1) An executive at a publishing house hasjust received two stock options as a bonus. Each of theseoptionsgives the executive the right (but not the obligation) to purchase one share of the publishing company’s stock for $50. The executive can (a) exercise bothoptions today, or (b) exercise one option today and exercise none or one option tomorrow,or (c) exercise no options today and exercise none, one or two options tomorrow. After tomorrow any options that haven’t been exercised become worthless. If the executive exercises an option, she must immediately sell the stock bought from the company at the market price in effect at that time. The stock price today is $54. The stock price tomorrow will be either $49 or $59 with equal probability, and it will be revealed tomorrow before the executive has to decide whether to exercise any options tomorrow. Draw a decision tree for this executive,taking care to label the action taken along each branch, to label who moves at each decision node (the executive or Nature), and to label the change in wealth at each terminal node. Assume there are no brokerage commissions or taxes.
2) Suppose the executive in Problem 1 is risk-neutral (i.e. assume utility is equal to the expected monetary payoff). Use backwards induction to determine her optimal course of action.
3) Use information sets to construct a decision tree for the executive in Problem 1 in which Nature moves first that is, out of chronological sequence.
4) Alter only the information sets in your decision tree for Problem 3, to depict the executive’s decision problem under the alternative assumption that she knows today what the firm’s stock price will be tomorrow (i.e.,has “insider information”). Use backwards induction to determine the executive’s optimal decision in this case.