question for 12.22 b how to calculate the value of american put option which is2.537please show me the details. why there is difference on node c

Hence the above answer is consistent 000 6.96 with risk-neutral valuation. Problem 12.22. A stock price is currently s40. Over each of the next two three-month periods it is expected to go up by or down by 10%. The risk-free interest rate is 12% per annum with continuous compounding. b. What is the value of a six-month European put option with a strike price of S42? What is the value of a six-month American put option with a strike price of S42? a. A tree describing the behavior of the stock price is shown in the figure below. The risk-neutral probability of an up move, p, is given by 0,12x3/12 0.90 0.6523 1.1-0.9 Calculating the expected payoff and discounting, we obtain the value of the option as [2.4 x 2x0.6523x0.3477+9.6x 0.34772 le -0,12x6/12 2.118 The value of the European option is 2.118. This can also be calculated by working back through the tree as shown in Figure S12.3. he second number at each node is the value of the European option. b. The value of the American option is shown as the third number at each node on the tree. It is 2.537. This is greater than the value of the European option because it is optimal to exercise early at node C. u u 2 a