Call price in the infinite-volatility limit

What does the price of a European call converge to as the volatility tends to infinity?

The current stock price $S_0$ (for a non-dividend stock). As $\sigma\to\infty$, $d_1\to+\infty$ and $d_2\to-\infty$, so $C=S_0N(d_1)-Ke^{-rT}N(d_2)\to S_0$. Intuitively the stock ends up near zero with probability close to one, so the strike is almost never paid, yet the stock's expectation is preserved; this hits the upper bound $C\le S_0$.