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 $25$ percent or down by $20$ percent. Exercise price

of an American Put option expiring at the end of the second period is $$40.$

A$.$ Find the stock price sequence.

B$.$ Determine the possible prices of the Put at expiration.

C$.$ Find the possible prices of the Put at the end of the first period.

D$.$ What is the current price of the Put?

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?