1.Consider the July 2009 IBM call and put options in Problem 3. Ignoring any interest you might earn over the remaining few days’ life of the options:
a. Compute the break-even IBM stock price for each option (i.e., the stock price at which your total profit from buying and then exercising the option would be zero).
b. Which call option is most likely to have a return of −100%?
c. If IBM’s stock price is $111 on the expiration day, which option will have the highest return?
2.You are long both a call and a put on the same share of stock with the same exercise date. The exercise price of the call is $40 and the exercise price of the put is $45. Plot the value of this combination as a function of the stock price on the exercise date.
3.You are long two calls on the same share of stock with the same exercise date. The exercise price of the first call is $40 and the exercise price of the second call is $60. In addition, you are short two otherwise identical calls, both with an exercise price of $50. Plot the value of this combination as a function of the stock price on the exercise date. What is the name of this combination of options?
4.A forward contract is a contract to purchase an asset at a fixed price on a particular date in the future. Both parties are obligated to fulfill the contract. Explain how to construct a forward contract on a share of stock from a position in options.
5.You own a share of Costco stock. You are worried that its price will fall and would like to insure yourself against this possibility. How can you purchase insurance against this possibility?
6.It is July 13, 2009, and you own IBM stock. You would like to insure that the value of your holdings will not fall significantly. Using the data in Problem 3, and expressing your answer in terms of a percentage of the current value of your portfolio:
a. What will it cost to insure that the value of your holdings will not fall below $95 per share between now and the third Friday in July?
b. What will it cost to insure that the value of your holdings will not fall below $95 per share between now and the third Friday in August?
c. What will it cost to insure that the value of your holdings will not fall below $100 per share between now and the third Friday in August?
7.Dynamic Energy Systems stock is currently trading for $33 per share. The stock pays no dividends. A one-year European put option on Dynamic with a strike price of $35 is currently trading for $2.10. If the risk-free interest rate is 10% per year, what is the price of a one-year European call option on Dynamic with a strike price of $35?
8.You happen to be checking the newspaper and notice an arbitrage opportunity. The current stock price of Intrawest is $20 per share and the one-year risk-free interest rate is 8%. A one year put on Intrawest with a strike price of $18 sells for $3.33, while the identical call sells for $7. Explain what you must do to exploit this arbitrage opportunity.
9.Consider the July 2009 IBM call and put options in Problem 3. Ignoring the negligible interest you might earn on TBills over the remaining few days’ life of the options, show that there is no arbitrage opportunity using put-call parity for the options with a $100 strike price. Specifically:
a. What is your profit/loss if you buy a call and TBills, and sell IBM stock and a put option?
b. What is your profit/loss if you buy IBM stock and a put option, and sell a call and TBills?
c. Explain why your answers to (a) and (b) are not both zero.
10.Suppose Amazon stock is trading for $70 per share, and Amazon pays no dividends.
a. What is the maximum possible price of a call option on Amazon?
b. What is the maximum possible price of a put option on Amazon with a strike price of $100?
c. What is the minimum possible value of a call option on Amazon stock with a strike price of $50?
d. What is the minimum possible value of an American put option on Amazon stock with a strike price of $100?