Before revision:  Even if the price has continuous paths, we show that out-of-the-money implied volatility diverges for small maturity, producing a very pronounced smile . When |\kappa| is much larger than t, the implied volatility is asymptotically an explicit function of just the ratio (\kappa / t) .
After revision:  Even if the price has continuous paths, we show that out-of-the-money implied volatility diverges for small maturity, producing a very pronounced smile .