Consider a European put option on a non-dividend-paying stock where the stock price is 50, the strike price is 50, the risk-free rate is 3.5% per annum, the volatility is 25% per annum, and the time to maturity is 6 months.

(a) Calculate u, d and p for a two-step tree. Explain u, d and p.

(b) Value the option using a two-step tree. Explain the result.

(c) Would be optimal to exercise earlier the American put option? Carefully explain.

(d) If it were an American call option would it be optimal to exercise earlier? Care-fully explain.