FA-61561 / Options payoff and settlement / Open access

European option value with continuous dividend yield: maturity uses a 360-day year · case 01

Time value is overstated for every maturity.

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

ROOT CAUSE

T is days/360.

VERIFIED REPAIR

Use calendar days over 365.

Unsuccessful approach: Adding one day to include expiry overstates T.

Case contract

Inputs kind, spot S, strike K, rate r, dividend yield q, volatility sigma and calendar days to expiry. T = days/365. At days == 0 return intrinsic value. Otherwise d1 = (ln(S/K) + (r - q + sigma^2/2)T)/(sigma sqrt T), d2 = d1 - sigma sqrt T, call = S e^{-qT} N(d1) - K e^{-rT} N(d2), put = K e^{-rT} N(-d2) - S e^{-qT} N(-d1). 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
import math
N = 1
observations = []
def solve(kind, S, K, r, q, sigma, days):
    def N(x):
        return 0.5 * (1 + math.erf(x / math.sqrt(2)))
    T = days / 360
    if days == 0:
        return round(max(S - K, 0.0) if kind == 'C' else max(K - S, 0.0), 6)
    d1 = (math.log(S / K) + (r - q + 0.5 * sigma ** 2) * T) / (sigma * math.sqrt(T))
    d2 = d1 - sigma * math.sqrt(T)
    if kind == 'C':
        v = S * math.exp(-q * T) * N(d1) - K * math.exp(-r * T) * N(d2)
    else:
        v = K * math.exp(-r * T) * N(-d2) - S * math.exp(-q * T) * N(-d1)
    return round(v, 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression year fraction basis 1', ['P', 90.0, 100.0, 0.05, 0.0, 0.35, 7], 9.929732], ['regression year fraction basis 2', ['C', 110.0, 100.0, 0.05, 0.0, 0.1, 730], 20.054633], ['partial repair probe 1', ['C', 90.0, 100.0, 0.05, 0.015, 0.35, 1], 0.0], ['partial repair probe 2', ['C', 110.0, 100.0, 0.0, 0.0, 0.35, 1], 10.0], ['boundary control 1', ['C', 110.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['boundary control 2', ['P', 90.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['normal control 1', ['P', 100.0, 95.0, 0.02, 0.0, 0.35, 0], 0.0], ['normal control 2', ['P', 90.0, 95.0, 0.0, 0.015, 0.2, 0], 5.0]], [['regression year fraction basis 1', ['P', 90.0, 105.0, 0.05, 0.0, 0.2, 7], 14.899363], ['regression year fraction basis 2', ['P', 90.0, 95.0, 0.0, 0.03, 0.35, 7], 5.342895], ['partial repair probe 1', ['C', 100.0, 105.0, 0.0, 0.0, 0.2, 1], 0.0], ['partial repair probe 2', ['P', 110.0, 100.0, 0.02, 0.0, 0.35, 1], 0.0], ['boundary control 1', ['P', 90.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['boundary control 2', ['C', 110.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['normal control 1', ['C', 90.0, 105.0, 0.02, 0.0, 0.1, 30], 0.0], ['normal control 2', ['P', 110.0, 100.0, 0.0, 0.0, 0.2, 0], 0.0]], [['regression year fraction basis 1', ['P', 110.0, 105.0, 0.02, 0.0, 0.2, 91], 2.06459], ['regression year fraction basis 2', ['P', 110.0, 100.0, 0.05, 0.0, 0.35, 365], 8.005014], ['partial repair probe 1', ['C', 100.0, 105.0, 0.05, 0.03, 0.2, 1], 0.0], ['partial repair probe 2', ['P', 110.0, 100.0, 0.02, 0.0, 0.35, 1], 0.0], ['boundary control 1', ['C', 110.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['boundary control 2', ['P', 90.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['normal control 1', ['P', 90.0, 100.0, 0.0, 0.03, 0.1, 0], 10.0], ['normal control 2', ['P', 110.0, 100.0, 0.05, 0.0, 0.35, 0], 0.0]], [['regression year fraction basis 1', ['P', 90.0, 95.0, 0.05, 0.03, 0.1, 730], 5.435985], ['regression year fraction basis 2', ['P', 100.0, 95.0, 0.05, 0.03, 0.35, 730], 13.789355], ['partial repair probe 1', ['C', 90.0, 100.0, 0.0, 0.0, 0.35, 1], 0.0], ['partial repair probe 2', ['P', 100.0, 105.0, 0.0, 0.0, 0.2, 1], 5.0], ['boundary control 1', ['P', 90.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['boundary control 2', ['C', 110.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['normal control 1', ['C', 110.0, 105.0, 0.0, 0.0, 0.1, 0], 5.0], ['normal control 2', ['P', 110.0, 95.0, 0.05, 0.015, 0.1, 0], 0.0]], [['regression year fraction basis 1', ['C', 90.0, 95.0, 0.05, 0.0, 0.1, 730], 7.238649], ['regression year fraction basis 2', ['C', 90.0, 100.0, 0.02, 0.0, 0.35, 30], 0.742384], ['partial repair probe 1', ['C', 100.0, 105.0, 0.05, 0.0, 0.2, 1], 0.0], ['partial repair probe 2', ['C', 90.0, 95.0, 0.05, 0.015, 0.2, 1], 0.0], ['boundary control 1', ['P', 90.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['boundary control 2', ['C', 110.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['normal control 1', ['P', 110.0, 95.0, 0.0, 0.015, 0.1, 30], 0.0], ['normal control 2', ['C', 90.0, 95.0, 0.0, 0.03, 0.1, 1], 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 year fraction basis 1	`9.929688`	`9.929732`	Failed
regression year fraction basis 2	`20.183244`	`20.054633`	Failed
partial repair probe 1	`0.0`	`0.0`	Passed
partial repair probe 2	`10.0`	`10.0`	Passed
boundary control 1	`10.0`	`10.0`	Passed
boundary control 2	`10.0`	`10.0`	Passed
normal control 1	`0.0`	`0.0`	Passed
normal control 2	`5.0`	`5.0`	Passed

SHA-256 / e2b10ab92f94c85a7959cf031384b414a045d820ac72b8180290a22b1dcde8ea

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(kind, S, K, r, q, sigma, days):
    def N(x):
        return 0.5 * (1 + math.erf(x / math.sqrt(2)))
    T = (days + 1) / 365
    if days == 0:
        return round(max(S - K, 0.0) if kind == 'C' else max(K - S, 0.0), 6)
    d1 = (math.log(S / K) + (r - q + 0.5 * sigma ** 2) * T) / (sigma * math.sqrt(T))
    d2 = d1 - sigma * math.sqrt(T)
    if kind == 'C':
        v = S * math.exp(-q * T) * N(d1) - K * math.exp(-r * T) * N(d2)
    else:
        v = K * math.exp(-r * T) * N(-d2) - S * math.exp(-q * T) * N(-d1)
    return round(v, 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression year fraction basis 1', ['P', 90.0, 100.0, 0.05, 0.0, 0.35, 7], 9.929732], ['regression year fraction basis 2', ['C', 110.0, 100.0, 0.05, 0.0, 0.1, 730], 20.054633], ['partial repair probe 1', ['C', 90.0, 100.0, 0.05, 0.015, 0.35, 1], 0.0], ['partial repair probe 2', ['C', 110.0, 100.0, 0.0, 0.0, 0.35, 1], 10.0], ['boundary control 1', ['C', 110.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['boundary control 2', ['P', 90.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['normal control 1', ['P', 100.0, 95.0, 0.02, 0.0, 0.35, 0], 0.0], ['normal control 2', ['P', 90.0, 95.0, 0.0, 0.015, 0.2, 0], 5.0]], [['regression year fraction basis 1', ['P', 90.0, 105.0, 0.05, 0.0, 0.2, 7], 14.899363], ['regression year fraction basis 2', ['P', 90.0, 95.0, 0.0, 0.03, 0.35, 7], 5.342895], ['partial repair probe 1', ['C', 100.0, 105.0, 0.0, 0.0, 0.2, 1], 0.0], ['partial repair probe 2', ['P', 110.0, 100.0, 0.02, 0.0, 0.35, 1], 0.0], ['boundary control 1', ['P', 90.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['boundary control 2', ['C', 110.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['normal control 1', ['C', 90.0, 105.0, 0.02, 0.0, 0.1, 30], 0.0], ['normal control 2', ['P', 110.0, 100.0, 0.0, 0.0, 0.2, 0], 0.0]], [['regression year fraction basis 1', ['P', 110.0, 105.0, 0.02, 0.0, 0.2, 91], 2.06459], ['regression year fraction basis 2', ['P', 110.0, 100.0, 0.05, 0.0, 0.35, 365], 8.005014], ['partial repair probe 1', ['C', 100.0, 105.0, 0.05, 0.03, 0.2, 1], 0.0], ['partial repair probe 2', ['P', 110.0, 100.0, 0.02, 0.0, 0.35, 1], 0.0], ['boundary control 1', ['C', 110.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['boundary control 2', ['P', 90.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['normal control 1', ['P', 90.0, 100.0, 0.0, 0.03, 0.1, 0], 10.0], ['normal control 2', ['P', 110.0, 100.0, 0.05, 0.0, 0.35, 0], 0.0]], [['regression year fraction basis 1', ['P', 90.0, 95.0, 0.05, 0.03, 0.1, 730], 5.435985], ['regression year fraction basis 2', ['P', 100.0, 95.0, 0.05, 0.03, 0.35, 730], 13.789355], ['partial repair probe 1', ['C', 90.0, 100.0, 0.0, 0.0, 0.35, 1], 0.0], ['partial repair probe 2', ['P', 100.0, 105.0, 0.0, 0.0, 0.2, 1], 5.0], ['boundary control 1', ['P', 90.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['boundary control 2', ['C', 110.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['normal control 1', ['C', 110.0, 105.0, 0.0, 0.0, 0.1, 0], 5.0], ['normal control 2', ['P', 110.0, 95.0, 0.05, 0.015, 0.1, 0], 0.0]], [['regression year fraction basis 1', ['C', 90.0, 95.0, 0.05, 0.0, 0.1, 730], 7.238649], ['regression year fraction basis 2', ['C', 90.0, 100.0, 0.02, 0.0, 0.35, 30], 0.742384], ['partial repair probe 1', ['C', 100.0, 105.0, 0.05, 0.0, 0.2, 1], 0.0], ['partial repair probe 2', ['C', 90.0, 95.0, 0.05, 0.015, 0.2, 1], 0.0], ['boundary control 1', ['P', 90.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['boundary control 2', ['C', 110.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['normal control 1', ['P', 110.0, 95.0, 0.0, 0.015, 0.1, 30], 0.0], ['normal control 2', ['C', 90.0, 95.0, 0.0, 0.03, 0.1, 1], 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 year fraction basis 1	`9.930832`	`9.929732`	Failed
regression year fraction basis 2	`20.06733`	`20.054633`	Failed
partial repair probe 1	`1.3e-05`	`0.0`	Failed
partial repair probe 2	`10.000077`	`10.0`	Failed
boundary control 1	`10.0`	`10.0`	Passed
boundary control 2	`10.0`	`10.0`	Passed
normal control 1	`0.0`	`0.0`	Passed
normal control 2	`5.0`	`5.0`	Passed

SHA-256 / 1bbd17acee87c299a68b216cef8c13c3df95f68bd1aca2c7e970c5b48af6b717

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(kind, S, K, r, q, sigma, days):
    def N(x):
        return 0.5 * (1 + math.erf(x / math.sqrt(2)))
    T = days / 365
    if days == 0:
        return round(max(S - K, 0.0) if kind == 'C' else max(K - S, 0.0), 6)
    d1 = (math.log(S / K) + (r - q + 0.5 * sigma ** 2) * T) / (sigma * math.sqrt(T))
    d2 = d1 - sigma * math.sqrt(T)
    if kind == 'C':
        v = S * math.exp(-q * T) * N(d1) - K * math.exp(-r * T) * N(d2)
    else:
        v = K * math.exp(-r * T) * N(-d2) - S * math.exp(-q * T) * N(-d1)
    return round(v, 6)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression year fraction basis 1', ['P', 90.0, 100.0, 0.05, 0.0, 0.35, 7], 9.929732], ['regression year fraction basis 2', ['C', 110.0, 100.0, 0.05, 0.0, 0.1, 730], 20.054633], ['partial repair probe 1', ['C', 90.0, 100.0, 0.05, 0.015, 0.35, 1], 0.0], ['partial repair probe 2', ['C', 110.0, 100.0, 0.0, 0.0, 0.35, 1], 10.0], ['boundary control 1', ['C', 110.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['boundary control 2', ['P', 90.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['normal control 1', ['P', 100.0, 95.0, 0.02, 0.0, 0.35, 0], 0.0], ['normal control 2', ['P', 90.0, 95.0, 0.0, 0.015, 0.2, 0], 5.0]], [['regression year fraction basis 1', ['P', 90.0, 105.0, 0.05, 0.0, 0.2, 7], 14.899363], ['regression year fraction basis 2', ['P', 90.0, 95.0, 0.0, 0.03, 0.35, 7], 5.342895], ['partial repair probe 1', ['C', 100.0, 105.0, 0.0, 0.0, 0.2, 1], 0.0], ['partial repair probe 2', ['P', 110.0, 100.0, 0.02, 0.0, 0.35, 1], 0.0], ['boundary control 1', ['P', 90.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['boundary control 2', ['C', 110.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['normal control 1', ['C', 90.0, 105.0, 0.02, 0.0, 0.1, 30], 0.0], ['normal control 2', ['P', 110.0, 100.0, 0.0, 0.0, 0.2, 0], 0.0]], [['regression year fraction basis 1', ['P', 110.0, 105.0, 0.02, 0.0, 0.2, 91], 2.06459], ['regression year fraction basis 2', ['P', 110.0, 100.0, 0.05, 0.0, 0.35, 365], 8.005014], ['partial repair probe 1', ['C', 100.0, 105.0, 0.05, 0.03, 0.2, 1], 0.0], ['partial repair probe 2', ['P', 110.0, 100.0, 0.02, 0.0, 0.35, 1], 0.0], ['boundary control 1', ['C', 110.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['boundary control 2', ['P', 90.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['normal control 1', ['P', 90.0, 100.0, 0.0, 0.03, 0.1, 0], 10.0], ['normal control 2', ['P', 110.0, 100.0, 0.05, 0.0, 0.35, 0], 0.0]], [['regression year fraction basis 1', ['P', 90.0, 95.0, 0.05, 0.03, 0.1, 730], 5.435985], ['regression year fraction basis 2', ['P', 100.0, 95.0, 0.05, 0.03, 0.35, 730], 13.789355], ['partial repair probe 1', ['C', 90.0, 100.0, 0.0, 0.0, 0.35, 1], 0.0], ['partial repair probe 2', ['P', 100.0, 105.0, 0.0, 0.0, 0.2, 1], 5.0], ['boundary control 1', ['P', 90.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['boundary control 2', ['C', 110.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['normal control 1', ['C', 110.0, 105.0, 0.0, 0.0, 0.1, 0], 5.0], ['normal control 2', ['P', 110.0, 95.0, 0.05, 0.015, 0.1, 0], 0.0]], [['regression year fraction basis 1', ['C', 90.0, 95.0, 0.05, 0.0, 0.1, 730], 7.238649], ['regression year fraction basis 2', ['C', 90.0, 100.0, 0.02, 0.0, 0.35, 30], 0.742384], ['partial repair probe 1', ['C', 100.0, 105.0, 0.05, 0.0, 0.2, 1], 0.0], ['partial repair probe 2', ['C', 90.0, 95.0, 0.05, 0.015, 0.2, 1], 0.0], ['boundary control 1', ['P', 90.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['boundary control 2', ['C', 110.0, 100.0, 0.05, 0.0, 0.2, 0], 10.0], ['normal control 1', ['P', 110.0, 95.0, 0.0, 0.015, 0.1, 30], 0.0], ['normal control 2', ['C', 90.0, 95.0, 0.0, 0.03, 0.1, 1], 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 year fraction basis 1	`9.929732`	`9.929732`	Passed
regression year fraction basis 2	`20.054633`	`20.054633`	Passed
partial repair probe 1	`0.0`	`0.0`	Passed
partial repair probe 2	`10.0`	`10.0`	Passed
boundary control 1	`10.0`	`10.0`	Passed
boundary control 2	`10.0`	`10.0`	Passed
normal control 1	`0.0`	`0.0`	Passed
normal control 2	`5.0`	`5.0`	Passed

SHA-256 / 033b0fd603e39849ee2e7de220aa1e88946f6bee5842753fb49bf178c5fd9fa2

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 2026-09-29T14:46:56.398436+00:00.

Case digest / a5e6b5f8c4cf5ebed789c0f4cbe507bcb2df2952b0658a436aacdc474ac6dc2d