Alibaba Group (9988) is trading at $110 per share. The stock is anticipated to pay no dividends. It has an annualized volatility of 45%. The interest rate is 5% per annum with continuous compounding. Consider a 3-month American put option on Alibaba with a strike of $110. Construct a 2-period binomial model to answer the following questions.

(a) Calculate the up and down factors. Draw and determine the stock price process at each node. (5 marks)

(b) Determine the risk-neutral probabilities. Compute the American put price at each node. (8 marks)

(c) How much is the early exercise premium if any? (5 marks)

(d) Explain why early exercise of an American put option on dividend-paying asset may be not optimal.