Consider a 3-month European put option on a non-dividend-paying stock with a current price $50. The strike price is $48. The current interest rate is 5%, compounded continuously. Assume the stock price evolves according to a three-period CRR binomial tree with volatility 33%.

(a) Find the option price. Show all the trees.

(b) Suppose you write one put option. Find the number of shares of stock needed to replicate the short put with stock at each step from the beginning if the stock price goes up in the 1st period and goes down in the second period.