Find the subgame perfect equilibrium

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Reference no: EM131911958

An executive has been given two stock options as a bonus. Each option gives the executive the right (but not the obligation) to purchase one share of the company’s stock for $50, as long as she does it before the close of the stock market tomorrow afternoon. When the executive exercises either option, she must immediately sell the stock bought from the company at the market price in effect at the time. The stock price today is $55, so if she exercises either option today she is guaranteed a profit of $5 per option exercised. The stock price tomorrow will be either $45 or $65 with equal probability. This means that if she waits until tomorrow and the stock price rises to $65, she can exercise any remaining options for a profit of $15 per option. On the other hand, if the stock price falls to $45, then exercising either option results in a loss of $5 per option. Today the executive can (i) exercise both options, (ii) exercise one option today and wait until tomorrow to decide about the second one, and (iii) exercise neither option today and wait until tomorrow to decide what to do about both. Tomorrow the executive must either exercise any remaining option(s) or let them expire unused. (a) Draw a game tree for this game between the executive and Nature; find the subgame perfect equilibrium. Remember to label the action taken along each branch, who moves at each decision node (the executive or Nature), and the total change in the executive’s wealth at each terminal node. Assume that there are no brokerage commissions or taxes. The executive is risk-neutral and her actual payoff (utility) at each terminal node equals the change in total wealth. The executive maximizes her expected utility. (b) Suppose that the executive knows today what the firm’s stock price will be tomorrow (she has "insider information"). Draw a second game tree that reflects these changes (now Nature moves first) and finds the executive’s optimal strategy. Could the executive’s actions today and tomorrow be used to show that she had insider information at the time she acted? (compare the optimal strategies in (a) and (b)).

Reference no: EM131911958

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