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Keep the same underlying model
Current underlying is 100, period factor 1.05 and terminal states 130/80. This claim is specified directly to pay 50/10; it is not mislabeled as a standard call with an unstated strike.
Construct the holdings
Δ=(50−10)/50=0.8. Terminal cash is 10−0.8×80=−54, so current cash is −54/1.05=−51.428571. Current replication cost is 80−51.428571=28.571429.
Reproduce the price independently
The underlying gives q=0.5. Weighted claim amount is 0.5×50+0.5×10=30. Discounting gives 30/1.05=28.571429.
| Check | Result |
|---|---|
| Higher replica | 104−54 = 50 |
| Lower replica | 64−54 = 10 |
| Current replication | 28.571429 |
| Weighted current value | 28.571429 |
Keep the claim definition visible
The example demonstrates a state-contingent payment that can be replicated in the two-state model. Its price follows the selected record and assumptions; it does not supply a market quotation or an actual probability estimate.