With A,B, and C finished, how would I do D & E?

2. We are interested in pricing an for 860 (ie. So 60). Supp volatility is o = .35, and the time this problem. (a) For a one-step binomial tree DO = 60). Suppose the annual rise free rate is 0 .02, the sco w the time to maturity is months. Use continuous compounding for T: 5 wing an at-the-money put option on a stock that is currently trading risk-free rate is ry 0.02, the stock's annualized step binomial tree, calculate the following the risk-neutral probability of an upward stock movement the amount of the w the amount of the upward movement, ard movement, and the amount of and the e downward move, d (using the Cox. Res and Rubinstein (1979) restriction). u= e 35 v3/12 = 1,2535 d = e. 35 /5/12 - ...3 V5/12 = 0,7978 0.21056 = 0.46201 p=erted 20.02 (5/12) 0.7978 ro= 0.4557 u-d 1.25 35-0.7998 (0) Find the value of the option today. Draw the one step binomial tree and clearly label the stock price and option value at each node. Max 160-75,21 ;o)=0 -0.020512) 75.21 [0.4620x0 + (1-0.4620) 60 X 12, 13 7 7 6.47 | 47.87 Max (60-47.87,0) = 12.13 12.13 Now, suppose you divide the time to maturity into 5 subperiods of equal length. (c) Calculate the following: the risk-neutral probability of an upward stock movement, the amount of the upward movement, u, and the amount of the downward moved (using the Cox, Ross, and Rubinstein (1979) restriction). N-5 t=1 r=.02 t- 15.2 So=60 #uf pero 5 u = e. 35/15 = 1.1694 a factor=1469 d = 1/u1=0.8551 1 movethent = 60 (1.1695 P = (0-2, 2-d/u-d 60=130.986 1-60 F70.986 sy 1.004-08551 -0.1489 - 0.3143 0.473751 8551 3 1.1644 - .5551 ward movement d = 1-P = 0.52625 60-90 (855175 + 40-27.415 (32.585 0.47375 Binomial Model (d) Find the current price of a European P icate the stock and option price at each node. European put option today. Draw out the binomial tree and (e) Again, assuming 5 subperiods, cal subperiods, calculate the current price of an American put option. Draw the binomial tree and indicate the stock and option price at le licate the stock and option price at each node. Also, highlight the nodes (if any) where it is optimal to exercise the option early