Problem 1 Suggest two different portfolios that produce the payoff diagram as in the graph below. Both portfolios may contain any amount of risk-free borrowing or lending, and the underlying stock. Portfolio 1 may contain call options but no put options. Portfolio 2 may contain put options but no call options. Assume the risk-free rate is rf = 10%. 25 20 15 10 5 S 10 15 20 25 30 35 40 0 -5 -10 -15 Problem 2 Suppose that a stock is currently trading at $60 per share, and the stock price can only take two possible values one year from now: it can either go up by 25% or down by 20%. The annual risk-free rate is 4%. Assume that the stock pays no dividends. You are interested in pricing an European put option on this stock. The option has a strike price of $66, and its maturity date is exactly one year from now. What is the payoff on the put option if the stock price goes up by 25%? b) What is the payoff on the put option if the stock price goes down by 20%? What is the price of the put option? Problem 3 For a two-period binomial model, you are given: Each period is one year. The current price for a non-dividend paying stock is $20. u = 1.2840, where u is one plus the rate of capital gain on the stock per period if the stock price goes up. d = 0.8607, where d is one plus the rate of capital loss on the stock per period if the stock price goes down. The risk-free interest rate is 5%. Calculate the price of an American call option on the stock with a strike price of $22