Consider applying the binomial method to price American options. Suppose that stock in the XYZ Company is priced at 50 = 100 and consider options that are at the money K = 100. The options mature in T = 1 year, which we divide into n = 3 periods, each of length At = E = g . The riskfree rate is r = 0.03 and XYZ stock has a volatility ofa = 0.6. (a) Calculate the magnitude of upticks u and downticks d, as well as the risk-neutral probability p. (b) Draw the stock price tree and calculate the payoffs to call and put options at each nal price. (c) Using backward induction, calculate the price of European call and put options. (d) Verify that putcall parity holds for European options. (e) Find the price of American call and put options. Is it ever worthwhile to exercise eady? (f) Does put-call parity hold for American options