a) A stock sells for $125. A call option on the stock has an exercise price of $110 and expires in 3 months. If the interest rate is 0.15 and the standard deviation of the stocks return is 0.30. What would be the price of a put option on the same stock with an exercise price of $140 and the same time (3 months) until expiration? Show all workings. (See below for the Cumulative Normal Distribution Table)
APPENDIX CUMULATIVE NORMAL DISTRIBUTION TABLE Nid) 5239 5319 d 1.66 1.68 5998 d --76 -74 -72 -70 -,68 -.66 -.64 -62 -60 -58 -.56 -54 -.52 -.50 - 48 - 46 d .06 08 .10 .12 .14 .16 .18 20 22 24 26 28 .30 32 34 36 38 40 1.70 1.72 1.74 1.76 1.78 1.80 1.82 1.84 1.86 Nid) .9515 9535 9554 9573 9591 .9608 9825 9641 9656 9671 .9686 9899 9713 9726 9738 9750 9761 9772 1.88 -3.00 -2.95 -2.90 -2.85 -2.80 -2.75 -2.70 -2.65 -2.60 -2.55 -2.50 -2.45 -2.40 -2.35 -2.30 -2.25 -2.20 -2.15 -2.10 -2.05 -2.00 -1.58 -1.56 -1.94 -1.92 -1.90 -1.88 -1.86 -1.84 -1.82 -1.80 -1.78 -1.76 -1.74 -1.72 -1.70 -1.88 -1.66 -1.84 -1.62 -1.60 Nid) .0013 .0016 .0019 0022 .0026 .0030 .0035 .0040 .0047 .0054 .0062 .0071 .0082 .0094 .0107 .0122 .0139 .0158 .0179 .0202 .0228 0239 .0250 .0262 .0274 .0287 .0301 0314 .0329 0344 .0359 .0375 .0392 0409 0427 0440 .0485 .0485 .0505 .0526 .0548 - 42 d -1.56 -1.56 -1.54 -1.52 -1.50 -1.48 -1.46 -144 -1.42 -1.40 -1.38 -1.36 -1.34 -1.32 -1.30 -128 -1.26 -1.24 -1.22 - 1.20 -1.18 -1.16 -1.14 -1.12 -1.10 -1.08 -1.06 -1.04 -1.02 -1.00 -98 -96 -94 -92 -90 -88 - 86 -84 -82 -80 -78 Nid) ,0571 .0594 0618 .0643 0668 .0694 .0721 .0749 .0778 0808 .0838 0089 0901 .0934 .0968 .1003 .1038 .1075 1112 .1151 .1190 .1230 .1271 .1314 .1357 .1401 1446 .1492 .1539 .1587 .1635 1685 1736 1788 1841 .1894 .1949 2005 2081 2119 2177 Nid) .8051 .8106 .8159 .8212 .8264 .8315 .8365 8413 8461 8506 .8554 .8599 .8643 .8686 .8729 8770 .8810 .8849 .8888 .8925 .8962 .8997 d .86 .88 .90 .92 .94 .96 .98 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 Nid) 2238 2297 2358 2420 .2483 2546 2611 2676 2743 2810 2877 2946 .3015 3085 3156 3228 3300 3372 3446 3520 3594 3669 3745 3821 .3897 3974 .4062 4129 4207 4286 4364 4443 .4522 4602 4681 4761 .4840 4920 .5000 5080 .5160 5478 5557 -5638 5714 5793 5871 5948 6026 6103 .6179 .6255 6331 .6406 .6480 .6554 6628 .6700 6772 6844 .6915 .6995 -7054 .7123 .7190 7257 .7324 .7399 .7454 .7518 .7580 .7642 .7704 7764 -7823 .7881 .7939 .7995 -.40 -.38 - 36 -34 - 32 -30 -28 -26 -24 -22 -20 1.90 1.92 1.94 1.96 1.98 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 9032 .9798 9821 9842 9861 9878 9893 9906 9918 9929 250 44 46 4B 50 52 54 56 58 .60 .62 .64 .66 .68 .70 .72 .74 .76 -78 .80 82 84 9939 1.40 1.42 1.44 2.55 2.60 -.16 2.66 1.46 1.48 1.50 1.52 1.54 9066 .9099 .9131 .9162 .9192 .9222 9251 .9279 .9306 .9332 9357 .9382 .9406 .9429 .9452 .9474 .9495 2.70 2.75 2.80 2.85 9946 9953 9960 9965 9970 9974 9978 9981 9984 9987 9969 1.56 -12 -10 -08 -.06 -.04 -.02 .00 .02 .04 2.90 1.58 1.80 1.62 2.95 3.00 3.06 1.64
