Consider the following statements related to options:

Statement 1: As the exercise price increases, all else being the same, the value of a put option will decrease, and the value of a call option will increase.

Statement 2: With an increase in the volatility of the underlying asset, both the value of the put and call option will increase.

State whether you agree or disagree with each statement and explain why by making reference to the intrinsic value and the time value of the option.