# A three-month call option is the right to buy stock at \$20

Chapter 17: Problems 1-10

1. A three-month call option is the right to buy stock at \$20. Currently the stock is selling for \$22 and the call is selling for \$5. You are considering buying 100 shares of the stock (\$2,200) or one call option (\$500).

a) If the price of the stock rises to \$29 within three months, what would be the profits or losses on each position? What would be the percentage gains or losses?

b) If the price of the stock declines to \$18 within three months, what would be the profits or losses on each position? What would be the percentage gains or losses?

c) If the price of the stock remained stable at \$22, what would be the percentage gains or losses at the expiration of the call option?

d) If you compare purchasing the stock to purchasing the call, why do the percentage gains and losses differ?

Problem 2

2. A particular call is the option to buy stock at \$25. It expires in six months and currently sells for \$4 when the price of the stock is \$26.

a) What is the intrinsic value of the call? What is the time premium paid for the call?

b) What will the value of this call be after six months if the price of the stock is \$20? \$25? \$30? \$40?

c) If the price of the stock rises to \$40 at the expiration date of the call, what is the percentage increase in the value of the call? Does this example illustrate favorable leverage?

d) If an individual buys the stock and sells this call, what is the cash outflow (i.e., net cost) and what will the profit on the position be after six months if the price of the stock is \$10? \$15? \$20? \$25? \$26? \$30? \$40?

e) If an individual sells this call naked, what will the profit or loss

Problem 6

6. A particular put is the option to sell stock at \$40. It expires after three months and currently sells for \$2 when the price of the stock is \$42.

A) If an investor buys this put, what will the profit be after three months if the price of the stock is \$45? \$40? \$35?

b) What will the profit from selling this put be after three months if the price of the stock is \$45? \$40? \$35?

c) Compare the answers to (a) and (b). What is the implication of the comparison?

Chapter 18: Problem 2: 1-15

2. A call option is the right to buy stock at \$50 a share. Currently the option has six months to expiration, the volatility of the stock (standard deviation) is 0.30, and the rate of interest is 10 percent (0.1 in Exhibit 18.2).

a) What is the value of the option according to the Black-Scholes model if the price of the stock is \$45, \$50, or \$55?

b) What is the value of the option when the price of the stock is \$50 and the option expires in six months, three months, or one month?

c) What is the value of the option when the price of the stock is \$50 and the interest rate is 5 percent, 10 percent, or 15 percent?

d) What is the value of the option when the price of the stock is \$50 and the volatility of the stock is 0.40, 0.30, or 0.10?

e) What generalizations can be derived from the solutions to these problems?

Problem 11 Ch 18

11. Black-Scholes demonstrates that the value of a put option increases the longer the time to expiration. Currently the price of a stock is \$100 and there are two put options to sell the stock at \$100. The three-month option sells for \$7.00 and the six-month option sells for \$4.50.

a) What would you and why?

b) How much do you earn or lose after three months at the following prices of the underlying stock: \$85, \$90, \$95, \$100, \$105, and \$110? Assume the worst-case scenario.

c) Is there any reason to anticipate earning a higher return than your answers in (b)?

Here’s the SOLUTION

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