One period replicating portfolios. (a) Suppose a stock (which pays no dividends) is trading at 100. Next period the stock will either go up by 27%, or go down by 23%. The stock pays no dividends. The simple one-period risk-free rate is 2%. i. What is the replicating portfolio for the ATM call on the stock maturing in one period? ii. So what's the call's price? iii. What is the replicating portfolio for the ATM put? iv. So what's the put's price? (b) Suppose a stock index is currently trading at 4000 (and to keep things simple, we assume it also pays no dividends-at least for now!). Next period the index will either go up by 9% or down by 11%. The simple one-period risk-free rate is 1%. i. What are the replicating portfolios for the one-period calls on the index struck at K = 3800 and K = 4200? ii. So what are these calls' price? iii. What are the replicating portfolios for the one-period puts with the same two strikes? iv. So what are these puts' price?