Problem 16-04 Consider the following questions on the pricing of options on the stock of ARB Inc.: a. A share of ARB stock sells for $78 and has a standard deviation of returns equal to 25% per year. The current risk-free rate is 8% and the stock pays two dividends: (1) a $3 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 $3 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 $73. 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 ( increase 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 increases to 40%, and (2) the risk-free rate increases to 9%. An increase in the volatility to 40% would decrease the call's value. An increase in the risk-free rate to 9% would decrease the call's value. Grade It Now Save & Continue Continue without saving APPENDIX Standard Normal Probabilities Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.09 0.0 0.1 0.2 0.3 0.4 0.5 .7257 0.6 0.7 0.8 0.9 1.0 .7764 .8051 .8078 .8289 .8599 1.2 1.3 1.4 1.5 .5000 5040 50805120516051995239.52795219 .5398 5438 .5478 .5517 .5557 .5596 -5636 .5675 .5714 .5793 .5832 .5871 .5910 .5948 .5987 .6026 .6064 .6103 .6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7580 .7611 .7642 .7673 .7704 .7734 .7794 .7823 .7881 .7910 .7939 .7967 .7995 .8023 .8106 .8159 .8186 .8212 .8238 .8264 .8315 .8340 .8365 .8413 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8643 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8849 .8860 .8888 .8907 .8925 .8943 .8962 .8980 .8997 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .9332 .9345 9357 9370 .9382 .9394 .9406 .9418 .9429 .9452 9463 .9474 .9484 .9495 .9505 .9515 .9525 9535 9554 9564 .9573 9582 .9591 .9599 .9608 .9616 .9625 .9641 9649 .9656 .9664 .9671 .9678 .9686 .9693 .9699 9713 .9719 9726 .9732 .9738 .9744 .9750 9756 .9761 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 9812 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 ,9854 .9861 .9864 .9868 .9871 .9875 .9878 .9881 9884 .9887 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 9913 .9918 .9920 .9922 9925 .9927 .9929 .9931 .9932 9934 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 ,9951 .9953 .9955 .9956 .9957 .9959 9960 .9961 .9962 .9963 .9965 .9966 .9967 .9968 .9970 .9971 .9972 .9973 .9974 .9975 .9976 9977 .9977 .9978 .9979 .9979 .9980 .9981 .9982 9982 .9983 9984 .9984 .9985 .9985 .9986 .9987998799879988 9988 9989 .99899989 9990 5359 .5753 .6141 .6517 .6879 .7224 .7549 .7852 .8133 .8389 .8621 .8830 .9015 .9177 .9319 9441 .9545 .9633 .9706 9767 9817 .9857 .9890 .9916 .9936 .9952 .9964 .9974 9981 .9986 .9990 1.6 1.7 1.8 1.9 2.0 23 2.4 2.5 2.6 2.7 .9969 2.8 2.9 3.0 Problem 16-04 Consider the following questions on the pricing of options on the stock of ARB Inc.: a. A share of ARB stock sells for $78 and has a standard deviation of returns equal to 25% per year. The current risk-free rate is 8% and the stock pays two dividends: (1) a $3 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 $3 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 $73. 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 ( increase 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 increases to 40%, and (2) the risk-free rate increases to 9%. An increase in the volatility to 40% would decrease the call's value. An increase in the risk-free rate to 9% would decrease the call's value. Grade It Now Save & Continue Continue without saving APPENDIX Standard Normal Probabilities Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.09 0.0 0.1 0.2 0.3 0.4 0.5 .7257 0.6 0.7 0.8 0.9 1.0 .7764 .8051 .8078 .8289 .8599 1.2 1.3 1.4 1.5 .5000 5040 50805120516051995239.52795219 .5398 5438 .5478 .5517 .5557 .5596 -5636 .5675 .5714 .5793 .5832 .5871 .5910 .5948 .5987 .6026 .6064 .6103 .6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7580 .7611 .7642 .7673 .7704 .7734 .7794 .7823 .7881 .7910 .7939 .7967 .7995 .8023 .8106 .8159 .8186 .8212 .8238 .8264 .8315 .8340 .8365 .8413 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8643 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8849 .8860 .8888 .8907 .8925 .8943 .8962 .8980 .8997 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .9332 .9345 9357 9370 .9382 .9394 .9406 .9418 .9429 .9452 9463 .9474 .9484 .9495 .9505 .9515 .9525 9535 9554 9564 .9573 9582 .9591 .9599 .9608 .9616 .9625 .9641 9649 .9656 .9664 .9671 .9678 .9686 .9693 .9699 9713 .9719 9726 .9732 .9738 .9744 .9750 9756 .9761 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 9812 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 ,9854 .9861 .9864 .9868 .9871 .9875 .9878 .9881 9884 .9887 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 9913 .9918 .9920 .9922 9925 .9927 .9929 .9931 .9932 9934 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 ,9951 .9953 .9955 .9956 .9957 .9959 9960 .9961 .9962 .9963 .9965 .9966 .9967 .9968 .9970 .9971 .9972 .9973 .9974 .9975 .9976 9977 .9977 .9978 .9979 .9979 .9980 .9981 .9982 9982 .9983 9984 .9984 .9985 .9985 .9986 .9987998799879988 9988 9989 .99899989 9990 5359 .5753 .6141 .6517 .6879 .7224 .7549 .7852 .8133 .8389 .8621 .8830 .9015 .9177 .9319 9441 .9545 .9633 .9706 9767 9817 .9857 .9890 .9916 .9936 .9952 .9964 .9974 9981 .9986 .9990 1.6 1.7 1.8 1.9 2.0 23 2.4 2.5 2.6 2.7 .9969 2.8 2.9 3.0