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Use higher minus lower consistently
Let Hu and Hd be claim amounts at terminal underlying prices Su and Sd. Require Su>Sd. A state-independent cash leg cancels when subtracting the two replication equations.
Solve the difference equation
Δ(Su−Sd)=Hu−Hd, giving the underlying holding. This is units per claim under the stated per-unit basis, not a currency amount or automatically a percentage of portfolio wealth.
Use the same state order in numerator and denominator.
Read the sign and scale
For a call paying 30/0 at 130/80, Δ=30/50=0.6. For a put paying 0/20, Δ=−20/50=−0.4. A negative value specifies a short underlying component in the replicating record.
Keep the one-period scope
The holding matches the two modeled state amounts. It is not a claim that a single unchanged position hedges every price path or a continuous-time Greek for all conditions. Multi-step or additional states need their own rebalancing or model treatment.