The current price of a non-dividend paying stock is $30. Use a two-step tree to value a put option on the stock with a strike price of $32 that expires in 6 months. Each step is 3 months, and in each step the stock price either moves up by 10% or moves down by 10%. Suppose that the risk free rate is 8% per annum with continuous compounding. What should be the EUROPEAN put option price today? If it was an AMERICAN PUT option, what should be the option price today? If the volatility was given as 30%, how would this change the AMERICAN PUT option price today?