Consider an American put option written on a non-dividend paying stock with a strike price of K = 120 and time-to-maturity T = 12 months. The current value of the stock is equal to S0 = 120. The value of the stock can either increase by u = 1.05 or decrease by d = 0.7 over each 6 months. The continuously compounded risk-free rate is 9% per annum. What is the price of the American put option today?

Please explain your answer and show your workings. Would you exercise the American put before maturity and if so, at which node? Explain your answer using your own words.

Quote your answer to FOUR decimal places Round the risk-neutral probability and the value of the option at all nodes to FOUR decimal places Use a dot (.) and not a comma (,) as a decimal separator Do NOT include units of measurement