A call bull spread can be constructed by simultaneously buying a call option at a strike price of K1 and selling a call option at a strike price of K2, where K1

Explain why this strategy must always involve some initial investment (i.e. cost some money now). [5 marks]

Suppose the current price of the underlying stock is S=50, the maturity is in half a year and that the strikes for the call options are K1=48, and K2=52, respectively. Calculate the price of the bull spread in the Black-Scholes-Merton model. [6 marks]

How do you think the price of the call bull spread would change if the maturity of the options were one year rather than half a year? Explain. [4 marks]

Explain how you can construct a strategy with the same payoff with positions in only European put options and the bank account. [5 marks]