FA-61816 / Options payoff and settlement / Open access

Put-call parity violation detector: the dividend yield is ignored · case 01

Pairs on dividend-paying underlyings are flagged as violations.

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

ROOT CAUSE

The spot term is not discounted by e^{-qT}.

THE FAILURE

The spot term is not discounted by e^{-qT}.

Unsuccessful approach: A linear 1 - qT approximation still differs from the exponential.

Case contract

Inputs call price C, put price P, S, K, r, T, dividend yield q and tolerance. v = (C - P) - (S e^{-qT} - K e^{-rT}). If |v| <= tol return ["none", 0.0]; if v > 0 return ["sell call buy put", v]; else ["buy call sell put", -v], amounts rounded 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
import math
N = 1
observations = []
def solve(C, P, S, K, r, T, q, tol):
    v = (C - P) - (S - K * math.exp(-r * T))
    if abs(v) <= tol:
        return ['none', 0.0]
    if v > 0:
        return ['sell call buy put', round(v, 6)]
    return ['buy call sell put', round(-v, 6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression dividend adjustment 1', [31.513, 8.25, 110.0, 90.0, 0.06, 1.0, 0.02, 0.01], ['sell call buy put', 0.199954]], ['regression dividend adjustment 2', [5.3445, 8.25, 95.0, 100.0, 0.03, 2.0, 0.02, 0.05], ['none', 0.0]], ['partial repair probe 1', [17.0912, 8.25, 100.0, 90.0, 0.06, 0.25, 0.02, 0.05], ['buy call sell put', 1.999973]], ['partial repair probe 2', [4.3289, 8.25, 100.0, 100.0, 0.0, 2.0, 0.02, 0.05], ['none', 0.0]], ['normal control 1', [27.2412, 4.0, 110.0, 90.0, 0.06, 1.0, 0.0, 0.05], ['buy call sell put', 1.999992]], ['normal control 2', [14.2899, 8.25, 95.0, 90.0, 0.06, 0.25, 0.0, 0.01], ['buy call sell put', 0.300025]], ['normal control 3', [12.2412, 4.0, 95.0, 90.0, 0.03, 2.0, 0.0, 0.05], ['buy call sell put', 1.999992]], ['normal control 4', [19.5912, 8.25, 95.0, 90.0, 0.03, 2.0, 0.0, 0.05], ['sell call buy put', 1.100008]]], [['regression dividend adjustment 1', [6.0302, 1.5, 95.0, 90.0, 0.0, 0.25, 0.02, 0.01], ['none', 0.0]], ['regression dividend adjustment 2', [4.3105, 8.25, 100.0, 105.0, 0.06, 0.25, 0.02, 0.01], ['none', 0.0]], ['partial repair probe 1', [4.9793, 4.0, 100.0, 100.0, 0.03, 1.0, 0.02, 0.01], ['none', 0.0]], ['partial repair probe 2', [21.8219, 4.0, 110.0, 90.0, 0.0, 1.0, 0.02, 0.01], ['none', 0.0]], ['normal control 1', [6.504, 1.5, 110.0, 105.0, 0.0, 2.0, 0.0, 0.05], ['none', 0.0]], ['normal control 2', [3.254, 8.25, 100.0, 105.0, 0.0, 1.0, 0.0, 0.05], ['none', 0.0]], ['normal control 3', [22.6, 1.5, 110.0, 90.0, 0.0, 1.0, 0.0, 0.05], ['sell call buy put', 1.1]], ['normal control 4', [7.1725, 1.5, 95.0, 90.0, 0.03, 0.25, 0.0, 0.01], ['none', 0.0]]], [['regression dividend adjustment 1', [-4.375, 8.25, 95.0, 105.0, 0.0, 2.0, 0.02, 0.01], ['sell call buy put', 1.100003]], ['regression dividend adjustment 2', [13.5402, 1.5, 110.0, 100.0, 0.06, 0.25, 0.02, 0.01], ['sell call buy put', 1.100021]], ['partial repair probe 1', [13.0201, 1.5, 100.0, 90.0, 0.03, 2.0, 0.02, 0.01], ['sell call buy put', 0.199964]], ['partial repair probe 2', [3.2868, 1.5, 110.0, 105.0, 0.0, 2.0, 0.02, 0.05], ['sell call buy put', 1.099962]], ['normal control 1', [4.3607, 8.25, 95.0, 105.0, 0.03, 2.0, 0.0, 0.01], ['none', 0.0]], ['normal control 2', [5.5734, 4.0, 95.0, 105.0, 0.06, 2.0, 0.0, 0.01], ['buy call sell put', 0.299954]], ['normal control 3', [4.35, 8.25, 95.0, 100.0, 0.0, 0.25, 0.0, 0.05], ['sell call buy put', 1.1]], ['normal control 4', [16.25, 8.25, 100.0, 90.0, 0.0, 2.0, 0.0, 0.01], ['buy call sell put', 2.0]]], [['regression dividend adjustment 1', [-0.6516, 1.5, 95.0, 105.0, 0.06, 2.0, 0.02, 0.05], ['buy call sell put', 0.299951]], ['regression dividend adjustment 2', [10.0829, 4.0, 100.0, 90.0, 0.0, 2.0, 0.02, 0.01], ['none', 0.0]], ['partial repair probe 1', [14.7622, 8.25, 95.0, 90.0, 0.03, 2.0, 0.02, 0.05], ['none', 0.0]], ['partial repair probe 2', [5.4145, 8.25, 100.0, 105.0, 0.06, 0.25, 0.02, 0.05], ['sell call buy put', 1.100006]], ['normal control 1', [1.3492, 8.25, 95.0, 105.0, 0.03, 1.0, 0.0, 0.05], ['none', 0.0]], ['normal control 2', [3.7, 4.0, 100.0, 100.0, 0.0, 1.0, 0.0, 0.05], ['buy call sell put', 0.3]], ['normal control 3', [12.558, 8.25, 95.0, 100.0, 0.06, 2.0, 0.0, 0.01], ['buy call sell put', 1.999956]], ['normal control 4', [10.1735, 8.25, 95.0, 100.0, 0.06, 1.0, 0.0, 0.05], ['sell call buy put', 1.099953]]], [['regression dividend adjustment 1', [0.215, 4.0, 95.0, 100.0, 0.06, 0.25, 0.02, 0.05], ['sell call buy put', 0.200008]], ['regression dividend adjustment 2', [9.2213, 8.25, 100.0, 100.0, 0.03, 1.0, 0.02, 0.05], ['none', 0.0]], ['partial repair probe 1', [10.1485, 8.25, 100.0, 100.0, 0.03, 2.0, 0.02, 0.01], ['none', 0.0]], ['partial repair probe 2', [-0.275, 8.25, 95.0, 100.0, 0.0, 2.0, 0.02, 0.05], ['sell call buy put', 0.200003]], ['normal control 1', [-0.996, 4.0, 100.0, 105.0, 0.0, 2.0, 0.0, 0.01], ['none', 0.0]], ['normal control 2', [21.2, 1.5, 110.0, 90.0, 0.0, 2.0, 0.0, 0.01], ['buy call sell put', 0.3]], ['normal control 3', [13.996, 4.0, 110.0, 100.0, 0.0, 2.0, 0.0, 0.01], ['none', 0.0]], ['normal control 4', [9.004, 4.0, 110.0, 105.0, 0.0, 2.0, 0.0, 0.05], ['none', 0.0]]]]
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 dividend adjustment 1	`['buy call sell put', 1.978192]`	`['sell call buy put', 0.199954]`	Failed
regression dividend adjustment 2	`['buy call sell put', 3.729047]`	`['none', 0.0]`	Failed
partial repair probe 1	`['buy call sell put', 2.498725]`	`['buy call sell put', 1.999973]`	Failed
partial repair probe 2	`['buy call sell put', 3.9211]`	`['none', 0.0]`	Failed
normal control 1	`['buy call sell put', 1.999992]`	`['buy call sell put', 1.999992]`	Passed
normal control 2	`['buy call sell put', 0.300025]`	`['buy call sell put', 0.300025]`	Passed
normal control 3	`['buy call sell put', 1.999992]`	`['buy call sell put', 1.999992]`	Passed
normal control 4	`['sell call buy put', 1.100008]`	`['sell call buy put', 1.100008]`	Passed

SHA-256 / 5673f054b919e0819fe8b13eca7f9b74ed152a0c2363bc6becf864b4ca59ff2c

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(C, P, S, K, r, T, q, tol):
    v = (C - P) - (S * (1 - q * T) - K * math.exp(-r * T))
    if abs(v) <= tol:
        return ['none', 0.0]
    if v > 0:
        return ['sell call buy put', round(v, 6)]
    return ['buy call sell put', round(-v, 6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression dividend adjustment 1', [31.513, 8.25, 110.0, 90.0, 0.06, 1.0, 0.02, 0.01], ['sell call buy put', 0.199954]], ['regression dividend adjustment 2', [5.3445, 8.25, 95.0, 100.0, 0.03, 2.0, 0.02, 0.05], ['none', 0.0]], ['partial repair probe 1', [17.0912, 8.25, 100.0, 90.0, 0.06, 0.25, 0.02, 0.05], ['buy call sell put', 1.999973]], ['partial repair probe 2', [4.3289, 8.25, 100.0, 100.0, 0.0, 2.0, 0.02, 0.05], ['none', 0.0]], ['normal control 1', [27.2412, 4.0, 110.0, 90.0, 0.06, 1.0, 0.0, 0.05], ['buy call sell put', 1.999992]], ['normal control 2', [14.2899, 8.25, 95.0, 90.0, 0.06, 0.25, 0.0, 0.01], ['buy call sell put', 0.300025]], ['normal control 3', [12.2412, 4.0, 95.0, 90.0, 0.03, 2.0, 0.0, 0.05], ['buy call sell put', 1.999992]], ['normal control 4', [19.5912, 8.25, 95.0, 90.0, 0.03, 2.0, 0.0, 0.05], ['sell call buy put', 1.100008]]], [['regression dividend adjustment 1', [6.0302, 1.5, 95.0, 90.0, 0.0, 0.25, 0.02, 0.01], ['none', 0.0]], ['regression dividend adjustment 2', [4.3105, 8.25, 100.0, 105.0, 0.06, 0.25, 0.02, 0.01], ['none', 0.0]], ['partial repair probe 1', [4.9793, 4.0, 100.0, 100.0, 0.03, 1.0, 0.02, 0.01], ['none', 0.0]], ['partial repair probe 2', [21.8219, 4.0, 110.0, 90.0, 0.0, 1.0, 0.02, 0.01], ['none', 0.0]], ['normal control 1', [6.504, 1.5, 110.0, 105.0, 0.0, 2.0, 0.0, 0.05], ['none', 0.0]], ['normal control 2', [3.254, 8.25, 100.0, 105.0, 0.0, 1.0, 0.0, 0.05], ['none', 0.0]], ['normal control 3', [22.6, 1.5, 110.0, 90.0, 0.0, 1.0, 0.0, 0.05], ['sell call buy put', 1.1]], ['normal control 4', [7.1725, 1.5, 95.0, 90.0, 0.03, 0.25, 0.0, 0.01], ['none', 0.0]]], [['regression dividend adjustment 1', [-4.375, 8.25, 95.0, 105.0, 0.0, 2.0, 0.02, 0.01], ['sell call buy put', 1.100003]], ['regression dividend adjustment 2', [13.5402, 1.5, 110.0, 100.0, 0.06, 0.25, 0.02, 0.01], ['sell call buy put', 1.100021]], ['partial repair probe 1', [13.0201, 1.5, 100.0, 90.0, 0.03, 2.0, 0.02, 0.01], ['sell call buy put', 0.199964]], ['partial repair probe 2', [3.2868, 1.5, 110.0, 105.0, 0.0, 2.0, 0.02, 0.05], ['sell call buy put', 1.099962]], ['normal control 1', [4.3607, 8.25, 95.0, 105.0, 0.03, 2.0, 0.0, 0.01], ['none', 0.0]], ['normal control 2', [5.5734, 4.0, 95.0, 105.0, 0.06, 2.0, 0.0, 0.01], ['buy call sell put', 0.299954]], ['normal control 3', [4.35, 8.25, 95.0, 100.0, 0.0, 0.25, 0.0, 0.05], ['sell call buy put', 1.1]], ['normal control 4', [16.25, 8.25, 100.0, 90.0, 0.0, 2.0, 0.0, 0.01], ['buy call sell put', 2.0]]], [['regression dividend adjustment 1', [-0.6516, 1.5, 95.0, 105.0, 0.06, 2.0, 0.02, 0.05], ['buy call sell put', 0.299951]], ['regression dividend adjustment 2', [10.0829, 4.0, 100.0, 90.0, 0.0, 2.0, 0.02, 0.01], ['none', 0.0]], ['partial repair probe 1', [14.7622, 8.25, 95.0, 90.0, 0.03, 2.0, 0.02, 0.05], ['none', 0.0]], ['partial repair probe 2', [5.4145, 8.25, 100.0, 105.0, 0.06, 0.25, 0.02, 0.05], ['sell call buy put', 1.100006]], ['normal control 1', [1.3492, 8.25, 95.0, 105.0, 0.03, 1.0, 0.0, 0.05], ['none', 0.0]], ['normal control 2', [3.7, 4.0, 100.0, 100.0, 0.0, 1.0, 0.0, 0.05], ['buy call sell put', 0.3]], ['normal control 3', [12.558, 8.25, 95.0, 100.0, 0.06, 2.0, 0.0, 0.01], ['buy call sell put', 1.999956]], ['normal control 4', [10.1735, 8.25, 95.0, 100.0, 0.06, 1.0, 0.0, 0.05], ['sell call buy put', 1.099953]]], [['regression dividend adjustment 1', [0.215, 4.0, 95.0, 100.0, 0.06, 0.25, 0.02, 0.05], ['sell call buy put', 0.200008]], ['regression dividend adjustment 2', [9.2213, 8.25, 100.0, 100.0, 0.03, 1.0, 0.02, 0.05], ['none', 0.0]], ['partial repair probe 1', [10.1485, 8.25, 100.0, 100.0, 0.03, 2.0, 0.02, 0.01], ['none', 0.0]], ['partial repair probe 2', [-0.275, 8.25, 95.0, 100.0, 0.0, 2.0, 0.02, 0.05], ['sell call buy put', 0.200003]], ['normal control 1', [-0.996, 4.0, 100.0, 105.0, 0.0, 2.0, 0.0, 0.01], ['none', 0.0]], ['normal control 2', [21.2, 1.5, 110.0, 90.0, 0.0, 2.0, 0.0, 0.01], ['buy call sell put', 0.3]], ['normal control 3', [13.996, 4.0, 110.0, 100.0, 0.0, 2.0, 0.0, 0.01], ['none', 0.0]], ['normal control 4', [9.004, 4.0, 110.0, 105.0, 0.0, 2.0, 0.0, 0.05], ['none', 0.0]]]]
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 dividend adjustment 1	`['sell call buy put', 0.221808]`	`['sell call buy put', 0.199954]`	Failed
regression dividend adjustment 2	`['sell call buy put', 0.070953]`	`['none', 0.0]`	Failed
partial repair probe 1	`['buy call sell put', 1.998725]`	`['buy call sell put', 1.999973]`	Failed
partial repair probe 2	`['sell call buy put', 0.0789]`	`['none', 0.0]`	Failed
normal control 1	`['buy call sell put', 1.999992]`	`['buy call sell put', 1.999992]`	Passed
normal control 2	`['buy call sell put', 0.300025]`	`['buy call sell put', 0.300025]`	Passed
normal control 3	`['buy call sell put', 1.999992]`	`['buy call sell put', 1.999992]`	Passed
normal control 4	`['sell call buy put', 1.100008]`	`['sell call buy put', 1.100008]`	Passed

SHA-256 / f3076973e3dd720b18474784baa74896e7c336e30387f048cf5db416da5a7805

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 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 2026-09-29T14:46:58.744028+00:00.

Case digest / f1824dd702bea94dc7f3dc7fce5ffcda13a87e9b94ca6f45a5a536c789a2c61d