Source: https://guthlabs.ai/docs/instruments/options-payoff-diagram/

instrument / verified-clean

# Options Payoff Diagram

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/options-payoff-diagram/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/options-payoff-diagram/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/options-payoff-diagram/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/options-payoff-diagram/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Finance, Economics & Business (educational only — never individualized investment, tax, or legal advice)

**Tranche**: tranche-6

**Evidence ID**: t6-071

**Ledger rows**: 1

No ledger note is attached.

## Review findings

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.

### Formula and scope findings

- 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.

### Unit assumptions

- 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.

## Boundary hardening

**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.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "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."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

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

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`