Problem 4: Spreads (15 marks] (a) Consider the following terminal payoff function of a portfolio: (T) E] -E ... ESD o Eo E; E Es-E- Suppose we are only given call options on the same underlying asset and the same expiration, but with different exercise prices Ej, i = 0,1,...,4, such that Ei+1 - E; = E1 - E., i = 1,2,3. Construct explicitly a portfolio whose terminal payoff diagram is as shown above with derivation. Write down the payoff of the constructed portfolio at the maturity and verify that it matches the payoff shown in the diagram. (b) Can you further generalise part (a) to the case in which Ei,o sis 4n, such that Ei+2 - E{+1 = Ei+1 - Ej, Vi> 0 a portfolio whose terminal payoff diagram is as shown below: (T) E: - Eo Ein-1 SIT 01 EEE e Es E: - E- Write down explicitly the corresponding portfolio with derivations. Problem 4: Spreads (15 marks] (a) Consider the following terminal payoff function of a portfolio: (T) E] -E ... ESD o Eo E; E Es-E- Suppose we are only given call options on the same underlying asset and the same expiration, but with different exercise prices Ej, i = 0,1,...,4, such that Ei+1 - E; = E1 - E., i = 1,2,3. Construct explicitly a portfolio whose terminal payoff diagram is as shown above with derivation. Write down the payoff of the constructed portfolio at the maturity and verify that it matches the payoff shown in the diagram. (b) Can you further generalise part (a) to the case in which Ei,o sis 4n, such that Ei+2 - E{+1 = Ei+1 - Ej, Vi> 0 a portfolio whose terminal payoff diagram is as shown below: (T) E: - Eo Ein-1 SIT 01 EEE e Es E: - E- Write down explicitly the corresponding portfolio with derivations