Options Payoff Diagram mechanism

Model scope

The core expiration formulas are standard and the educational-only label is appropriate. NEEDS_REVIEW is required because premium units, contract multipliers, short-leg signs, the S >= 0 domain, and the distinction between finite-range chart extrema and global extrema are not fully specified.

• The long-call and long-put formulas are standard expiration profit formulas, not merely gross payoffs, because they subtract premium; the output terminology should distinguish payoff from profit/loss.
• The short-leg convention is not explicitly defined. A short option leg must contribute the negative of its long-option profit, including the premium received.
• The instruction to 'combine legs' needs an explicit rule: sum signed per-leg profits, with long legs positive and short legs negative.
• Breakeven and maximum gain/loss require an explicit underlying-price domain, normally S >= 0. Without that constraint, put maximum gain and some spread results are not well-defined.
• For arbitrary multi-leg positions there may be multiple breakeven prices, no breakeven, or unbounded gain/loss; the output contract should support all of these cases.

Units and conventions

• S, K, and premium are in the same currency per underlying unit unless a contract multiplier is explicitly supplied.
• For a standard listed equity option, a contract multiplier of 100 underlying units is commonly used, but it must not be assumed silently.
• The formulas compute expiration profit/loss per underlying unit: long call = max(S-K,0)-premium and long put = max(K-S,0)-premium.
• A short leg is the negative of the corresponding long-leg profit, and all legs in a spread use the same underlying price and currency units.
• Underlying prices are assumed nonnegative: S >= 0.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "position": "long call",
    "legs": [
      {
        "type": "call",
        "strike": 100,
        "premium": 7,
        "side": "long",
        "multiplier": 1
      }
    ],
    "underlying_price_domain": "S >= 0",
    "sampled_underlying_prices": [
      80,
      100,
      120
    ]
  },
  "expected_outputs": {
    "sampled_points": [
      {
        "S": 80,
        "profit_loss": -7
      },
      {
        "S": 100,
        "profit_loss": -7
      },
      {
        "S": 120,
        "profit_loss": 13
      }
    ],
    "breakeven_prices": [
      107
    ],
    "max_gain": "unbounded as S increases",
    "max_loss": -7,
    "curve_features": {
      "roots": [
        107
      ],
      "kinks": [
        {
          "S": 100,
          "profit_loss": -7
        }
      ],
      "asymptotes": [],
      "intersections": []
    }
  },
  "working": "For each price, P/L = max(S - 100, 0) - 7. S=80: max(80-100,0)-7 = max(-20,0)-7 = 0-7 = -7. S=100: max(100-100,0)-7 = 0-7 = -7. S=120: max(120-100,0)-7 = 20-7 = 13. Breakeven: max(S-100,0)-7=0; on the in-the-money branch, S-100=7, so S=107. For S <= 100 the loss is -7; for S > 100 profit increases without bound. The payoff kink is at S=100."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The extreme-magnitude vector produces Infinity from 1e308-(-1e308), and a plotting engine that accepts the input without validation can generate a nonfinite payoff curve. The short-leg premium convention is also hazardous if the UI does not explicitly distinguish premium received from premium paid.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json