Past exam of the mathematics course of the University of Cambridge / 2008 / ii / Paper 1 / 28J / b / 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 isThis is an explicit arbitrage.