An executive at a publishing house has just 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 publishing company's stock for $50, as long as he does it before the closing of the stock market tomorrow afternoon. When the executive exercises either option (recall, he has two), he must immediately sell the stock bought from the company at the market prize in effect at the time. An option can only be exercised once. The stock's price today is $55. The executive knows this price today before deciding what to do today. Hence, if he exercises either option today he is guaranteed a profit of $5 per option exercised. The stock price tomorrow will either be $45 or $65 with equal probability. The executive will know the price tomorrow before deciding what to do that day. This means that if he waits until tomorrow and the stock price rises to $65, he can exercise any remaining options for a profit of $15 per option exercised. On the other hand, if the stock price falls to $45, then exercising either option would result in a loss of $5 per option exercised, which the executive obviously will not do, then preferring to let any option left expire unused. Today the executive can: (1) exercise both options; (2) exercise one option today and wait until tomorrow to decide about the second one; or, (3) exercise neither option today and wait until tomorrow to decide what to do about both. Tomorrow the executive must either exercise any option(s) not already cashed in or let it (them) expire unused. For each of the three strategies just described, draw a tree to represent the lottery it induces over his profits.
An executive at a publishing house has just 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 publishing company's stock for $50, as long as he does it before the closing of the stock market tomorrow afternoon. When the executive exercises either option (recall, he has two), he must immediately sell the stock bought from the company at the market prize in effect at the time. An option can only be exercised once.
The stock's price today is $55. The executive knows this price today before deciding what to do today. Hence, if he exercises either option today he is guaranteed a profit of $5 per option exercised. The stock price tomorrow will either be $45 or $65 with equal probability. The executive will know the price tomorrow before deciding what to do that day. This means that if he waits until tomorrow and the stock price rises to $65, he can exercise any remaining options for a profit of $15 per option exercised. On the other hand, if the stock price falls to $45, then exercising either option would result in a loss of $5 per option exercised, which the executive obviously will not do, then preferring to let any option left expire unused.
Today the executive can: (1) exercise both options; (2) exercise one option today and wait until tomorrow to decide about the second one; or, (3) exercise neither option today and wait until tomorrow to decide what to do about both. Tomorrow the executive must either exercise any option(s) not already cashed in or let it (them) expire unused.
For each of the three strategies just described, draw a tree to represent the lottery it induces over his profits.
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