Consider an American put option on a nondividend paying stock when the stock price is $60, the strike price is $63, the risk-free rate is 4%, the volatility is 20%, and the time to maturity is six months. You are to value this put option with 4-step binomial tree model. Refer to the tree displayed below, and compute the values of missing variables:

(i) Pseudo-probability of going up (marked AAA in the tree)

(ii) Stock Price at 1st time step (marked BBB in the tree)

(iii) Option Value at 1st time step (marked CCC in the tree)

(iv) Option Value at time=0 (marked DDD in the tree)

D H 79.61379 0 69.11459 0 A B E F 1 At each node: 2 Upper value = Underlying Asset Price 3 Lower value = Option Price 4 Values in red are a result of early exercise. 5 6 Strike price = 63 7 Discount factor per step = 0.9950 8 Time step, dt = 0.1250 years, 45.63 days 9 Growth factor per step, a = 1.0050 10 Probability of up move, p =AAAA 11 Up step size, u = 1.0733 74.17867 12 Down step size, d = 0.9317 13 69.11459 14 0.69077 15 BBBB 64.39624 16 CCCC 1.439552 17 60 60 18 DDDD 4.146678 19 55.90389 55.90389 20 7.372625 7.096115 21 52.08741 22 10.91259 23 48.53147 24 14.46853 25 26 27 Node Time: 28 0.0000 0.1250 0.2500 0.3750 29 60 52.08741 10.91259 45.2183 17.7817 0.5000 2n