Solution
= Solution
As $\sigma\to\infty$, $d_1\to+\infty$ and $d_2\to-\infty$, so the <European call option> price tends to $\boxed{S_0}$. If its traded price $C>S_0$, sell a call, buy one share, and invest the surplus $C-S_0$ at the risk-free rate. The initial net cost is zero, and the maturity payoff is
$$
S_T-(S_T-K)^++(C-S_0)e^{rT}=\min(S_T,K)+(C-S_0)e^{rT}>0.
$$
This is an explicit <arbitrage>.