Question

Gary Levin is the chief executive officer of Mountainbrook Trading Company. The board of directors has just granted Mr. Levin 18,000 at-the-money European call options on the company’s stock, which is currently trading at $105 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 3 percent.

Use the Black–Scholes model to calculate the value of the stock options.

Value of option grant?

Answer 1

Current Stock Price = $ 105, Option Strike Price = $ 105 (as the call option is at-the-money)

Standard Deviation = 56 % and T-Bill Rate = Risk Free Rate = 3 % continuously compounded

The Black Scholes Formula to calculate option price C is as given below:

where and

d1 = [ln(105/105) + 5 x (0.03 + {(0.56)^(2)}/2)] / [0.56 x (5)^(0.5)] = 0.7458884

and d2 = d1 - 0.56 x (5)^(0.5) = - 0.5063097

C = S x N(d1) - [K x N(d2)] / e^(0.03 x 5) = 105 x 0.772133 - [{105 x 0.30632}/e^(0.03 x 5)] = $ 53.3905 or $ 53.39 approximately