3 Option Pricing. a An investor who believes a stock will rise in the future can construct a bull spread for that stock. One way to construct such a spread is to buy a call with strike price Ki and sell a call with the same expiration date but with a strike price of K2 > Kj. Is the initial cost of the spread positive or negative? Justify your answer. b Suppose that over the period 0 to I a certain stock pays a dividend whose present value is D. Derive a put-call parity relation for European options at time t = 0, expiring at T for this stock. C Consider an options contract with a payoff function at time T equal to max(0.5S, S-K) where S is the price of a stock and K is a fixed strike price. Let P be the price of the stock at time t = 0 and let C1 and C2 be the prices of ordinary calls with strike prices K and 2K, respectively. Find a fair price for this options contract. d Show that European and American call options have the same value. e Under what conditions does a European and American put option have the same value? The five parts carry equal marks. 3 Option Pricing. a An investor who believes a stock will rise in the future can construct a bull spread for that stock. One way to construct such a spread is to buy a call with strike price Ki and sell a call with the same expiration date but with a strike price of K2 > Kj. Is the initial cost of the spread positive or negative? Justify your answer. b Suppose that over the period 0 to I a certain stock pays a dividend whose present value is D. Derive a put-call parity relation for European options at time t = 0, expiring at T for this stock. C Consider an options contract with a payoff function at time T equal to max(0.5S, S-K) where S is the price of a stock and K is a fixed strike price. Let P be the price of the stock at time t = 0 and let C1 and C2 be the prices of ordinary calls with strike prices K and 2K, respectively. Find a fair price for this options contract. d Show that European and American call options have the same value. e Under what conditions does a European and American put option have the same value? The five parts carry equal marks