FA-61441 / Options payoff and settlement / Open access

Discretely monitored barrier option payoff: an observation exactly at the barrier is not a hit · case 01

Paths that touch the barrier level exactly are treated as never touching it.

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

ROOT CAUSE

Both barrier comparisons are strict.

VERIFIED REPAIR

Treat an observation equal to the barrier as a hit.

Unsuccessful approach: Fixing only the up-barrier comparison leaves down barriers strict.

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 = rebate 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 touch inclusivity 1', ['down-in-put', [100.0, 90.0, 90.0, 90.0, 94.5], 95, 90.0, 1.5], 0.5], ['regression touch inclusivity 2', ['up-out-call', [100.0, 90.0, 94.5], 95, 100.0, 1.5], 1.5], ['partial repair probe 1', ['down-in-call', [100.0, 110.0, 115.5, 115.5, 115.5], 105, 100.0, 0.0], 10.5], ['partial repair probe 2', ['down-in-put', [100.0, 93.0, 102.3, 97.18, 87.46, 96.21], 105, 87.46, 0.0], 8.79], ['boundary control 1', ['down-in-put', [100.0, 95.0], 100, 90.0, 1.0], 1.0], ['normal control 1', ['up-in-call', [100.0, 105.0, 113.4, 124.74], 105, 113.4, 3.0], 19.74], ['normal control 2', ['down-in-call', [100.0, 105.0, 105.0, 110.25], 100, 80.0, 0.0], 0.0], ['normal control 3', ['up-in-call', [100.0, 100.0, 100.0, 93.0], 105, 115.0, 0.0], 0.0]], [['regression touch inclusivity 1', ['up-out-put', [100.0, 110.0, 104.5, 97.19, 90.39, 84.06, 79.86], 105, 110.0, 1.5], 1.5], ['regression touch inclusivity 2', ['up-out-put', [100.0, 90.0, 99.0, 89.1, 84.64, 76.18, 70.85, 67.31], 105, 100.0, 0.0], 0.0], ['partial repair probe 1', ['down-out-put', [100.0, 90.0, 81.0, 76.95, 71.56, 77.28, 69.55, 73.03], 100, 69.55, 1.5], 1.5], ['partial repair probe 2', ['down-out-put', [100.0, 108.0, 100.44, 110.48, 119.32], 105, 100.0, 1.5], 1.5], ['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, 100.0, 90.0, 94.5, 102.06, 112.27, 123.5], 100, 80.0, 1.5], 0], ['normal control 2', ['up-out-call', [100.0, 110.0, 121.0, 130.68], 100, 95.0, 3.0], 3.0], ['normal control 3', ['down-in-put', [100.0, 108.0, 118.8], 95, 80.0, 3.0], 3.0]], [['regression touch inclusivity 1', ['down-in-put', [100.0, 108.0, 116.64, 125.97, 138.57, 124.71], 100, 100.0, 3.0], 0], ['regression touch inclusivity 2', ['down-in-call', [100.0, 105.0, 115.5, 109.72, 98.75, 93.81, 93.81], 95, 93.81, 1.5], 0], ['partial repair probe 1', ['down-in-put', [100.0, 90.0, 83.7, 79.52, 75.54, 75.54], 105, 75.54, 1.5], 29.46], ['partial repair probe 2', ['down-in-put', [100.0, 95.0, 88.35], 95, 88.35, 0.0], 6.65], ['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, 115.5, 124.74, 130.98, 117.88], 105, 90.0, 0.0], 0], ['normal control 2', ['up-in-call', [100.0, 95.0, 95.0, 102.6, 97.47, 105.27, 97.9], 105, 115.0, 1.5], 1.5], ['normal control 3', ['up-out-call', [100.0, 93.0, 93.0, 102.3, 107.42], 95, 110.0, 0.0], 12.42]], [['regression touch inclusivity 1', ['up-out-call', [100.0, 110.0, 110.0, 99.0], 105, 110.0, 3.0], 3.0], ['regression touch inclusivity 2', ['up-in-call', [100.0, 90.0, 81.0], 95, 100.0, 3.0], 0], ['partial repair probe 1', ['down-out-put', [100.0, 100.0, 93.0], 95, 93.0, 3.0], 3.0], ['partial repair probe 2', ['down-in-call', [100.0, 90.0, 99.0, 99.0, 99.0, 92.07, 92.07], 105, 90.0, 3.0], 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, 93.0, 93.0, 83.7, 87.89], 105, 120.0, 1.5], 0], ['normal control 2', ['down-in-call', [100.0, 93.0, 83.7, 83.7, 77.84, 77.84, 72.39], 100, 105.0, 0.0], 0], ['normal control 3', ['down-out-put', [100.0, 100.0, 95.0, 95.0, 88.35], 100, 95.0, 0.0], 0.0]], [['regression touch inclusivity 1', ['down-out-put', [100.0, 93.0, 83.7], 105, 83.7, 3.0], 3.0], ['regression touch inclusivity 2', ['down-in-call', [100.0, 110.0, 121.0], 95, 100.0, 0.0], 26.0], ['partial repair probe 1', ['down-in-put', [100.0, 108.0, 102.6, 112.86, 107.22, 115.8, 125.06], 105, 100.0, 3.0], 0], ['partial repair probe 2', ['down-out-put', [100.0, 90.0, 94.5, 102.06, 102.06, 107.16, 117.88], 95, 90.0, 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, 90.0, 99.0, 89.1, 89.1], 105, 105.0, 3.0], 3.0], ['normal control 2', ['up-out-call', [100.0, 108.0, 100.44], 100, 100.0, 1.5], 1.5], ['normal control 3', ['up-out-put', [100.0, 90.0, 97.2, 92.34, 85.88, 77.29], 105, 120.0, 3.0], 27.71]]]
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 touch inclusivity 1	`1.5`	`0.5`	Failed
regression touch inclusivity 2	`0`	`1.5`	Failed
partial repair probe 1	`0.0`	`10.5`	Failed
partial repair probe 2	`0.0`	`8.79`	Failed
boundary control 1	`1.0`	`1.0`	Passed
normal control 1	`19.74`	`19.74`	Passed
normal control 2	`0.0`	`0.0`	Passed
normal control 3	`0.0`	`0.0`	Passed

SHA-256 / 9354b5346f9841d9687b0dcadc2523166de40f60a529af6aeacf71e084435bfc

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 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 touch inclusivity 1', ['down-in-put', [100.0, 90.0, 90.0, 90.0, 94.5], 95, 90.0, 1.5], 0.5], ['regression touch inclusivity 2', ['up-out-call', [100.0, 90.0, 94.5], 95, 100.0, 1.5], 1.5], ['partial repair probe 1', ['down-in-call', [100.0, 110.0, 115.5, 115.5, 115.5], 105, 100.0, 0.0], 10.5], ['partial repair probe 2', ['down-in-put', [100.0, 93.0, 102.3, 97.18, 87.46, 96.21], 105, 87.46, 0.0], 8.79], ['boundary control 1', ['down-in-put', [100.0, 95.0], 100, 90.0, 1.0], 1.0], ['normal control 1', ['up-in-call', [100.0, 105.0, 113.4, 124.74], 105, 113.4, 3.0], 19.74], ['normal control 2', ['down-in-call', [100.0, 105.0, 105.0, 110.25], 100, 80.0, 0.0], 0.0], ['normal control 3', ['up-in-call', [100.0, 100.0, 100.0, 93.0], 105, 115.0, 0.0], 0.0]], [['regression touch inclusivity 1', ['up-out-put', [100.0, 110.0, 104.5, 97.19, 90.39, 84.06, 79.86], 105, 110.0, 1.5], 1.5], ['regression touch inclusivity 2', ['up-out-put', [100.0, 90.0, 99.0, 89.1, 84.64, 76.18, 70.85, 67.31], 105, 100.0, 0.0], 0.0], ['partial repair probe 1', ['down-out-put', [100.0, 90.0, 81.0, 76.95, 71.56, 77.28, 69.55, 73.03], 100, 69.55, 1.5], 1.5], ['partial repair probe 2', ['down-out-put', [100.0, 108.0, 100.44, 110.48, 119.32], 105, 100.0, 1.5], 1.5], ['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, 100.0, 90.0, 94.5, 102.06, 112.27, 123.5], 100, 80.0, 1.5], 0], ['normal control 2', ['up-out-call', [100.0, 110.0, 121.0, 130.68], 100, 95.0, 3.0], 3.0], ['normal control 3', ['down-in-put', [100.0, 108.0, 118.8], 95, 80.0, 3.0], 3.0]], [['regression touch inclusivity 1', ['down-in-put', [100.0, 108.0, 116.64, 125.97, 138.57, 124.71], 100, 100.0, 3.0], 0], ['regression touch inclusivity 2', ['down-in-call', [100.0, 105.0, 115.5, 109.72, 98.75, 93.81, 93.81], 95, 93.81, 1.5], 0], ['partial repair probe 1', ['down-in-put', [100.0, 90.0, 83.7, 79.52, 75.54, 75.54], 105, 75.54, 1.5], 29.46], ['partial repair probe 2', ['down-in-put', [100.0, 95.0, 88.35], 95, 88.35, 0.0], 6.65], ['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, 115.5, 124.74, 130.98, 117.88], 105, 90.0, 0.0], 0], ['normal control 2', ['up-in-call', [100.0, 95.0, 95.0, 102.6, 97.47, 105.27, 97.9], 105, 115.0, 1.5], 1.5], ['normal control 3', ['up-out-call', [100.0, 93.0, 93.0, 102.3, 107.42], 95, 110.0, 0.0], 12.42]], [['regression touch inclusivity 1', ['up-out-call', [100.0, 110.0, 110.0, 99.0], 105, 110.0, 3.0], 3.0], ['regression touch inclusivity 2', ['up-in-call', [100.0, 90.0, 81.0], 95, 100.0, 3.0], 0], ['partial repair probe 1', ['down-out-put', [100.0, 100.0, 93.0], 95, 93.0, 3.0], 3.0], ['partial repair probe 2', ['down-in-call', [100.0, 90.0, 99.0, 99.0, 99.0, 92.07, 92.07], 105, 90.0, 3.0], 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, 93.0, 93.0, 83.7, 87.89], 105, 120.0, 1.5], 0], ['normal control 2', ['down-in-call', [100.0, 93.0, 83.7, 83.7, 77.84, 77.84, 72.39], 100, 105.0, 0.0], 0], ['normal control 3', ['down-out-put', [100.0, 100.0, 95.0, 95.0, 88.35], 100, 95.0, 0.0], 0.0]], [['regression touch inclusivity 1', ['down-out-put', [100.0, 93.0, 83.7], 105, 83.7, 3.0], 3.0], ['regression touch inclusivity 2', ['down-in-call', [100.0, 110.0, 121.0], 95, 100.0, 0.0], 26.0], ['partial repair probe 1', ['down-in-put', [100.0, 108.0, 102.6, 112.86, 107.22, 115.8, 125.06], 105, 100.0, 3.0], 0], ['partial repair probe 2', ['down-out-put', [100.0, 90.0, 94.5, 102.06, 102.06, 107.16, 117.88], 95, 90.0, 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, 90.0, 99.0, 89.1, 89.1], 105, 105.0, 3.0], 3.0], ['normal control 2', ['up-out-call', [100.0, 108.0, 100.44], 100, 100.0, 1.5], 1.5], ['normal control 3', ['up-out-put', [100.0, 90.0, 97.2, 92.34, 85.88, 77.29], 105, 120.0, 3.0], 27.71]]]
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 touch inclusivity 1	`1.5`	`0.5`	Failed
regression touch inclusivity 2	`1.5`	`1.5`	Passed
partial repair probe 1	`0.0`	`10.5`	Failed
partial repair probe 2	`0.0`	`8.79`	Failed
boundary control 1	`1.0`	`1.0`	Passed
normal control 1	`19.74`	`19.74`	Passed
normal control 2	`0.0`	`0.0`	Passed
normal control 3	`0.0`	`0.0`	Passed

SHA-256 / fb52f5b3dc57612878fbd464108e547e27beaccf8cd949a73fa9eb425c307495

3 / The verified repair

Exit 0

"""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 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 touch inclusivity 1', ['down-in-put', [100.0, 90.0, 90.0, 90.0, 94.5], 95, 90.0, 1.5], 0.5], ['regression touch inclusivity 2', ['up-out-call', [100.0, 90.0, 94.5], 95, 100.0, 1.5], 1.5], ['partial repair probe 1', ['down-in-call', [100.0, 110.0, 115.5, 115.5, 115.5], 105, 100.0, 0.0], 10.5], ['partial repair probe 2', ['down-in-put', [100.0, 93.0, 102.3, 97.18, 87.46, 96.21], 105, 87.46, 0.0], 8.79], ['boundary control 1', ['down-in-put', [100.0, 95.0], 100, 90.0, 1.0], 1.0], ['normal control 1', ['up-in-call', [100.0, 105.0, 113.4, 124.74], 105, 113.4, 3.0], 19.74], ['normal control 2', ['down-in-call', [100.0, 105.0, 105.0, 110.25], 100, 80.0, 0.0], 0.0], ['normal control 3', ['up-in-call', [100.0, 100.0, 100.0, 93.0], 105, 115.0, 0.0], 0.0]], [['regression touch inclusivity 1', ['up-out-put', [100.0, 110.0, 104.5, 97.19, 90.39, 84.06, 79.86], 105, 110.0, 1.5], 1.5], ['regression touch inclusivity 2', ['up-out-put', [100.0, 90.0, 99.0, 89.1, 84.64, 76.18, 70.85, 67.31], 105, 100.0, 0.0], 0.0], ['partial repair probe 1', ['down-out-put', [100.0, 90.0, 81.0, 76.95, 71.56, 77.28, 69.55, 73.03], 100, 69.55, 1.5], 1.5], ['partial repair probe 2', ['down-out-put', [100.0, 108.0, 100.44, 110.48, 119.32], 105, 100.0, 1.5], 1.5], ['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, 100.0, 90.0, 94.5, 102.06, 112.27, 123.5], 100, 80.0, 1.5], 0], ['normal control 2', ['up-out-call', [100.0, 110.0, 121.0, 130.68], 100, 95.0, 3.0], 3.0], ['normal control 3', ['down-in-put', [100.0, 108.0, 118.8], 95, 80.0, 3.0], 3.0]], [['regression touch inclusivity 1', ['down-in-put', [100.0, 108.0, 116.64, 125.97, 138.57, 124.71], 100, 100.0, 3.0], 0], ['regression touch inclusivity 2', ['down-in-call', [100.0, 105.0, 115.5, 109.72, 98.75, 93.81, 93.81], 95, 93.81, 1.5], 0], ['partial repair probe 1', ['down-in-put', [100.0, 90.0, 83.7, 79.52, 75.54, 75.54], 105, 75.54, 1.5], 29.46], ['partial repair probe 2', ['down-in-put', [100.0, 95.0, 88.35], 95, 88.35, 0.0], 6.65], ['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, 115.5, 124.74, 130.98, 117.88], 105, 90.0, 0.0], 0], ['normal control 2', ['up-in-call', [100.0, 95.0, 95.0, 102.6, 97.47, 105.27, 97.9], 105, 115.0, 1.5], 1.5], ['normal control 3', ['up-out-call', [100.0, 93.0, 93.0, 102.3, 107.42], 95, 110.0, 0.0], 12.42]], [['regression touch inclusivity 1', ['up-out-call', [100.0, 110.0, 110.0, 99.0], 105, 110.0, 3.0], 3.0], ['regression touch inclusivity 2', ['up-in-call', [100.0, 90.0, 81.0], 95, 100.0, 3.0], 0], ['partial repair probe 1', ['down-out-put', [100.0, 100.0, 93.0], 95, 93.0, 3.0], 3.0], ['partial repair probe 2', ['down-in-call', [100.0, 90.0, 99.0, 99.0, 99.0, 92.07, 92.07], 105, 90.0, 3.0], 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, 93.0, 93.0, 83.7, 87.89], 105, 120.0, 1.5], 0], ['normal control 2', ['down-in-call', [100.0, 93.0, 83.7, 83.7, 77.84, 77.84, 72.39], 100, 105.0, 0.0], 0], ['normal control 3', ['down-out-put', [100.0, 100.0, 95.0, 95.0, 88.35], 100, 95.0, 0.0], 0.0]], [['regression touch inclusivity 1', ['down-out-put', [100.0, 93.0, 83.7], 105, 83.7, 3.0], 3.0], ['regression touch inclusivity 2', ['down-in-call', [100.0, 110.0, 121.0], 95, 100.0, 0.0], 26.0], ['partial repair probe 1', ['down-in-put', [100.0, 108.0, 102.6, 112.86, 107.22, 115.8, 125.06], 105, 100.0, 3.0], 0], ['partial repair probe 2', ['down-out-put', [100.0, 90.0, 94.5, 102.06, 102.06, 107.16, 117.88], 95, 90.0, 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, 90.0, 99.0, 89.1, 89.1], 105, 105.0, 3.0], 3.0], ['normal control 2', ['up-out-call', [100.0, 108.0, 100.44], 100, 100.0, 1.5], 1.5], ['normal control 3', ['up-out-put', [100.0, 90.0, 97.2, 92.34, 85.88, 77.29], 105, 120.0, 3.0], 27.71]]]
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 touch inclusivity 1	`0.5`	`0.5`	Passed
regression touch inclusivity 2	`1.5`	`1.5`	Passed
partial repair probe 1	`10.5`	`10.5`	Passed
partial repair probe 2	`8.79`	`8.79`	Passed
boundary control 1	`1.0`	`1.0`	Passed
normal control 1	`19.74`	`19.74`	Passed
normal control 2	`0.0`	`0.0`	Passed
normal control 3	`0.0`	`0.0`	Passed

SHA-256 / e0247e08ec622d09bd24781b1737498a4ae20a555a5c6264ba1052c21ecfa584

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 2026-09-29T14:46:55.226537+00:00.

Case digest / f3ecbf06fc738b5cf0ffe3a245c5b4f2cd0a2ce8c3fce3c33b73a62dee98bd27