Consider the following questions on the pricing of options on the stock of ARB Inc.: a. A share of ARB stock sells for $80 and has a standard deviation of returns equal to 24% per year. The current risk-free rate is 8% and the stock pays two dividends: (1) a $2 dividend just prior to the option's 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-Scholes value for a 91-day European-style call option with an exercise price of $75. Use the modifyed model that assumes the dividend yield is paid continuously. You may use Appendix D to answer the question. Do not round intermediate calculations. Round your answer to the nearest cent. b. What would be the price of a 91-day European-style put option on ARB stock having the same exercise price? Do not round intermediate calculations. Round your answer to the nearest cent. $ 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. You may use Appendix D to answer the question. Do not round intermediate calculations. Round your answer to the nearest cent. The price would by $ d. Briefly describe (without calculations) how your answer in Part a would differ under the following separate circumstances: (1) the volatility of ARB stock decreases to 9%, and (2) the risk-free rate increases to 9%. A decrease in the volatility to 9% would the call's value. An increase in the risk-free rate to 9% would the call's value. Consider the following questions on the pricing of options on the stock of ARB Inc.: a. A share of ARB stock sells for $80 and has a standard deviation of returns equal to 24% per year. The current risk-free rate is 8% and the stock pays two dividends: (1) a $2 dividend just prior to the option's 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-Scholes value for a 91-day European-style call option with an exercise price of $75. Use the modifyed model that assumes the dividend yield is paid continuously. You may use Appendix D to answer the question. Do not round intermediate calculations. Round your answer to the nearest cent. b. What would be the price of a 91-day European-style put option on ARB stock having the same exercise price? Do not round intermediate calculations. Round your answer to the nearest cent. $ 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. You may use Appendix D to answer the question. Do not round intermediate calculations. Round your answer to the nearest cent. The price would by $ d. Briefly describe (without calculations) how your answer in Part a would differ under the following separate circumstances: (1) the volatility of ARB stock decreases to 9%, and (2) the risk-free rate increases to 9%. A decrease in the volatility to 9% would the call's value. An increase in the risk-free rate to 9% would the call's value
