FA-61696 / Options payoff and settlement / Open access

Lookback option payoff: the fixed-strike put uses the path maximum · case 01

Fixed-strike puts rarely pay.

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

ROOT CAUSE

The put branch uses max(path) instead of min(path).

VERIFIED REPAIR

Use the path minimum.

Unsuccessful approach: Using only the final price turns it into a vanilla put.

Case contract

Inputs kind, the observed path including initial and final prices, and strike. float-call pays final - min(path); float-put pays max(path) - final; fixed-call pays max(max(path) - K, 0); fixed-put pays max(K - min(path), 0). 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):
    final = path[-1]
    if kind == 'float-call':
        pay = final - min(path)
    elif kind == 'float-put':
        pay = max(path) - final
    elif kind == 'fixed-call':
        pay = max(max(path) - strike, 0)
    else:
        pay = max(strike - max(path), 0)
    return round(pay, 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression fixed put extreme 1', ['fixed-put', [100.0, 95.0, 85.5, 94.05, 103.45, 107.59], 90], 4.5], ['regression fixed put extreme 2', ['fixed-put', [100.0, 90.0, 85.5, 88.92, 88.92, 80.03], 90], 9.97], ['partial repair probe 1', ['fixed-put', [100.0, 90.0, 81.0, 72.9, 80.19, 72.17, 75.06], 100], 27.83], ['partial repair probe 2', ['fixed-put', [100.0, 104.0, 104.0], 115], 15.0], ['boundary control 1', ['float-call', [90.0, 100.0, 95.0], 100], 5.0], ['normal control 1', ['fixed-call', [100.0, 104.0, 114.4], 90], 24.4], ['normal control 2', ['float-put', [97.81, 108.68, 114.4, 110.0, 110.0, 100.0], 115], 14.4], ['normal control 3', ['float-put', [84.47, 88.92, 93.6, 104.0, 100.0], 100], 4.0]], [['regression fixed put extreme 1', ['fixed-put', [100.0, 95.0, 90.25, 93.86, 89.17, 80.25, 88.28], 100], 19.75], ['regression fixed put extreme 2', ['fixed-put', [72.9, 81.0, 90.0, 100.0], 100], 27.1], ['partial repair probe 1', ['fixed-put', [118.11, 124.33, 119.55, 114.95, 104.5, 95.0, 100.0], 100], 5.0], ['partial repair probe 2', ['fixed-put', [83.63, 92.92, 84.47, 81.22, 85.5, 90.0, 100.0], 100], 18.78], ['boundary control 1', ['float-call', [90.0, 100.0, 95.0], 100], 5.0], ['normal control 1', ['float-call', [95.0, 100.0], 90], 5.0], ['normal control 2', ['float-call', [87.85, 84.47, 88.92, 98.8, 104.0, 100.0], 105], 15.53], ['normal control 3', ['fixed-call', [100.0, 110.0, 114.4, 108.68, 108.68, 103.25, 113.58], 90], 24.4]], [['regression fixed put extreme 1', ['fixed-put', [100.0, 100.0, 110.0, 114.4, 125.84, 119.55], 105], 5.0], ['regression fixed put extreme 2', ['fixed-put', [100.0, 104.0, 114.4, 125.84, 125.84], 105], 5.0], ['partial repair probe 1', ['fixed-put', [100.0, 90.0, 99.0, 108.9, 113.26], 105], 15.0], ['partial repair probe 2', ['fixed-put', [90.0, 90.0, 90.0, 100.0], 105], 15.0], ['boundary control 1', ['float-call', [90.0, 100.0, 95.0], 100], 5.0], ['normal control 1', ['float-put', [100.0, 104.0, 93.6, 88.92], 105], 15.08], ['normal control 2', ['float-put', [100.0, 100.0, 95.0, 85.5, 81.22, 73.1], 105], 26.9], ['normal control 3', ['float-put', [114.4, 104.0, 100.0], 105], 14.4]], [['regression fixed put extreme 1', ['fixed-put', [100.0, 95.0, 98.8, 98.8, 108.68, 119.55], 115], 20.0], ['regression fixed put extreme 2', ['fixed-put', [100.0, 90.0, 81.0, 76.95, 84.65, 93.12], 105], 28.05], ['partial repair probe 1', ['fixed-put', [98.8, 95.0, 95.0, 100.0], 100], 5.0], ['partial repair probe 2', ['fixed-put', [100.0, 100.0, 100.0, 104.0, 114.4, 118.98, 123.74], 105], 5.0], ['boundary control 1', ['float-call', [90.0, 100.0, 95.0], 100], 5.0], ['normal control 1', ['fixed-call', [100.0, 95.0, 95.0], 115], 0], ['normal control 2', ['float-call', [100.0, 110.0, 104.5, 99.27, 89.34], 105], 0.0], ['normal control 3', ['float-call', [100.0, 90.0, 90.0, 90.0, 99.0, 108.9], 115], 18.9]], [['regression fixed put extreme 1', ['fixed-put', [104.5, 110.0, 100.0], 115], 15.0], ['regression fixed put extreme 2', ['fixed-put', [100.0, 90.0, 85.5], 100], 14.5], ['partial repair probe 1', ['fixed-put', [100.0, 95.0, 90.25, 93.86, 103.25, 113.58, 102.22], 115], 24.75], ['partial repair probe 2', ['fixed-put', [100.0, 104.0, 108.16, 102.75, 106.86], 115], 15.0], ['boundary control 1', ['float-call', [90.0, 100.0, 95.0], 100], 5.0], ['normal control 1', ['fixed-put', [110.0, 100.0], 100], 0.0], ['normal control 2', ['float-put', [100.0, 104.0], 100], 0.0], ['normal control 3', ['fixed-call', [100.0, 90.0, 90.0, 81.0], 105], 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 fixed put extreme 1	`0`	`4.5`	Failed
regression fixed put extreme 2	`0`	`9.97`	Failed
partial repair probe 1	`0.0`	`27.83`	Failed
partial repair probe 2	`11.0`	`15.0`	Failed
boundary control 1	`5.0`	`5.0`	Passed
normal control 1	`24.4`	`24.4`	Passed
normal control 2	`14.4`	`14.4`	Passed
normal control 3	`4.0`	`4.0`	Passed

SHA-256 / 833471dd23acf6c4cca223fa40768b574d4bc0c589177671bd6b7a069d957915

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(kind, path, strike):
    final = path[-1]
    if kind == 'float-call':
        pay = final - min(path)
    elif kind == 'float-put':
        pay = max(path) - final
    elif kind == 'fixed-call':
        pay = max(max(path) - strike, 0)
    else:
        pay = max(strike - final, 0)
    return round(pay, 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression fixed put extreme 1', ['fixed-put', [100.0, 95.0, 85.5, 94.05, 103.45, 107.59], 90], 4.5], ['regression fixed put extreme 2', ['fixed-put', [100.0, 90.0, 85.5, 88.92, 88.92, 80.03], 90], 9.97], ['partial repair probe 1', ['fixed-put', [100.0, 90.0, 81.0, 72.9, 80.19, 72.17, 75.06], 100], 27.83], ['partial repair probe 2', ['fixed-put', [100.0, 104.0, 104.0], 115], 15.0], ['boundary control 1', ['float-call', [90.0, 100.0, 95.0], 100], 5.0], ['normal control 1', ['fixed-call', [100.0, 104.0, 114.4], 90], 24.4], ['normal control 2', ['float-put', [97.81, 108.68, 114.4, 110.0, 110.0, 100.0], 115], 14.4], ['normal control 3', ['float-put', [84.47, 88.92, 93.6, 104.0, 100.0], 100], 4.0]], [['regression fixed put extreme 1', ['fixed-put', [100.0, 95.0, 90.25, 93.86, 89.17, 80.25, 88.28], 100], 19.75], ['regression fixed put extreme 2', ['fixed-put', [72.9, 81.0, 90.0, 100.0], 100], 27.1], ['partial repair probe 1', ['fixed-put', [118.11, 124.33, 119.55, 114.95, 104.5, 95.0, 100.0], 100], 5.0], ['partial repair probe 2', ['fixed-put', [83.63, 92.92, 84.47, 81.22, 85.5, 90.0, 100.0], 100], 18.78], ['boundary control 1', ['float-call', [90.0, 100.0, 95.0], 100], 5.0], ['normal control 1', ['float-call', [95.0, 100.0], 90], 5.0], ['normal control 2', ['float-call', [87.85, 84.47, 88.92, 98.8, 104.0, 100.0], 105], 15.53], ['normal control 3', ['fixed-call', [100.0, 110.0, 114.4, 108.68, 108.68, 103.25, 113.58], 90], 24.4]], [['regression fixed put extreme 1', ['fixed-put', [100.0, 100.0, 110.0, 114.4, 125.84, 119.55], 105], 5.0], ['regression fixed put extreme 2', ['fixed-put', [100.0, 104.0, 114.4, 125.84, 125.84], 105], 5.0], ['partial repair probe 1', ['fixed-put', [100.0, 90.0, 99.0, 108.9, 113.26], 105], 15.0], ['partial repair probe 2', ['fixed-put', [90.0, 90.0, 90.0, 100.0], 105], 15.0], ['boundary control 1', ['float-call', [90.0, 100.0, 95.0], 100], 5.0], ['normal control 1', ['float-put', [100.0, 104.0, 93.6, 88.92], 105], 15.08], ['normal control 2', ['float-put', [100.0, 100.0, 95.0, 85.5, 81.22, 73.1], 105], 26.9], ['normal control 3', ['float-put', [114.4, 104.0, 100.0], 105], 14.4]], [['regression fixed put extreme 1', ['fixed-put', [100.0, 95.0, 98.8, 98.8, 108.68, 119.55], 115], 20.0], ['regression fixed put extreme 2', ['fixed-put', [100.0, 90.0, 81.0, 76.95, 84.65, 93.12], 105], 28.05], ['partial repair probe 1', ['fixed-put', [98.8, 95.0, 95.0, 100.0], 100], 5.0], ['partial repair probe 2', ['fixed-put', [100.0, 100.0, 100.0, 104.0, 114.4, 118.98, 123.74], 105], 5.0], ['boundary control 1', ['float-call', [90.0, 100.0, 95.0], 100], 5.0], ['normal control 1', ['fixed-call', [100.0, 95.0, 95.0], 115], 0], ['normal control 2', ['float-call', [100.0, 110.0, 104.5, 99.27, 89.34], 105], 0.0], ['normal control 3', ['float-call', [100.0, 90.0, 90.0, 90.0, 99.0, 108.9], 115], 18.9]], [['regression fixed put extreme 1', ['fixed-put', [104.5, 110.0, 100.0], 115], 15.0], ['regression fixed put extreme 2', ['fixed-put', [100.0, 90.0, 85.5], 100], 14.5], ['partial repair probe 1', ['fixed-put', [100.0, 95.0, 90.25, 93.86, 103.25, 113.58, 102.22], 115], 24.75], ['partial repair probe 2', ['fixed-put', [100.0, 104.0, 108.16, 102.75, 106.86], 115], 15.0], ['boundary control 1', ['float-call', [90.0, 100.0, 95.0], 100], 5.0], ['normal control 1', ['fixed-put', [110.0, 100.0], 100], 0.0], ['normal control 2', ['float-put', [100.0, 104.0], 100], 0.0], ['normal control 3', ['fixed-call', [100.0, 90.0, 90.0, 81.0], 105], 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 fixed put extreme 1	`0`	`4.5`	Failed
regression fixed put extreme 2	`9.97`	`9.97`	Passed
partial repair probe 1	`24.94`	`27.83`	Failed
partial repair probe 2	`11.0`	`15.0`	Failed
boundary control 1	`5.0`	`5.0`	Passed
normal control 1	`24.4`	`24.4`	Passed
normal control 2	`14.4`	`14.4`	Passed
normal control 3	`4.0`	`4.0`	Passed

SHA-256 / 699ed7e522981f38fc32a54bf31023fd62a12a6f76da33b829638b993fbdd3dd

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(kind, path, strike):
    final = path[-1]
    if kind == 'float-call':
        pay = final - min(path)
    elif kind == 'float-put':
        pay = max(path) - final
    elif kind == 'fixed-call':
        pay = max(max(path) - strike, 0)
    else:
        pay = max(strike - min(path), 0)
    return round(pay, 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression fixed put extreme 1', ['fixed-put', [100.0, 95.0, 85.5, 94.05, 103.45, 107.59], 90], 4.5], ['regression fixed put extreme 2', ['fixed-put', [100.0, 90.0, 85.5, 88.92, 88.92, 80.03], 90], 9.97], ['partial repair probe 1', ['fixed-put', [100.0, 90.0, 81.0, 72.9, 80.19, 72.17, 75.06], 100], 27.83], ['partial repair probe 2', ['fixed-put', [100.0, 104.0, 104.0], 115], 15.0], ['boundary control 1', ['float-call', [90.0, 100.0, 95.0], 100], 5.0], ['normal control 1', ['fixed-call', [100.0, 104.0, 114.4], 90], 24.4], ['normal control 2', ['float-put', [97.81, 108.68, 114.4, 110.0, 110.0, 100.0], 115], 14.4], ['normal control 3', ['float-put', [84.47, 88.92, 93.6, 104.0, 100.0], 100], 4.0]], [['regression fixed put extreme 1', ['fixed-put', [100.0, 95.0, 90.25, 93.86, 89.17, 80.25, 88.28], 100], 19.75], ['regression fixed put extreme 2', ['fixed-put', [72.9, 81.0, 90.0, 100.0], 100], 27.1], ['partial repair probe 1', ['fixed-put', [118.11, 124.33, 119.55, 114.95, 104.5, 95.0, 100.0], 100], 5.0], ['partial repair probe 2', ['fixed-put', [83.63, 92.92, 84.47, 81.22, 85.5, 90.0, 100.0], 100], 18.78], ['boundary control 1', ['float-call', [90.0, 100.0, 95.0], 100], 5.0], ['normal control 1', ['float-call', [95.0, 100.0], 90], 5.0], ['normal control 2', ['float-call', [87.85, 84.47, 88.92, 98.8, 104.0, 100.0], 105], 15.53], ['normal control 3', ['fixed-call', [100.0, 110.0, 114.4, 108.68, 108.68, 103.25, 113.58], 90], 24.4]], [['regression fixed put extreme 1', ['fixed-put', [100.0, 100.0, 110.0, 114.4, 125.84, 119.55], 105], 5.0], ['regression fixed put extreme 2', ['fixed-put', [100.0, 104.0, 114.4, 125.84, 125.84], 105], 5.0], ['partial repair probe 1', ['fixed-put', [100.0, 90.0, 99.0, 108.9, 113.26], 105], 15.0], ['partial repair probe 2', ['fixed-put', [90.0, 90.0, 90.0, 100.0], 105], 15.0], ['boundary control 1', ['float-call', [90.0, 100.0, 95.0], 100], 5.0], ['normal control 1', ['float-put', [100.0, 104.0, 93.6, 88.92], 105], 15.08], ['normal control 2', ['float-put', [100.0, 100.0, 95.0, 85.5, 81.22, 73.1], 105], 26.9], ['normal control 3', ['float-put', [114.4, 104.0, 100.0], 105], 14.4]], [['regression fixed put extreme 1', ['fixed-put', [100.0, 95.0, 98.8, 98.8, 108.68, 119.55], 115], 20.0], ['regression fixed put extreme 2', ['fixed-put', [100.0, 90.0, 81.0, 76.95, 84.65, 93.12], 105], 28.05], ['partial repair probe 1', ['fixed-put', [98.8, 95.0, 95.0, 100.0], 100], 5.0], ['partial repair probe 2', ['fixed-put', [100.0, 100.0, 100.0, 104.0, 114.4, 118.98, 123.74], 105], 5.0], ['boundary control 1', ['float-call', [90.0, 100.0, 95.0], 100], 5.0], ['normal control 1', ['fixed-call', [100.0, 95.0, 95.0], 115], 0], ['normal control 2', ['float-call', [100.0, 110.0, 104.5, 99.27, 89.34], 105], 0.0], ['normal control 3', ['float-call', [100.0, 90.0, 90.0, 90.0, 99.0, 108.9], 115], 18.9]], [['regression fixed put extreme 1', ['fixed-put', [104.5, 110.0, 100.0], 115], 15.0], ['regression fixed put extreme 2', ['fixed-put', [100.0, 90.0, 85.5], 100], 14.5], ['partial repair probe 1', ['fixed-put', [100.0, 95.0, 90.25, 93.86, 103.25, 113.58, 102.22], 115], 24.75], ['partial repair probe 2', ['fixed-put', [100.0, 104.0, 108.16, 102.75, 106.86], 115], 15.0], ['boundary control 1', ['float-call', [90.0, 100.0, 95.0], 100], 5.0], ['normal control 1', ['fixed-put', [110.0, 100.0], 100], 0.0], ['normal control 2', ['float-put', [100.0, 104.0], 100], 0.0], ['normal control 3', ['fixed-call', [100.0, 90.0, 90.0, 81.0], 105], 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 fixed put extreme 1	`4.5`	`4.5`	Passed
regression fixed put extreme 2	`9.97`	`9.97`	Passed
partial repair probe 1	`27.83`	`27.83`	Passed
partial repair probe 2	`15.0`	`15.0`	Passed
boundary control 1	`5.0`	`5.0`	Passed
normal control 1	`24.4`	`24.4`	Passed
normal control 2	`14.4`	`14.4`	Passed
normal control 3	`4.0`	`4.0`	Passed

SHA-256 / d2a5d4b631b6841dc4dc3ecf4d1de50c734332ba07bcd20a595bbb671e598079

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 2026-09-29T14:46:57.722419+00:00.

Case digest / 08e0898eea1cf937e49ef6c82fee69730264027f5828b92073238d6c146f1624