A stock that does not pay dividend is trading at $100. The stock price will increase by 10% or decrease by 10% in one year. After that, the stock price will increase or decrease by 20% in the second year. The risk-free interest rate is 5% per annum with continuous compounding. Value a two-year American put option with strike price of $102. Note that risk-neutral probabilities or replicating portfolios may differ across two periods. You must also check for early exercise.