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?