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Read the put’s state amounts
With terminal prices 130 and 80, the put pays zero and 20. Keep higher-minus-lower ordering for both payoff and underlying differences. The period factor remains 1.05.
Solve the short underlying component
Δ=(0−20)/(130−80)=−0.4. In the lower state the underlying component is −32. Reaching payoff 20 requires terminal cash 52, with current cash 52/1.05=49.523810.
Verify the signs in each state
| State | Underlying component | Terminal cash | Matched put |
|---|---|---|---|
| Higher | −52 | +52 | 0 |
| Lower | −32 | +52 | 20 |
Reconcile the current amount
The short underlying component has current value −40. Add current cash 49.523810 to get put value 9.523810. The negative holding is a model position, not a negative option value or a reason to take its absolute value.