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Two-state risk-free domain condition

Under the selected both-states-possible model, lower price < current price × period factor < higher price.

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Compare amounts at the same date

Grow the current underlying price at the stated risk-free period factor. Compare that future amount with the two terminal prices. For 100, 130/80 and 5%, the grown value is 105 and lies strictly inside the interval.

Inspect an incompatible record

If both terminal prices are 110 and 130 while the grown current price is 105, solving for a weight produces a negative higher-state value. It cannot serve as a positive interior state price in the selected model.

Keep equality separate from an interior model

A grown price equal to an endpoint gives a zero weight for one state. The tool rejects this boundary under its assumption that both states are possible and the interior pricing setup is required.

Original domain checks
Terminal intervalGrown current priceTool status
80 to 130105Interior
110 to 130105Outside
80 to 105105Boundary

Do not turn input rejection into a market accusation

The rejected record may contain a convention mismatch or deliberately be a test case. It does not prove actual executable market arbitrage. Review the inputs and assumptions before interpreting the result.

Further references