Problem 3 (American put with continuous dividend, 9pts). Consider an American put option. The time to maturity is 2 years. We adopt a two-step binomial tree, with each step equals to one year. Moreover, in each time step, the stock price either moves up by 20% or moves down by 20%. The strike price of the option is $52. The current stock price is $50. The risk-free interest rate is 7% per annum in continuous compounding. The continuous dividend rate is 2% per annum. Calculate the price of the American put option