A European binary ( or Digital) option pays $5 if stock ends above $56 after 3 months and nothing otherwise. The following 3-period binomial tree represents the MONTHLY stock price movements:

Assuming continuously compounded interest rate of r=3% and no dividends, find the REPLICATING PORTFOLIOS for each date if the stock prices moves according to

S(0) = 60 --> S(1) = 63.60 ---> S(2) = 61.06 ---> S(3) = 58.61

Verify that your replicating strategy is self-financing at each step.