FA-61461 / Options payoff and settlement / Open access

Discretely monitored barrier option payoff: a knocked-out option pays nothing · case 01

Knock-out rebates are never paid.

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

ROOT CAUSE

The knock-out branch returns 0 when hit.

THE FAILURE

The knock-out branch returns 0 when hit.

Unsuccessful approach: Paying the rebate only when the option was in the money at expiry is not the contract.

Case contract

Inputs kind (up/down, in/out, call/put), observed path including initial and final price, strike, barrier and rebate. The barrier is hit if any observation is >= barrier (up) or <= barrier (down). Knock-out: rebate if hit else vanilla on the final price. Knock-in: vanilla if hit else rebate. Round to 6.

Why this case matters

Option expiry, exercise and settlement engines move cash and shares; a wrong branch misstates obligations.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(kind, path, strike, barrier, rebate):
    up = kind.startswith('up')
    hit = any(p >= barrier for p in path) if up else any(p <= barrier for p in path)
    final = path[-1]
    vanilla = max(final - strike, 0) if kind.endswith('call') else max(strike - final, 0)
    if '-out-' in kind:
        pay = 0.0 if hit else vanilla
    else:
        pay = vanilla if hit else rebate
    return round(pay, 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression knock-out rebate 1', ['up-out-call', [100.0, 105.0, 115.5, 103.95], 95, 115.0, 3.0], 3.0], ['regression knock-out rebate 2', ['up-out-call', [100.0, 105.0, 113.4, 107.73, 102.34, 92.11, 85.66, 92.51], 95, 113.4, 3.0], 3.0], ['partial repair probe 1', ['up-out-put', [100.0, 110.0, 104.5, 114.95, 109.2, 98.28, 106.14], 105, 110.0, 3.0], 3.0], ['partial repair probe 2', ['down-out-put', [100.0, 105.0, 113.4, 102.06, 112.27, 101.04, 106.09, 106.09], 100, 113.4, 3.0], 3.0], ['boundary control 1', ['down-in-put', [100.0, 95.0], 100, 90.0, 1.0], 1.0], ['normal control 1', ['down-out-put', [100.0, 110.0, 99.0, 94.05], 105, 80.0, 3.0], 10.95], ['normal control 2', ['down-in-call', [100.0, 95.0, 99.75, 94.76], 95, 85.0, 3.0], 3.0], ['normal control 3', ['down-out-put', [100.0, 93.0, 97.65, 92.77, 88.13], 105, 85.0, 0.0], 16.87]], [['regression knock-out rebate 1', ['up-out-call', [100.0, 93.0, 102.3, 97.18, 87.46, 87.46, 78.71], 105, 95.0, 3.0], 3.0], ['regression knock-out rebate 2', ['up-out-call', [100.0, 110.0, 104.5, 99.27, 109.2, 109.2], 95, 110.0, 3.0], 3.0], ['partial repair probe 1', ['up-out-call', [100.0, 110.0, 102.3, 95.14, 85.63, 77.07, 69.36], 100, 110.0, 3.0], 3.0], ['partial repair probe 2', ['up-out-put', [100.0, 108.0, 100.44, 110.48, 121.53, 133.68], 100, 133.68, 3.0], 3.0], ['boundary control 1', ['down-in-put', [100.0, 95.0], 100, 90.0, 1.0], 1.0], ['normal control 1', ['up-out-call', [100.0, 105.0, 99.75, 104.74], 105, 115.0, 0.0], 0], ['normal control 2', ['down-in-call', [100.0, 100.0, 90.0, 83.7, 75.33], 105, 90.0, 1.5], 0], ['normal control 3', ['up-out-put', [100.0, 93.0, 88.35], 95, 120.0, 1.5], 6.65]], [['regression knock-out rebate 1', ['down-out-put', [100.0, 93.0, 83.7, 75.33, 71.56, 75.14, 81.15], 100, 80.0, 3.0], 3.0], ['regression knock-out rebate 2', ['up-out-put', [100.0, 90.0, 81.0, 87.48, 87.48, 87.48], 100, 87.48, 1.5], 1.5], ['partial repair probe 1', ['down-out-put', [100.0, 90.0, 99.0, 103.95], 95, 90.0, 3.0], 3.0], ['partial repair probe 2', ['up-out-put', [100.0, 100.0, 110.0, 104.5], 95, 104.5, 3.0], 3.0], ['boundary control 1', ['down-in-put', [100.0, 95.0], 100, 90.0, 1.0], 1.0], ['normal control 1', ['down-in-put', [100.0, 105.0, 94.5, 87.89, 79.1, 73.56, 68.41], 100, 85.0, 0.0], 31.59], ['normal control 2', ['up-out-call', [100.0, 105.0, 97.65, 102.53, 102.53], 100, 115.0, 1.5], 2.53], ['normal control 3', ['down-in-call', [100.0, 90.0, 99.0, 92.07, 101.28, 94.19, 101.73], 100, 90.0, 1.5], 1.73]], [['regression knock-out rebate 1', ['up-out-put', [100.0, 90.0, 83.7, 83.7, 75.33, 79.1, 85.43, 85.43], 105, 83.7, 3.0], 3.0], ['regression knock-out rebate 2', ['down-out-put', [100.0, 90.0, 81.0, 76.95, 76.95], 105, 80.0, 1.5], 1.5], ['partial repair probe 1', ['up-out-call', [100.0, 90.0, 85.5, 94.05], 105, 90.0, 1.5], 1.5], ['partial repair probe 2', ['up-out-put', [100.0, 108.0, 118.8], 100, 110.0, 3.0], 3.0], ['boundary control 1', ['down-in-put', [100.0, 95.0], 100, 90.0, 1.0], 1.0], ['normal control 1', ['down-in-put', [100.0, 108.0, 97.2], 100, 97.2, 1.5], 2.8], ['normal control 2', ['down-in-put', [100.0, 93.0, 97.65], 100, 85.0, 3.0], 3.0], ['normal control 3', ['down-out-put', [100.0, 105.0, 110.25, 102.53], 100, 85.0, 3.0], 0]], [['regression knock-out rebate 1', ['up-out-put', [100.0, 105.0, 110.25, 115.76, 104.18, 114.6, 103.14], 95, 115.0, 3.0], 3.0], ['regression knock-out rebate 2', ['up-out-put', [100.0, 90.0, 85.5, 85.5, 94.05], 95, 95.0, 1.5], 1.5], ['partial repair probe 1', ['up-out-put', [100.0, 108.0, 113.4], 105, 95.0, 3.0], 3.0], ['partial repair probe 2', ['up-out-call', [100.0, 95.0, 90.25, 81.23, 89.35, 84.88, 91.67], 95, 95.0, 3.0], 3.0], ['boundary control 1', ['down-in-put', [100.0, 95.0], 100, 90.0, 1.0], 1.0], ['normal control 1', ['down-out-put', [100.0, 100.0, 105.0], 105, 85.0, 1.5], 0.0], ['normal control 2', ['down-in-call', [100.0, 108.0, 113.4], 100, 105.0, 1.5], 13.4], ['normal control 3', ['up-out-put', [100.0, 100.0, 93.0], 105, 115.0, 1.5], 12.0]]]
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 knock-out rebate 1	`0.0`	`3.0`	Failed
regression knock-out rebate 2	`0.0`	`3.0`	Failed
partial repair probe 1	`0.0`	`3.0`	Failed
partial repair probe 2	`0.0`	`3.0`	Failed
boundary control 1	`1.0`	`1.0`	Passed
normal control 1	`10.95`	`10.95`	Passed
normal control 2	`3.0`	`3.0`	Passed
normal control 3	`16.87`	`16.87`	Passed

SHA-256 / e5dc8c43a9df747efded157391ffd0e57cac6ec1e8bf34d30926b421b2950cb9

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(kind, path, strike, barrier, rebate):
    up = kind.startswith('up')
    hit = any(p >= barrier for p in path) if up else any(p <= barrier for p in path)
    final = path[-1]
    vanilla = max(final - strike, 0) if kind.endswith('call') else max(strike - final, 0)
    if '-out-' in kind:
        pay = (rebate if vanilla > 0 else 0.0) if hit else vanilla
    else:
        pay = vanilla if hit else rebate
    return round(pay, 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression knock-out rebate 1', ['up-out-call', [100.0, 105.0, 115.5, 103.95], 95, 115.0, 3.0], 3.0], ['regression knock-out rebate 2', ['up-out-call', [100.0, 105.0, 113.4, 107.73, 102.34, 92.11, 85.66, 92.51], 95, 113.4, 3.0], 3.0], ['partial repair probe 1', ['up-out-put', [100.0, 110.0, 104.5, 114.95, 109.2, 98.28, 106.14], 105, 110.0, 3.0], 3.0], ['partial repair probe 2', ['down-out-put', [100.0, 105.0, 113.4, 102.06, 112.27, 101.04, 106.09, 106.09], 100, 113.4, 3.0], 3.0], ['boundary control 1', ['down-in-put', [100.0, 95.0], 100, 90.0, 1.0], 1.0], ['normal control 1', ['down-out-put', [100.0, 110.0, 99.0, 94.05], 105, 80.0, 3.0], 10.95], ['normal control 2', ['down-in-call', [100.0, 95.0, 99.75, 94.76], 95, 85.0, 3.0], 3.0], ['normal control 3', ['down-out-put', [100.0, 93.0, 97.65, 92.77, 88.13], 105, 85.0, 0.0], 16.87]], [['regression knock-out rebate 1', ['up-out-call', [100.0, 93.0, 102.3, 97.18, 87.46, 87.46, 78.71], 105, 95.0, 3.0], 3.0], ['regression knock-out rebate 2', ['up-out-call', [100.0, 110.0, 104.5, 99.27, 109.2, 109.2], 95, 110.0, 3.0], 3.0], ['partial repair probe 1', ['up-out-call', [100.0, 110.0, 102.3, 95.14, 85.63, 77.07, 69.36], 100, 110.0, 3.0], 3.0], ['partial repair probe 2', ['up-out-put', [100.0, 108.0, 100.44, 110.48, 121.53, 133.68], 100, 133.68, 3.0], 3.0], ['boundary control 1', ['down-in-put', [100.0, 95.0], 100, 90.0, 1.0], 1.0], ['normal control 1', ['up-out-call', [100.0, 105.0, 99.75, 104.74], 105, 115.0, 0.0], 0], ['normal control 2', ['down-in-call', [100.0, 100.0, 90.0, 83.7, 75.33], 105, 90.0, 1.5], 0], ['normal control 3', ['up-out-put', [100.0, 93.0, 88.35], 95, 120.0, 1.5], 6.65]], [['regression knock-out rebate 1', ['down-out-put', [100.0, 93.0, 83.7, 75.33, 71.56, 75.14, 81.15], 100, 80.0, 3.0], 3.0], ['regression knock-out rebate 2', ['up-out-put', [100.0, 90.0, 81.0, 87.48, 87.48, 87.48], 100, 87.48, 1.5], 1.5], ['partial repair probe 1', ['down-out-put', [100.0, 90.0, 99.0, 103.95], 95, 90.0, 3.0], 3.0], ['partial repair probe 2', ['up-out-put', [100.0, 100.0, 110.0, 104.5], 95, 104.5, 3.0], 3.0], ['boundary control 1', ['down-in-put', [100.0, 95.0], 100, 90.0, 1.0], 1.0], ['normal control 1', ['down-in-put', [100.0, 105.0, 94.5, 87.89, 79.1, 73.56, 68.41], 100, 85.0, 0.0], 31.59], ['normal control 2', ['up-out-call', [100.0, 105.0, 97.65, 102.53, 102.53], 100, 115.0, 1.5], 2.53], ['normal control 3', ['down-in-call', [100.0, 90.0, 99.0, 92.07, 101.28, 94.19, 101.73], 100, 90.0, 1.5], 1.73]], [['regression knock-out rebate 1', ['up-out-put', [100.0, 90.0, 83.7, 83.7, 75.33, 79.1, 85.43, 85.43], 105, 83.7, 3.0], 3.0], ['regression knock-out rebate 2', ['down-out-put', [100.0, 90.0, 81.0, 76.95, 76.95], 105, 80.0, 1.5], 1.5], ['partial repair probe 1', ['up-out-call', [100.0, 90.0, 85.5, 94.05], 105, 90.0, 1.5], 1.5], ['partial repair probe 2', ['up-out-put', [100.0, 108.0, 118.8], 100, 110.0, 3.0], 3.0], ['boundary control 1', ['down-in-put', [100.0, 95.0], 100, 90.0, 1.0], 1.0], ['normal control 1', ['down-in-put', [100.0, 108.0, 97.2], 100, 97.2, 1.5], 2.8], ['normal control 2', ['down-in-put', [100.0, 93.0, 97.65], 100, 85.0, 3.0], 3.0], ['normal control 3', ['down-out-put', [100.0, 105.0, 110.25, 102.53], 100, 85.0, 3.0], 0]], [['regression knock-out rebate 1', ['up-out-put', [100.0, 105.0, 110.25, 115.76, 104.18, 114.6, 103.14], 95, 115.0, 3.0], 3.0], ['regression knock-out rebate 2', ['up-out-put', [100.0, 90.0, 85.5, 85.5, 94.05], 95, 95.0, 1.5], 1.5], ['partial repair probe 1', ['up-out-put', [100.0, 108.0, 113.4], 105, 95.0, 3.0], 3.0], ['partial repair probe 2', ['up-out-call', [100.0, 95.0, 90.25, 81.23, 89.35, 84.88, 91.67], 95, 95.0, 3.0], 3.0], ['boundary control 1', ['down-in-put', [100.0, 95.0], 100, 90.0, 1.0], 1.0], ['normal control 1', ['down-out-put', [100.0, 100.0, 105.0], 105, 85.0, 1.5], 0.0], ['normal control 2', ['down-in-call', [100.0, 108.0, 113.4], 100, 105.0, 1.5], 13.4], ['normal control 3', ['up-out-put', [100.0, 100.0, 93.0], 105, 115.0, 1.5], 12.0]]]
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 knock-out rebate 1	`3.0`	`3.0`	Passed
regression knock-out rebate 2	`0.0`	`3.0`	Failed
partial repair probe 1	`0.0`	`3.0`	Failed
partial repair probe 2	`0.0`	`3.0`	Failed
boundary control 1	`1.0`	`1.0`	Passed
normal control 1	`10.95`	`10.95`	Passed
normal control 2	`3.0`	`3.0`	Passed
normal control 3	`16.87`	`16.87`	Passed

SHA-256 / 31ac47f3d874aefd9623506cc13477def588d788aadafb27263e3c3a206a96c2

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.

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Verification & scope

A deterministic toy contract stated explicitly in the contract field; no claim of conformance to any exchange or clearing rulebook. 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 2026-09-29T14:46:55.493592+00:00.

Case digest / adc2395c76f7eb23d1d7d1877329cda17738e5312c51fcf5842ffc01d37e4121