Please give any ideas or comments for the following questions.

A stock has been traded on the exchange for several years. Today the stock is trading at S₀ = $64. You have analysed its price history for the last 12 months, and believe that the stock return has the following statistical properties:

Mean: = 0.06

Volatility: = 0.25

In addition, you have also observed a risk-free interest rate of r = 2% per annum, continuously compounded.

(a)Assuming the stock does not pay out any dividends, build a two-period binomial tree, and price a 8-month European put option with strike K = 60. Calculate and explain the dynamic replication strategy needed to match the option payoff in all possible outcomes.

(b)Price the corresponding European call option, and use a model-free relationship to verify your answer.

(c)In Excel, price the option in part (a) using an eight-period binomial tree.

(d)Suppose the company suddenly announces a change of dividend policy, paying out dividend at rate of = 12% per annum (with monthly dividends of 1%) in the future. Assuming the current stock price is unaffected, investigate the impact of on the option price in part (c).

(e)If you instead hold an American version of this call option, would the announcement affect your exercise strategy? Explain how or why not.