Problems to Lecture 9 Problem 2 (Option combinations). One popular option combination is called a bull spread and consists of one long European call with the strike price Ki and one short European call with the strike K2 > Kj. The payoff to the buyer of a bull spread is given by max(ST-K1,0) max(ST- K2,0), where Sy is the price of the underlying stock on maturity. We assume that the stock pays no dividends. The initial stock price So = 100, the continuously compounded risk-free interest rate r = 5%, the time to maturity T = 1 year, and the following strike prices: Ki = 105 and K2 = 115. The option prices are C = 11.98 (with K) and C2 = 8.34 (with K2). In your answers consider the following future stock prices ST E {90, 100, 110, 120, 130}. a) Compute the payoffs and profits to this bull spread for each future stock price. b) Plot the payoff and profit to this bull spread. c) Find the break-even price of the stock, St, at which the profit is zero. d) Compute the returns to the buyer of this bull spread for each future stock price