Consider the following questions on the pricing of options on the stock of ARB Inc.:
a. A share of ARB stock sells for $75 and has a standard deviation of returns equal to 20 percent per year. The current risk-free rate is 9 percent and the stock pays two dividends:
(1) a $2 dividend just prior to the options expiration day, which is 91 days from now (i.e., exactly one-quarter of a year), and (2) a $2 dividend 182 days from now (i.e., exactly one-half year). Calculate the Black-Schools value for a European-style call option with an exercise price of $70.
b. What would be the price of a 91-day European-style put option on ARB stock having the same exercise price?
c. Calculate the change in the call option’s value that would occur if ARB’s management suddenly decided to suspend dividend payments and this action had no effect on the price of the company’s stock.
d. Briefly describe (without calculations) how your answer in Part a would differ under the following separate circumstances: (1) the volatility of ARB stock increases to 30 percent, and (2) the risk-free rate decreases to 8 percent.