Problem:
Gary Levin is the chief executive officer of Mountainbrook Trading Company. The board of directors has just granted Mr. Levin 20,000 at-the-money European call options on Mountainbrook's stock, which is currently trading at $50 per share. Mountainbrook's stock pays no dividends. The options will expire in 4 years, and the annual variance of the continuously compounded returns on Mountainbrook's stock is 0.25. Treasury bills that mature in four years currently yield a continuously compounded interest rate of 6 percent per annum.
1. Use the Black-Scholes model to calculate the value of Mr. Levin's stock options.
2. You are Mr. Levin's financial adviser. He must choose between the previously mentioned stock option package and an immediate $450,000 bonus. If he is risk-neutral, which would you recommend?
3. How would your answer to (b) change if Mr. Levin were risk-averse and he could not sell the options prior to expiration?