Solution
= Solution
At $B=K$, homogeneity gives
$$
\frac{S_0}{K}C(K^2/S_0,K)=C(K,S_0)=P(S_0,K).
$$
The price is therefore $C(S_0,K)-P(S_0,K)$. Zero-rate <put-call parity> yields
$$
\boxed{C_{\rm out}=S_0-K}.
$$
= Solution
At $B=K$, homogeneity gives
$$
\frac{S_0}{K}C(K^2/S_0,K)=C(K,S_0)=P(S_0,K).
$$
The price is therefore $C(S_0,K)-P(S_0,K)$. Zero-rate <put-call parity> yields
$$
\boxed{C_{\rm out}=S_0-K}.
$$