2c) Let us consider a down-and-out call option. Consider the case where E>X where E is the exercise price. What happens to the value function of the barrier option when S -> infinity (S being the asset price)? What happens to the value function when S=X (X being the barrier level)?

2d) Consider the quantity:

Show that when you set S = E, you obtain the quantity:

which is the same as:

where we set S' = X²/S. The above is also the same as:

where x' = log(S'/E)