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Calculate both holder payoffs
The hypothetical call pays max(130−100,0)=30 in the higher state and max(80−100,0)=0 in the lower. The factor from today to that expiry is 1.05. No paid option premium is used as an input to this valuation.
Solve the replicating holdings
Subtracting the two terminal equations gives Δ=(30−0)/(130−80)=0.6. To make the lower state zero, terminal cash must be −0.6×80=−48. Its current value is −48/1.05=−45.714286.
Check the complete terminal portfolio
| State | Underlying holding value | Cash repayment | Matched call amount |
|---|---|---|---|
| Higher | 0.6×130 = 78 | −48 | 30 |
| Lower | 0.6×80 = 48 | −48 | 0 |
Add the time-zero costs
The underlying holding costs 60 today. Subtract current borrowing 45.714286 to obtain model value 14.285714. The match uses fractional units and common-rate financing assumptions; real costs or funding restrictions would require another model.