Chapter 3 Questions and problems 2, 4, 5, 6, 8

2. What would happen in the options market if the price of an American call were less than the value Max(0, S 0 X)? Would your answer differ if the option were European? Explain.

4. Explain why an option's time value is greatest when the stock price is near the exercise price and why it nearly disappears when the option is deep-in or out-of-the-money.

5. Critique the following statement made by an options investor: " My call option is very deep-in-the-money. I don't see how it can go any higher. I think I should exercise it. "

Cengage, Learning Australia, and Don M. Chance.

6. Call prices are directly related to the stock's volatility, yet higher volatility means that the stock price can go lower. How would you resolve this apparent paradox?

8. Why do higher interest rates lead to higher call option prices but lower put option prices?

Chapter 4 Questions and problems 7, 8

7. Consider a stock worth $25 that can go up or down by 15 percent per period. The risk-free rate is 10 percent. Use one binomial period.

a. Determine the two possible stock prices for the next period.

b. Determine the intrinsic values at the expiration of a European call option with an exercise price of $25.

c. Find the value of the option today.

d. Construct a hedge by combining a position in the stock with a position in the call. Show that the return on the hedge is the risk-free rate regardless of the outcome, assuming that the call sells for the value you obtained in part c.

e. Determine the rate of return from a riskless hedge if the call is selling for $3.50 when the hedge is initiated.

8. Consider a two-period, two-state world. Let the current stock price be 45 and the risk-free rate be 5 percent. Each period the stock price can go either up by 10 percent or down by 10 percent. A call option expiring at the end of the second period has an exercise price of 40.

a. Find the stock price sequence.

b. Determine the possible prices of the call at expiration.

c. Find the possible prices of the call at the end of the first period.

d. What is the current price of the call?

e. What is the initial hedge ratio?

f. What are the two possible hedge ratios at the end of the first period?

g. Construct an example showing that the hedge works. Make sure the example illustrates how the hedge portfolio earns the risk-free rate over both periods.

h. What would an investor do if the call were overpriced? If it were underpriced?

Chapter 5 Question and problems 2, 4, 5

2. Consider a stock currently priced at $80. In the next period, the stock can either increase by 30 percent or decrease by 15 percent. Assume a call option with an exercise price of $80 and a risk-free rate of 6 percent. Suppose the call option is currently trading at $12. If the option is mispriced, what amount of riskless return can be earned using a riskless hedge?

4. How is the volatility of the underlying stock reflected in the binomial model?

5. Why are the up and down parameters adjusted when the number of periods is extended? Recall that in introducing the binomial model, we illustrated one and two-period examples, but we did not adjust the parameters. What is the difference in these two examples? Why did we adjust the parameters in one case and not in the other?