Consider the binomial model for an American call and put on a stock whose price is $60. The exercise price for both the put and the call is $45. The standard deviation of the stock returns is 30 percent per annum, and the risk-free rate is 5 percent per annum. The options expire in 90 days. The stock will pay a dividend equal to 3 percent of its value in 50 days.
(a) Draw the three-period stock tree and the corresponding trees for the call and the put.
(b) Compute the price of these options using the three-period trees.
(c) Explain when, if ever, each option should be exercised.