], [2041, 10, 18], 0.05, 6], 0.260914], ['partial repair probe 1', [[2030, 8, 6], [2031, 11, 1], [2031, 4, 19], 0.0675, 12], 4.734247], ['partial repair probe 2', [[2031, 8, 7], [2033, 2, 28], [2031, 10, 22], 0.02, 12], 0.416438], ['boundary control 1', [[2024, 1, 10], [2024, 9, 15], [2024, 9, 16], 0.05, 6], 'settlement outside first period'], ['normal control 1', [[2035, 2, 3], [2035, 5, 4], [2035, 2, 3], 0.045, 3], 0.0], ['normal control 2', [[2019, 11, 10], [2020, 3, 3], [2019, 11, 7], 0.045, 6], 'settlement outside first period'], ['normal control 3', [[2007, 12, 27], [2008, 1, 1], [2007, 12, 27], 0.05, 1], 0.0]], [['regression coupon per quasi period 1', [[2040, 8, 29], [2040, 9, 6], [2040, 8, 31], 0.03, 3], 0.016304], ['regression coupon per quasi period 2', [[2030, 7, 25], [2030, 9, 15], [2030, 9, 15], 0.05, 3], 0.706522], ['partial repair probe 1', [[2015, 7, 5], [2018, 1, 31], [2017, 9, 10], 0.02, 12], 4.367123], ['partial repair probe 2', [[2023, 11, 5], [2025, 4, 30], [2025, 4, 30], 0.03, 12], 4.45082], ['boundary control 1', [[2024, 1, 10], [2024, 9, 15], [2024, 9, 16], 0.05, 6], 'settlement outside first period'], ['normal control 1', [[2038, 1, 19], [2038, 3, 31], [2038, 1, 19], 0.03, 6], 0.0], ['normal control 2', [[2012, 6, 22], [2012, 7, 20], [2012, 6, 22], 0.0675, 1], 0.0], ['normal control 3', [[2000, 6, 21], [2001, 1, 22], [2000, 12, 7], 0.02, 12], 0.923497]], [['regression coupon per quasi period 1', [[2003, 9, 19], [2003, 9, 30], [2003, 9, 22], 0.03, 1], 0.024194], ['regression coupon per quasi period 2', [[2014, 12, 1], [2014, 12, 28], [2014, 12, 27], 0.03, 1], 0.216667], ['partial repair probe 1', [[2034, 4, 21], [2035, 9, 1], [2035, 6, 28], 0.05, 12], 5.931507], ['partial repair probe 2', [[2007, 7, 11], [2008, 11, 28], [2008, 1, 9], 0.0675, 12], 3.363631], ['boundary control 1', [[2024, 1, 10], [2024, 9, 15], [2024, 9, 16], 0.05, 6], 'settlement outside first period'], ['normal control 1', [[2001, 12, 2], [2003, 4, 13], [2001, 12, 2], 0.05, 12], 0.0], ['normal control 2', [[2012, 10, 11], [2014, 5, 30], [2012, 10, 8], 0.05, 12], 'settlement outside first period'], ['normal control 3', [[2009, 2, 26], [2009, 11, 12], [2009, 2, 26], 0.05, 3], 0.0]], [['regression coupon per quasi period 1', [[2029, 8, 10], [2029, 9, 30], [2029, 9, 30], 0.0675, 1], 0.925403], ['regression coupon per quasi period 2', [[2014, 9, 3], [2014, 11, 30], [2014, 9, 15], 0.045, 1], 0.145161], ['partial repair probe 1', [[2003, 6, 28], [2006, 2, 11], [2005, 1, 15], 0.0675, 12], 10.468488], ['partial repair probe 2', [[2014, 1, 8], [2016, 8, 1], [2014, 9, 23], 0.0675, 12], 4.771233], ['boundary control 1', [[2024, 1, 10], [2024, 9, 15], [2024, 9, 16], 0.05, 6], 'settlement outside first period'], ['normal control 1', [[2020, 3, 5], [2021, 2, 28], [2020, 6, 30], 0.03, 12], 0.959016], ['normal control 2', [[2007, 2, 26], [2007, 12, 16], [2007, 2, 23], 0.05, 12], 'settlement outside first period'], ['normal control 3', [[2003, 4, 30], [2003, 7, 31], [2003, 5, 22], 0.05, 12], 0.30137]], [['regression coupon per quasi period 1', [[2034, 6, 17], [2034, 7, 16], [2034, 6, 27], 0.045, 1], 0.125], ['regression coupon per quasi period 2', [[2010, 7, 5], [2010, 8, 1], [2010, 7, 14], 0.03, 6], 0.074586], ['partial repair probe 1', [[2032, 8, 31], [2034, 4, 30], [2032, 12, 30], 0.03, 12], 0.994521], ['partial repair probe 2', [[2026, 2, 25], [2027, 4, 30], [2027, 2, 11], 0.045, 12], 4.327397], ['boundary control 1', [[2024, 1, 10], [2024, 9, 15], [2024, 9, 16], 0.05, 6], 'settlement outside first period'], ['normal control 1', [[2029, 1, 21], [2029, 5, 29], [2029, 1, 21], 0.02, 6], 0.0], ['normal control 2', [[2019, 5, 3], [2019, 7, 29], [2019, 4, 30], 0.08, 3], 'settlement outside first period'], ['normal control 3', [[2001, 12, 9], [2002, 5, 1], [2001, 12, 6], 0.08, 6], 'settlement outside first period']]]
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 coupon per quasi period 1	`0.021739`	`0.005435`	Failed
regression coupon per quasi period 2	`0.260914`	`0.260914`	Passed
partial repair probe 1	`2.367123`	`4.734247`	Failed
partial repair probe 2	`0.208219`	`0.416438`	Failed
boundary control 1	`settlement outside first period`	`settlement outside first period`	Passed
normal control 1	`0.0`	`0.0`	Passed
normal control 2	`settlement outside first period`	`settlement outside first period`	Passed
normal control 3	`0.0`	`0.0`	Passed

SHA-256 / 2f88fa8d62b1dee1ce5f923429665f1c62e100c4b0dc5ed2ab03fc2f579ab759

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 2026-09-29T14:46:51.684115+00:00.

Case digest / efd52d0a353e6823333144a573b0a01cf7a4a6735f7c2978c34d6f2ba1f55de0