quantitative methods in finance

Consider an American put option with a maturity of one year and strike price 60 written on an underlying that pays no dividends. Suppose that S(0)=60, the volatility =35% per year and the risk-free rate r=6% per year. Let's use a binomial tree of two periods. i. Verify that with the usual choices we get u=1.28 and d=.7803. Also check that q=0.5007. (You can round up to .5.) Consider the option of working the tree backwards (don't forget to check the possibility of exercising early!). ii. Describe in each node the strategy that replicates. Verify that this strategy is self-financing and that it replicates the payoff