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Alibaba Group (9988) is currently trading at $110. The stock is anticipated to pay no dividends. It has a 45 percent yearly volatility. With continued compounding, the interest rate is 5% each year. Consider a $100 strike 3-month American put option on Alibaba. To answer the following questions, build a 2-period binomial model.

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

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

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

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