# Finance

Created 10/30/1996
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# Problem Set #7: Options

## (Due before section on Monday, December 3)

1. Suppose that you hold a call option on a share of stock, and also "owe" a share of stock--that is, you have sold it short. What is the total payoff to your portfolio on the exercise date if the price of the stock is above the strike price?

2. Suppose that you hold a call option on a share of stock, and also "owe" a share of stock--that is, you have sold it short. What is the total payoff to your portfolio on the exercise dateif the price of the stock is below the strike price?

3. Suppose that you are writing a call option on a stock selling for \$40 per share with a \$30 exercise price. The stock's standard deviation is 6% per month; the option matures in 3 months; the risk-free interest rate is 4% per year. Use appendix table 6 to calculate the value of this call option--what would be a fair price to sell it for?

4. Suppose that you are writing a call option on a stock selling for \$40 per share with a \$30 exercise price. The stock's standard deviation is 6% per month; the option matures in 3 months; the risk-free interest rate is 4% per year. Use appendix table 7 to calculate what initial hedge position in the stock you should take if you sell the option to a customer and wish to neutralize your risk. Should you buy or should you sell the stock? How much of the stock should you buy or sell?

5. If, in question 4, the stock price goes up in the next month what, qualitatively, do you do in order to maintain your hedged position? Do you buy more stock, or sell more stock?

6. Over the coming year the common stock of Dandelion, Inc., will either halve to \$50 from its current level of \$100, or rise to \$200. The 1-year risk-free interest rate is 5%. What is the delta of a one-year call option on Dandelion stock with a strike price of \$170? What is the value of such an option?

7. [Problem 19, chapter 20]. In 1988 the Bond Corporation sold some land it owed near Rome for \$110 million; it had originally purchased the land for \$36 million; as a result the transaction boosted Bond's reported 1988 earnings by \$74 million. In 1989 a TV program revealed that Bond had given the purchaser a put option to sell the land back to Bond for \$110 million within a year, and that Bond had paid the purchaser \$20 million for a call option to buy the land back for \$110 million within a year. (a) What happens if the land is worth more than \$110 million when the options expire? (b) What happens if the land is worth less than \$110 million. (c) What is the implicit risk-free interest rate that would make sense of this transaction? (d) The TV program argued that the land was not really sold--hence no profit should have been reported. Do you agree? Why or why not?

8. [Problem 23, chapter 20]. Consider the following three six-month call options:

 Exercise Price Option Price \$90 \$5 \$100 \$11 \$110 \$15

Suppose that you can both buy and sell call options. How would you make money by trading in these three options?

9. Suppose that the price of Carbonics stock can go up by 15% or down by 13% in the next year from the current stock price of \$60, and that only these two outcomes are possible. Suppose, further, that the safe interest rate is 10% per year. What is the value of a call option on Carbonics stock? How much of a hedge in the stock would be required to replicate the option's payoffs? How would these values change if the interest rate were 5% per year?

# Finance

Created 10/30/1996
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