The Hang Seng TECH Index (HSTECH) is currently trading at 8,100. The index is anticipated to pay no dividends in the next 8 months. It has an annualized volatility of 30%. The interest rate is 5% per annum with continuous compounding. Consider a 6-month American put option on HSTECH with a strike of 8,200. Construct a 2-period binomial model to answer the following questions.

(a) Draw and determine the stock index process at each node. (6 marks)

(b) Compute the prices of the American put option at each node. (7 marks)

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

(d) Explain why early exercise of an American put option on non-dividend-paying asset may be optimal. (2 marks)