You observe the market prices of European options written on a non-dividend paying stock expiring in one month. a. Suppose you write a call option with X=$35 and buy a call with X=$45. Graph the profit/loss of the individual call positions and the combined option portfolio as a function of the stock price at the expiry. Also indicate at what stock price you will just break even on the graph. (6 marks) b. Now suppose you further buy a put option with X=$35 and write a put option with X=$45 in addition to the call option positions in part a) - i.e., now your portfolio consists of short call and long put with X=35 and long call and short put at X=45. Graph the payoff of the individual option positions and the combined option portfolio as a function of the stock price at the expiry. (3 marks) c. In light of your answer in part b) above, what should be the one-month risk-free rate to rule out any arbitrage. Hint: The arbitrage-free one-month risk-free rate should be the same: Rf= (risk-free cash flow in one month) / (initial cost of the risk-free investment) for any risk-free investment generating a constant cash flow in one month