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Write the original hypothetical record
Current underlying price is 100. At the one modeled expiry it can be 130 or 80, and the risk-free growth factor for that whole interval is 1.05. A call with strike 100 has expiry amounts 30 and zero. These are invented model inputs, not a market forecast.
Check the risk-free grown current price
The amount 100×1.05=105 lies strictly between 80 and 130. This is the selected model’s consistent interior setup when both states are possible and borrowing/lending share the stated rate. The branch names higher and lower order the terminal prices.
| Field | Value | Role |
|---|---|---|
| Current price | 100 | Time-zero underlying cost |
| Higher terminal | 130 | One possible expiry price |
| Lower terminal | 80 | Other expiry price |
| Period factor | 1.05 | Same modeled interval |
Compute the contract amounts first
Use the expiry payoff expressions to calculate the claim in both states. A premium from another quote is not used to define these payoffs. The current model value is then derived from replication or pricing weights.
Retain what the model omits
The illustration assumes no underlying income, one expiry, European payoff and compatible frictionless borrowing/lending. More states, early exercise, transaction constraints or actual forecasting require additional work.