In the Delta of a replicating portfolio, which formula correctly defines Delta?

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Multiple Choice

In the Delta of a replicating portfolio, which formula correctly defines Delta?

Delta in a replicating portfolio is the hedge ratio, showing how much of the underlying to hold to match the option’s payoff. In a two-state world, the option moves from V_d to V_u as the stock goes from S_d to S_u, so the appropriate measure is the slope of that change: Δ = (V_u - V_d) / (S_u - S_d). This captures how sensitive the option value is to changes in the underlying price and provides the correct amount of stock to hold for replication. The other forms either add values, reverse the order, or use a negative denominator, which do not represent that slope and won’t yield the correct hedge.

Delta in a replicating portfolio is the hedge ratio, showing how much of the underlying to hold to match the option’s payoff. In a two-state world, the option moves from V_d to V_u as the stock goes from S_d to S_u, so the appropriate measure is the slope of that change: Δ = (V_u - V_d) / (S_u - S_d). This captures how sensitive the option value is to changes in the underlying price and provides the correct amount of stock to hold for replication. The other forms either add values, reverse the order, or use a negative denominator, which do not represent that slope and won’t yield the correct hedge.

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