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Model claim value and replicating quantity

A claim price and hedge ratio have different units and are not alternative names for the same output.

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Read the two original call outputs

The example gives model call value 14.285714 per claim and replicating underlying quantity 0.6 units. The first is a current currency amount under the selected unit basis; the second is a holding quantity.

Include the cash component

The stock holding alone costs 60, not 14.285714. Current cash −45.714286 completes the replica. Equating Δ×S0 with the option price would omit that funding component.

Different units
OutputValueInterpretation
Δ0.6Underlying units per claim
ΔS060Current stock-component cost
B−45.714286Current cash component
Claim value14.285714Total current model cost

Interpret a negative quantity

The put has Δ=−0.4 but positive model value 9.523810 because a positive cash component completes its replica. Negative holding does not imply a negative option price.

Keep practical trade sizes separate

Actual contract multipliers or indivisible holdings can require scaling and constraints. This model computes per-unit fractional holdings; it does not specify a trade order or claim continuous-time hedge performance.

Further references