= Let So 100, and consider a 3-period binomial tree model in which in every period, 1-year long, there is 60% chance of u = 1.1 increase, or a 40% chance of d = decrease. Assume that the stock pays no dividends, and the continuously compounded interest rate is 2%. 1. Compute the value of an American call and put option with strike price K money). = 100 (at-the- 2. Are the American options computed in point (1.) exercised before maturity? Discuss the intuition. 3. Let the continuously compounded interest rate be 5%. What are the values of the two ATM American options? Compute the times of early exercise and discuss. = 4. In case (1.)-(2.), with interest rate still at r 2%, suppose that the firm now pays a 5% proportional dividend per year (that is, for each share, the dividend in a given year is equal to 5% of the current stock price). How does your answer to point (3.) change? Discuss.