a) Suppose the price of a stock today is 100. ATM call and put options are traded on this stock. The options mature in 24 months. Both European and American options are traded. The annualized variance of the rate of return on the stock is 9%. The discount risk-free rate is 8% per annum. Use the binomial option pricing approach with a time step of 8 months to price European and American call and put options on the stock. (35 marks)

b) Youre planning to scale down the operations of your manufacturing plant by 70% sometime in the next six months. Suppose the value of the plant today is 100m. Your plan is to save 70% from contraction. Risk uncertainty in the operating environment is estimated by an annualized variance of 25% in cash flows. The risk-free rate of return is 8% per annum. Use the binomial options pricing approach with a time step of three months to value the option to scale down operations. Is there an optimal time for taking such an action? Explain.