Consider an American put option on a non-dividend-paying stock where the stock price is $40, the strike price is $50, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is six months.

(a) Calculate u, d, a and p for a two-step tree. [Use 4 decimal places in your calculations.]

(b) Value the option using a two-step tree. [Give your final answer to 2 decimal places.]