Gary Levin is the chief executive officer of Mountainbrook Trading Company. The board of directors has just granted Mr. Levin 22,000 at-the-money European call options on the company’s stock, which is currently trading at $95 per share. The stock pays no dividends. The options will expire in five years, and the standard deviation of the returns on the stock is 56 percent. Treasury bills that mature in five years currently yield a continuously compounded interest rate of 5.8 percent.
Use the Black–Scholes model to calculate the value of the stock options.