Which of the following statements is not correct with respect to a European call option:

An increase in volatility increases the value of the option, and so do increases in the price of the underlying and the risk free rate. However, since a European option can only be exercised at expiry, an increase in the time to expiry may not necessarily increase the value of the option as it may increase the uncertainty around a more certain payout.

Consider the extreme case of a deep in the money European call option that has 1 day left to expiry, and a payout is certain. Now imagine the time to expiry is increased by say, 6 months. Now the payout is no longer certain as no one knows what the value of the underlying will end up at after 6 months. In such a case, the value of the option would decline. But this applies only to a European option. An American option, which can be exercised any time, will not be affected by this reasoning.