FA-61511 / Options payoff and settlement / Open access

Option strategy max gain, max loss and breakevens: the zero underlying price is not evaluated · case 01

Long puts and long stock report the wrong extreme at a zero price.

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

ROOT CAUSE

Breakpoints are only the strikes.

VERIFIED REPAIR

Include 0 as a breakpoint.

Unsuccessful approach: Adding 0 only when a put is present still misses stock legs.

Case contract

Inputs legs [kind C/P/S, strike (purchase price for stock S), signed qty, premium] and a multiplier. Expiry value V(S) = multiplier * sum(q*(intrinsic - premium)) for options and q*(S - price) for stock, in exact fractions. Breakpoints are 0 and every strike. Tail slope = V(top+1)-V(top). Max gain is None if the slope > 0 else the max over breakpoints; max loss is None if slope < 0 else the min. Breakevens are zeros at breakpoints and linear-interpolated sign changes between them and in the tail. Return [gain, loss, breakevens] rounded to 4.

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
from fractions import Fraction
N = 1
observations = []
def solve(legs, multiplier):
    def value(S):
        t = Fraction(0)
        for kind, k, q, prem in legs:
            p = Fraction(str(prem))
            if kind == 'C':
                t += q * (max(S - k, 0) - p)
            elif kind == 'P':
                t += q * (max(k - S, 0) - p)
            else:
                t += q * (S - k)
        return t * multiplier
    pts = sorted(set(leg[1] for leg in legs))
    top = pts[-1]
    slope = value(top + 1) - value(top)
    vals = [value(p) for p in pts]
    gain = None if slope > 0 else max(vals)
    loss = None if slope < 0 else min(vals)
    bes = []
    for a, b in zip(pts, pts[1:]):
        va, vb = value(a), value(b)
        if va == 0:
            bes.append(Fraction(a))
        elif va * vb < 0:
            bes.append(a - va * (b - a) / (vb - va))
    vt = value(top)
    if vt == 0:
        bes.append(Fraction(top))
    elif vt * slope < 0:
        bes.append(top - vt / slope)
    def r4(x):
        return None if x is None else float(round(x, 4))
    return [r4(gain), r4(loss), [r4(x) for x in sorted(set(bes))]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression zero price breakpoint 1', [[['S', 90, -1, 0.0], ['C', 95, -1, 1.25], ['P', 90, 2, 2.0], ['P', 115, -2, 1.25]], 1], [39.75, None, [39.75]]], ['regression zero price breakpoint 2', [[['P', 105, -2, 0.5]], 1], [1.0, -209.0, [104.5]]], ['partial repair probe 1', [[['S', 95, -1, 0.0]], 1], [95.0, None, [95.0]]], ['partial repair probe 2', [[['C', 105, 1, 2.0], ['C', 95, 2, 3.4], ['S', 105, 1, 0.0], ['C', 115, -2, 2.0]], 100], [None, -10980.0, [99.9333]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['P', 95, -2, 0.5], ['S', 90, -1, 0.0]], 100], [-400.0, None, []]], ['normal control 2', [[['S', 115, 2, 0.0], ['C', 95, -2, 2.0], ['C', 85, -1, 1.25], ['C', 90, -1, 0.5]], 1], [-49.25, None, []]], ['normal control 3', [[['C', 90, -1, 2.0]], 100], [200.0, None, [92.0]]]], [['regression zero price breakpoint 1', [[['S', 115, -2, 0.0], ['P', 80, 1, 3.4]], 1], [306.6, None, [113.3]]], ['regression zero price breakpoint 2', [[['P', 100, -1, 1.25], ['C', 85, 1, 7.75], ['C', 100, 1, 0.5], ['C', 120, -1, 1.25]], 100], [None, -10575.0, [95.375]]], ['partial repair probe 1', [[['S', 120, -1, 0.0]], 1], [120.0, None, [120.0]]], ['partial repair probe 2', [[['S', 90, -1, 0.0]], 100], [9000.0, None, [90.0]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 85, -1, 3.4]], 100], [340.0, None, [88.4]]], ['normal control 2', [[['C', 85, -1, 5.1]], 1], [5.1, None, [90.1]]], ['normal control 3', [[['P', 95, 1, 2.0], ['C', 105, 2, 1.25], ['P', 105, -1, 5.1]], 100], [None, -940.0, [104.4]]]], [['regression zero price breakpoint 1', [[['P', 100, -2, 3.4], ['S', 115, 1, 0.0]], 1], [None, -308.2, [108.2]]], ['regression zero price breakpoint 2', [[['P', 100, -1, 2.0]], 100], [200.0, -9800.0, [98.0]]], ['partial repair probe 1', [[['S', 85, -2, 0.0], ['S', 85, 2, 0.0]], 1], [0.0, 0.0, [0.0, 85.0]]], ['partial repair probe 2', [[['C', 105, -1, 0.5], ['S', 115, -1, 0.0]], 100], [11550.0, None, [110.25]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 115, -1, 7.75]], 1], [7.75, None, [122.75]]], ['normal control 2', [[['S', 85, -1, 0.0], ['C', 80, -1, 2.0], ['P', 85, -1, 7.75]], 1], [9.75, None, [87.375]]], ['normal control 3', [[['C', 85, 1, 7.75], ['C', 95, -1, 5.1]], 1], [7.35, -2.65, [87.65]]]], [['regression zero price breakpoint 1', [[['C', 110, 1, 5.1], ['P', 115, -1, 5.1]], 1], [None, -115.0, [112.5]]], ['regression zero price breakpoint 2', [[['P', 80, 1, 0.5], ['C', 105, 1, 1.25], ['C', 105, 2, 5.1]], 1], [None, -11.95, [68.05, 108.9833]]], ['partial repair probe 1', [[['S', 105, 1, 0.0]], 100], [None, -10500.0, [105.0]]], ['partial repair probe 2', [[['C', 80, 1, 2.0], ['S', 90, 2, 0.0]], 1], [None, -182.0, [87.3333]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 80, 1, 2.0], ['C', 80, 2, 5.1], ['C', 110, -2, 0.5]], 100], [None, -1120.0, [83.7333]]], ['normal control 2', [[['P', 115, 1, 7.75], ['C', 85, 2, 7.75]], 100], [None, 675.0, []]], ['normal control 3', [[['C', 80, 1, 5.1], ['P', 90, 2, 1.25], ['P', 90, -1, 2.0]], 1], [None, 4.4, []]]], [['regression zero price breakpoint 1', [[['S', 80, 1, 0.0], ['C', 105, -1, 1.25]], 1], [26.25, -78.75, [78.75]]], ['regression zero price breakpoint 2', [[['P', 110, -1, 5.1], ['P', 100, -1, 0.5], ['P', 85, -2, 5.1]], 100], [1580.0, -36420.0, [97.1]]], ['partial repair probe 1', [[['C', 120, 1, 2.0], ['S', 90, 1, 0.0], ['S', 120, 2, 0.0], ['S', 100, 1, 0.0]], 100], [None, -43200.0, [108.0]]], ['partial repair probe 2', [[['S', 95, 1, 0.0], ['S', 115, 2, 0.0]], 1], [None, -325.0, [108.3333]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 100, 2, 2.0], ['C', 85, 1, 3.4]], 1], [None, -7.4, [92.4]]], ['normal control 2', [[['C', 110, -1, 7.75]], 1], [7.75, None, [117.75]]], ['normal control 3', [[['C', 110, 1, 1.25]], 100], [None, -125.0, [111.25]]]]]
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 zero price breakpoint 1	`[-45.25, None, []]`	`[39.75, None, [39.75]]`	Failed
regression zero price breakpoint 2	`[1.0, 1.0, []]`	`[1.0, -209.0, [104.5]]`	Failed
partial repair probe 1	`[0.0, None, [95.0]]`	`[95.0, None, [95.0]]`	Failed
partial repair probe 2	`[None, -1480.0, [99.9333]]`	`[None, -10980.0, [99.9333]]`	Failed
boundary control 1	`[None, -200.0, [102.0]]`	`[None, -200.0, [102.0]]`	Passed
normal control 1	`[-400.0, None, []]`	`[-400.0, None, []]`	Passed
normal control 2	`[-49.25, None, []]`	`[-49.25, None, []]`	Passed
normal control 3	`[200.0, None, [92.0]]`	`[200.0, None, [92.0]]`	Passed

SHA-256 / 30a9d72e16aa3fb5c979baf0cc4ebb5744cb4091471c3e93b740a3b4f7324c1a

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(legs, multiplier):
    def value(S):
        t = Fraction(0)
        for kind, k, q, prem in legs:
            p = Fraction(str(prem))
            if kind == 'C':
                t += q * (max(S - k, 0) - p)
            elif kind == 'P':
                t += q * (max(k - S, 0) - p)
            else:
                t += q * (S - k)
        return t * multiplier
    pts = sorted(set(([0] if any(l[0] == 'P' for l in legs) else []) + [leg[1] for leg in legs]))
    top = pts[-1]
    slope = value(top + 1) - value(top)
    vals = [value(p) for p in pts]
    gain = None if slope > 0 else max(vals)
    loss = None if slope < 0 else min(vals)
    bes = []
    for a, b in zip(pts, pts[1:]):
        va, vb = value(a), value(b)
        if va == 0:
            bes.append(Fraction(a))
        elif va * vb < 0:
            bes.append(a - va * (b - a) / (vb - va))
    vt = value(top)
    if vt == 0:
        bes.append(Fraction(top))
    elif vt * slope < 0:
        bes.append(top - vt / slope)
    def r4(x):
        return None if x is None else float(round(x, 4))
    return [r4(gain), r4(loss), [r4(x) for x in sorted(set(bes))]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression zero price breakpoint 1', [[['S', 90, -1, 0.0], ['C', 95, -1, 1.25], ['P', 90, 2, 2.0], ['P', 115, -2, 1.25]], 1], [39.75, None, [39.75]]], ['regression zero price breakpoint 2', [[['P', 105, -2, 0.5]], 1], [1.0, -209.0, [104.5]]], ['partial repair probe 1', [[['S', 95, -1, 0.0]], 1], [95.0, None, [95.0]]], ['partial repair probe 2', [[['C', 105, 1, 2.0], ['C', 95, 2, 3.4], ['S', 105, 1, 0.0], ['C', 115, -2, 2.0]], 100], [None, -10980.0, [99.9333]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['P', 95, -2, 0.5], ['S', 90, -1, 0.0]], 100], [-400.0, None, []]], ['normal control 2', [[['S', 115, 2, 0.0], ['C', 95, -2, 2.0], ['C', 85, -1, 1.25], ['C', 90, -1, 0.5]], 1], [-49.25, None, []]], ['normal control 3', [[['C', 90, -1, 2.0]], 100], [200.0, None, [92.0]]]], [['regression zero price breakpoint 1', [[['S', 115, -2, 0.0], ['P', 80, 1, 3.4]], 1], [306.6, None, [113.3]]], ['regression zero price breakpoint 2', [[['P', 100, -1, 1.25], ['C', 85, 1, 7.75], ['C', 100, 1, 0.5], ['C', 120, -1, 1.25]], 100], [None, -10575.0, [95.375]]], ['partial repair probe 1', [[['S', 120, -1, 0.0]], 1], [120.0, None, [120.0]]], ['partial repair probe 2', [[['S', 90, -1, 0.0]], 100], [9000.0, None, [90.0]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 85, -1, 3.4]], 100], [340.0, None, [88.4]]], ['normal control 2', [[['C', 85, -1, 5.1]], 1], [5.1, None, [90.1]]], ['normal control 3', [[['P', 95, 1, 2.0], ['C', 105, 2, 1.25], ['P', 105, -1, 5.1]], 100], [None, -940.0, [104.4]]]], [['regression zero price breakpoint 1', [[['P', 100, -2, 3.4], ['S', 115, 1, 0.0]], 1], [None, -308.2, [108.2]]], ['regression zero price breakpoint 2', [[['P', 100, -1, 2.0]], 100], [200.0, -9800.0, [98.0]]], ['partial repair probe 1', [[['S', 85, -2, 0.0], ['S', 85, 2, 0.0]], 1], [0.0, 0.0, [0.0, 85.0]]], ['partial repair probe 2', [[['C', 105, -1, 0.5], ['S', 115, -1, 0.0]], 100], [11550.0, None, [110.25]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 115, -1, 7.75]], 1], [7.75, None, [122.75]]], ['normal control 2', [[['S', 85, -1, 0.0], ['C', 80, -1, 2.0], ['P', 85, -1, 7.75]], 1], [9.75, None, [87.375]]], ['normal control 3', [[['C', 85, 1, 7.75], ['C', 95, -1, 5.1]], 1], [7.35, -2.65, [87.65]]]], [['regression zero price breakpoint 1', [[['C', 110, 1, 5.1], ['P', 115, -1, 5.1]], 1], [None, -115.0, [112.5]]], ['regression zero price breakpoint 2', [[['P', 80, 1, 0.5], ['C', 105, 1, 1.25], ['C', 105, 2, 5.1]], 1], [None, -11.95, [68.05, 108.9833]]], ['partial repair probe 1', [[['S', 105, 1, 0.0]], 100], [None, -10500.0, [105.0]]], ['partial repair probe 2', [[['C', 80, 1, 2.0], ['S', 90, 2, 0.0]], 1], [None, -182.0, [87.3333]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 80, 1, 2.0], ['C', 80, 2, 5.1], ['C', 110, -2, 0.5]], 100], [None, -1120.0, [83.7333]]], ['normal control 2', [[['P', 115, 1, 7.75], ['C', 85, 2, 7.75]], 100], [None, 675.0, []]], ['normal control 3', [[['C', 80, 1, 5.1], ['P', 90, 2, 1.25], ['P', 90, -1, 2.0]], 1], [None, 4.4, []]]], [['regression zero price breakpoint 1', [[['S', 80, 1, 0.0], ['C', 105, -1, 1.25]], 1], [26.25, -78.75, [78.75]]], ['regression zero price breakpoint 2', [[['P', 110, -1, 5.1], ['P', 100, -1, 0.5], ['P', 85, -2, 5.1]], 100], [1580.0, -36420.0, [97.1]]], ['partial repair probe 1', [[['C', 120, 1, 2.0], ['S', 90, 1, 0.0], ['S', 120, 2, 0.0], ['S', 100, 1, 0.0]], 100], [None, -43200.0, [108.0]]], ['partial repair probe 2', [[['S', 95, 1, 0.0], ['S', 115, 2, 0.0]], 1], [None, -325.0, [108.3333]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 100, 2, 2.0], ['C', 85, 1, 3.4]], 1], [None, -7.4, [92.4]]], ['normal control 2', [[['C', 110, -1, 7.75]], 1], [7.75, None, [117.75]]], ['normal control 3', [[['C', 110, 1, 1.25]], 100], [None, -125.0, [111.25]]]]]
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 zero price breakpoint 1	`[39.75, None, [39.75]]`	`[39.75, None, [39.75]]`	Passed
regression zero price breakpoint 2	`[1.0, -209.0, [104.5]]`	`[1.0, -209.0, [104.5]]`	Passed
partial repair probe 1	`[0.0, None, [95.0]]`	`[95.0, None, [95.0]]`	Failed
partial repair probe 2	`[None, -1480.0, [99.9333]]`	`[None, -10980.0, [99.9333]]`	Failed
boundary control 1	`[None, -200.0, [102.0]]`	`[None, -200.0, [102.0]]`	Passed
normal control 1	`[-400.0, None, []]`	`[-400.0, None, []]`	Passed
normal control 2	`[-49.25, None, []]`	`[-49.25, None, []]`	Passed
normal control 3	`[200.0, None, [92.0]]`	`[200.0, None, [92.0]]`	Passed

SHA-256 / 54eb426c19e7682caea9fa703f31c73b285ea954458f3f15b757b5c0dff280b1

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(legs, multiplier):
    def value(S):
        t = Fraction(0)
        for kind, k, q, prem in legs:
            p = Fraction(str(prem))
            if kind == 'C':
                t += q * (max(S - k, 0) - p)
            elif kind == 'P':
                t += q * (max(k - S, 0) - p)
            else:
                t += q * (S - k)
        return t * multiplier
    pts = sorted(set([0] + [leg[1] for leg in legs]))
    top = pts[-1]
    slope = value(top + 1) - value(top)
    vals = [value(p) for p in pts]
    gain = None if slope > 0 else max(vals)
    loss = None if slope < 0 else min(vals)
    bes = []
    for a, b in zip(pts, pts[1:]):
        va, vb = value(a), value(b)
        if va == 0:
            bes.append(Fraction(a))
        elif va * vb < 0:
            bes.append(a - va * (b - a) / (vb - va))
    vt = value(top)
    if vt == 0:
        bes.append(Fraction(top))
    elif vt * slope < 0:
        bes.append(top - vt / slope)
    def r4(x):
        return None if x is None else float(round(x, 4))
    return [r4(gain), r4(loss), [r4(x) for x in sorted(set(bes))]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression zero price breakpoint 1', [[['S', 90, -1, 0.0], ['C', 95, -1, 1.25], ['P', 90, 2, 2.0], ['P', 115, -2, 1.25]], 1], [39.75, None, [39.75]]], ['regression zero price breakpoint 2', [[['P', 105, -2, 0.5]], 1], [1.0, -209.0, [104.5]]], ['partial repair probe 1', [[['S', 95, -1, 0.0]], 1], [95.0, None, [95.0]]], ['partial repair probe 2', [[['C', 105, 1, 2.0], ['C', 95, 2, 3.4], ['S', 105, 1, 0.0], ['C', 115, -2, 2.0]], 100], [None, -10980.0, [99.9333]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['P', 95, -2, 0.5], ['S', 90, -1, 0.0]], 100], [-400.0, None, []]], ['normal control 2', [[['S', 115, 2, 0.0], ['C', 95, -2, 2.0], ['C', 85, -1, 1.25], ['C', 90, -1, 0.5]], 1], [-49.25, None, []]], ['normal control 3', [[['C', 90, -1, 2.0]], 100], [200.0, None, [92.0]]]], [['regression zero price breakpoint 1', [[['S', 115, -2, 0.0], ['P', 80, 1, 3.4]], 1], [306.6, None, [113.3]]], ['regression zero price breakpoint 2', [[['P', 100, -1, 1.25], ['C', 85, 1, 7.75], ['C', 100, 1, 0.5], ['C', 120, -1, 1.25]], 100], [None, -10575.0, [95.375]]], ['partial repair probe 1', [[['S', 120, -1, 0.0]], 1], [120.0, None, [120.0]]], ['partial repair probe 2', [[['S', 90, -1, 0.0]], 100], [9000.0, None, [90.0]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 85, -1, 3.4]], 100], [340.0, None, [88.4]]], ['normal control 2', [[['C', 85, -1, 5.1]], 1], [5.1, None, [90.1]]], ['normal control 3', [[['P', 95, 1, 2.0], ['C', 105, 2, 1.25], ['P', 105, -1, 5.1]], 100], [None, -940.0, [104.4]]]], [['regression zero price breakpoint 1', [[['P', 100, -2, 3.4], ['S', 115, 1, 0.0]], 1], [None, -308.2, [108.2]]], ['regression zero price breakpoint 2', [[['P', 100, -1, 2.0]], 100], [200.0, -9800.0, [98.0]]], ['partial repair probe 1', [[['S', 85, -2, 0.0], ['S', 85, 2, 0.0]], 1], [0.0, 0.0, [0.0, 85.0]]], ['partial repair probe 2', [[['C', 105, -1, 0.5], ['S', 115, -1, 0.0]], 100], [11550.0, None, [110.25]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 115, -1, 7.75]], 1], [7.75, None, [122.75]]], ['normal control 2', [[['S', 85, -1, 0.0], ['C', 80, -1, 2.0], ['P', 85, -1, 7.75]], 1], [9.75, None, [87.375]]], ['normal control 3', [[['C', 85, 1, 7.75], ['C', 95, -1, 5.1]], 1], [7.35, -2.65, [87.65]]]], [['regression zero price breakpoint 1', [[['C', 110, 1, 5.1], ['P', 115, -1, 5.1]], 1], [None, -115.0, [112.5]]], ['regression zero price breakpoint 2', [[['P', 80, 1, 0.5], ['C', 105, 1, 1.25], ['C', 105, 2, 5.1]], 1], [None, -11.95, [68.05, 108.9833]]], ['partial repair probe 1', [[['S', 105, 1, 0.0]], 100], [None, -10500.0, [105.0]]], ['partial repair probe 2', [[['C', 80, 1, 2.0], ['S', 90, 2, 0.0]], 1], [None, -182.0, [87.3333]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 80, 1, 2.0], ['C', 80, 2, 5.1], ['C', 110, -2, 0.5]], 100], [None, -1120.0, [83.7333]]], ['normal control 2', [[['P', 115, 1, 7.75], ['C', 85, 2, 7.75]], 100], [None, 675.0, []]], ['normal control 3', [[['C', 80, 1, 5.1], ['P', 90, 2, 1.25], ['P', 90, -1, 2.0]], 1], [None, 4.4, []]]], [['regression zero price breakpoint 1', [[['S', 80, 1, 0.0], ['C', 105, -1, 1.25]], 1], [26.25, -78.75, [78.75]]], ['regression zero price breakpoint 2', [[['P', 110, -1, 5.1], ['P', 100, -1, 0.5], ['P', 85, -2, 5.1]], 100], [1580.0, -36420.0, [97.1]]], ['partial repair probe 1', [[['C', 120, 1, 2.0], ['S', 90, 1, 0.0], ['S', 120, 2, 0.0], ['S', 100, 1, 0.0]], 100], [None, -43200.0, [108.0]]], ['partial repair probe 2', [[['S', 95, 1, 0.0], ['S', 115, 2, 0.0]], 1], [None, -325.0, [108.3333]]], ['boundary control 1', [[['C', 100, 1, 2.0]], 100], [None, -200.0, [102.0]]], ['normal control 1', [[['C', 100, 2, 2.0], ['C', 85, 1, 3.4]], 1], [None, -7.4, [92.4]]], ['normal control 2', [[['C', 110, -1, 7.75]], 1], [7.75, None, [117.75]]], ['normal control 3', [[['C', 110, 1, 1.25]], 100], [None, -125.0, [111.25]]]]]
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 zero price breakpoint 1	`[39.75, None, [39.75]]`	`[39.75, None, [39.75]]`	Passed
regression zero price breakpoint 2	`[1.0, -209.0, [104.5]]`	`[1.0, -209.0, [104.5]]`	Passed
partial repair probe 1	`[95.0, None, [95.0]]`	`[95.0, None, [95.0]]`	Passed
partial repair probe 2	`[None, -10980.0, [99.9333]]`	`[None, -10980.0, [99.9333]]`	Passed
boundary control 1	`[None, -200.0, [102.0]]`	`[None, -200.0, [102.0]]`	Passed
normal control 1	`[-400.0, None, []]`	`[-400.0, None, []]`	Passed
normal control 2	`[-49.25, None, []]`	`[-49.25, None, []]`	Passed
normal control 3	`[200.0, None, [92.0]]`	`[200.0, None, [92.0]]`	Passed

SHA-256 / 27e4d30e35e9b7ca01712acd9b28deb88d10aec2c685f1231a1a0434d4c4e022

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 2026-09-29T14:46:55.871207+00:00.

Case digest / 90c6489ced5f55d5badfab20033af7ca8302714a4be5ebd1b290295fbd4af03c