Need help with these questions. Need complete excel answers, please

1. Why doesn't put-call parity hold for American options? 2. Construct a portfolio that would have this payoff diagram: $45 $40 $35 $30 $25 Portfolio payof $20 $15 $10 $5 $0 $0 $10 $20 $30 $40 $50 $60 Stock price Note that the horizontal line at $15 continues to the right indefinitely and does not stop when the stock price is $50. 3. Draw a payoff diagram for each of the following portfolios: a. Buy a put X = $20, buy a call X = $30. b. Buy a put X = $50 (which costs $16.12), sell a put X = $45 (which costs $12.52), sell a put X = $40 (which costs $9.26), buy a put X = $30 (which costs $4.02). Draw the gross and net payoff diagram for this portfolio. c. Buy a put X = $40, buy a share of the underlying stock, sell a call X = $50 4. You think a stock's price is going to fall. If you're right, you could make money by (a) selling the stock short, (b) buying a put option, or (c) selling a call option. Write a few sentences explaining the pros and cons of each strategy. 5. A put and call option are written on the same underlying stock and they are both exactly at the money. Both are European options with the same expiration date, which is several months from now. The risk-free rate of interest is 1%. One of the following statements below is true. Which one, and why? a. b. c. d. The market value of the call is greater than the market value of the put. The market value of the put is greater than the market value of the call. The market value of the call is equal to the market value of the put You cannot say which option is more valuable without more information. 6. A certain common stock currently sells for $50. A call option on that stock with X = $50 and an expiration in one year costs $6.41. A put option on that stock, also with X = $50 and a one-year expiration costs $5.42. Explain how the payoff of buying 1 share of stock is very similar to the payoff of simultaneously buying one call and selling one put. Buying one share of stock requires $50, but buying one call and selling one put requires just $0.99. If the payoffs of these two investment strategies are very similar, but their costs are very different, is it always better to use the \"buy a call, sell a put\" strategy rather than just buying the stock? Why or why not? 7. A stock currently trades at $45, but may increase to $60 or fall to $35 over the next year. The risk-free rate is 5%. Using the binomial method, value a call option with X = $50. 8. Suppose that the actual market price of the call option in problem 7 is $5. Demonstrate that you could engage in arbitrage to take advantage of this mispricing. You need to show the up-front profit and show that your position is risk-free over the year. You should not assume that you can trade a fairly priced put option on this stock as part of your arbitrage transactions. 9. Just as in problem 7, a stock currently trades at $45, but may increase to $60 or fall to $35 over the next year. The risk-free rate is 5%. Using the binomial method, value a put option with X = $50. Show that the prices of the call (in problem 7) and the put (in this problem) satisfy put-call parity