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. What is the initial hedge ratio?
b. What are the two possible hedge ratios at the end of the first period?
c. 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.