Explanation

In the binomial option pricing framework, we can replicate option payoffs using the underlying asset and risk-free borrowing/lending.

For a short call option:

• Payoff = -max(S-K, 0)
• When S > K: Payoff = -(S-K) = K-S
• When S ≤ K: Payoff = 0

Replication strategy: To replicate a short call position, we need a strategy that:

• Has negative exposure to the stock when S > K
• Has zero exposure when S ≤ K

This is achieved by: Going long the underlying and borrowing cash (Option A)

Why this works:

• When you go long the stock, you have positive delta
• When you borrow cash, you create a fixed liability
• The combination creates a position that behaves like a short call:
  • If stock rises above strike, your long stock position gains value but is offset by the fixed borrowing cost
  • The net position has limited upside (like a short call)

Mathematically: The replication requires Δ shares of stock and borrowing B dollars: $\Delta = \frac{C⁺ - C⁻}{S⁺ - S⁻}$ $B = \frac{C⁻ - \Delta \times S⁻}{1+r}$

For a short call, the signs would be reversed, resulting in going long the underlying and borrowing cash.