Question

Find the value of an American put using the binomial option pricing model when S = 70, X = 70, r = 0.08, u =1.10, and d = 0.95. There are no dividends. Use n = 2 periods.

Answer 1

answer :
The estimated values for the stock prices are as given as below:
when S = 70, X = 70, r = 0.08, u =1.10, and d = 0.95.
Su = 70 ´ 1.10 = 77
Sd = 70 ´ 0.95 = 66.5
Suu = 77 ´ 1.10 = 84.7
Sud = Sdu = 66.5 ´ 1.1 = 73.15
Sdd = 66.5 ´ 0.95 = 63.175
The risk-neutral probability for the stock price to go up is
p* = (e^r – d)/ (u – d)
p* = (e^0.08 – 0.95)/(1.10 – 0.95)
p* = 0.8886
hence, the risk-neutral probability for the stock price to go low is 0.1114.
If the option is exercised at time 2, the worth of the call can be
Cuu = (84.7– 70)+ = 14.7
Cud = (73.5 – 70)+ = 3.5
Cdd = (63.175 – 70)+ = 0 .