A call option is the right to buy stock at $50 a share. Currently the option has six months to expiration, the volatility of the stock (standard deviation) is 0.30, and the rate of interest is 10 percent (0.1 in Exhibit 18.2).

a) What is the value of the option according to the Black-Scholes model if the price of the stock is $45, $50, or $55?

b) What is the value of the option when the price of the stock is $50 and the option expires in six months, three months, or one month?

c) What is the value of the option when the price of the stock is $50 and the interest rate is 5 percent, 10 percent, or 15 percent?

d) What is the value of the option when the price of the stock is $50 and the volatility of the stock is 0.40, 0.30, or 0.10?

e) What generalizations can be derived from the solutions to these problems?