30 points Consider a put option on a non-dividend paying stock where the stock price is $60, the strike price is $60, the risk-free rate is 2% per annum continuously compounded, the volatility is 20% per annum and the time to maturity is 1 year. (a) (15 pts.) Calculate the u, d, risk neutral probability for a two-step tree. Value the European put option using a two-step tree. (b) (15 pts.) What is the value of the put option if it is American? What is the exercise policy for this American put? Be specific of whether and when early exercising the option is optimal