12. You calculated the following values for a two-year at-the-money American put on a stock currently trading at $99: Su = $128.70 Sd = $79.20 Assume n = 2, the risk-free rate is 9% per annum, and the stock is expected to grow at the same rate for the next two years. (8 points) (a) Calculate and show the stock prices after two years in a binomial tree. (b) Calculate p and (1 p) rounding them to two-digit after decimal. (c) Calculate Pu2, Pud, Pd2, Pu, and Pd and show them in a binomial tree. (d) Calculate current price of the put. (e) Calculate the hedge ratio initially and subsequently.