A recent MBA graduate is considering an offer of employment at a biotech company, where she has been offered stock options as part of her compensation package. The options give her the right, but not the obligation, to buy 2500 shares of stock either one year from now or two years from now at a price of $50, which is the current market price of the stock. If the price of the stock has risen above $50 at either time, she can buy 2500 shares at $50 and then immediately sell at the current price, thereby making a risk-free profit. On the other hand, if the price of the stock has dropped below $50, she will not exercise the option because it is “out of the money” and she would loose money. Based on historical market information, she estimates that the stock price in the first year will either go up by 25% from its current price, with probability of 0.55, or it will go down by 15%, with probability of 0.45. In either case, she can exercise the options or wait to see what will happen in the second year. If she decides to wait, the in the second year, the stock price will again go up or down by the same amounts and with the same probabilities, starting from either the “up” or “down” price at the end of the first year.
(A) What is the optimal decision making policy regarding the options in all possible scenarios over the next two years?
(B) What is the expected value of the stock options? Ignore the time value of money (assume no discounting of future payoffs)
(C) If her estimates of the increases/decreases or probabilities are inaccurate, could the options have a negative EMV?
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