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A European binary (or Digital) option pays $10 if the stock ends above $57 after 3 months and nothing otherwise. The following 3-period binomial tree represents the monthly stock price movements: Assuming cont. 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 rightarrow S(1) = 63.60 rightarrow S(2) = 61.06 rightarrow S(3) = 58.61 Verify that your replicating strategy is self-financing at each step. Note that you do not need to calculate the hedge positions for the entire tree (only along the path) but you need till the prices.
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