Assume the following data: Stock price = $45; Exercise price = $52; continuously compounded risk-free rate...

 

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Assume the following data: Stock price = $45; Exercise price = $52; continuously compounded risk-free rate = 5.4; Continuously compounded variance = 0.18; Expiration = 8 months. Calculate the value of a European call option. Use the Black-Scholes formula. APPENDIX A Z .00 -5.0 .000000287 -4.5 .00000340 -4.0 .0000317 -3.5 000233 Cumulative Probability TABLE A Standard Normal Cumulative Probabilities .00 .01 .02 .03 .04 .05 Z -16 -1.6 -1.5 -1.4 12 -1.3 -1.2 .0003 .0003 .0003 0002 .0003 .0005 .0007 0007 0010 .0010 .0014 -3.4 .0003 .0003 .0003 .0003 .0003 .0003 -3.3 .0005 .0005 0005 .0004 .0004 .0004 .0004 .0004 .0004 -3.2 .0007 .0007 .0006 .0006 .0006 .0006 .0006 0005 .0005 -3.1 .0010 .0009 ,0009 .0009 ,0008 .0008 .0008 .0008 .0007 -3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 -2.9 .0019 .0018 0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 -2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 0021 .0020 -2.7 .0035 0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 0026 -2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 0037 0036 -2.5 ,0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 ,0048 -2.4 ,0082 0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 B .0099 CA .0019 .0064 -0000 COO -2.3 .0107 .0102 .0096 .0094 Co 0122 0144 .0091 .0089 wwww M .0084 www -2.2 0139 0132 0129 0125 104 -2.1 .0154 .0162 .0158 0104 20100 Te 0212 .0207 .0202 0197 -2.0 -1.9 Max .0179 Mirz 0228 0440 -1.1 -1.0 00 -0.9 -0.8 Bien -0.7 0104 40% .0287 0287 .0281 -1.8 .0359 .0351 .0344 0808 0909 0136 20130 0174 STA .0222 0222 LOFT .1357 -1.7 .0446 .0436 .0427 0548 0548 .0537 .0526 .0516 0668 0668 .0655 .0643 0630 0778 .0778 .0764 .0749 0764 .0793 0793 0851 .0951 .0968 LIGI 1121 1151 .1131 .0170 20170 .0217 0217 .0274 Jar .1335 New .1562 0924 0934 uu 1112 .1314 1214 0166 1000 150 .1539 Cumulative probability for z is the area under the standard normal curve to the left of z 2358 ( 0268 .0262 0400 -0204 .0336 .0329 0418 .0409 .0505 .0618 0912 .0918 .06 .1093 1003 .07 .0150 .0146 0130 0146 .0192 .0188 0404 0121 0172 .0256 .0250 .0244 .0322 .0314 .0307 .0401 .0392 .0384 0384 0485 .0475 .0465 0475 0465 .0495 .0485 .0606 .0594 .0721 0721 .0708 .0901 .0885 0869 .0869 0853 .0735 0995 0801 1028 .1075 .1292 .1271 .1251 .1056 .1038 DEL 1220 .1230 w .1446 1000 ICIE 1515 .1711 1685 www SHEE 1977 .1949 Sp .2266 .2236 140 1402 .1492 .1469 .08 0119 0116 MAY .0087 MANI 0113 0115 .0838 1002 1020 .1020 .1003 1310 100 ICON .1210 .1190 900 .1423 .1401 *Dow 123O .1587 .1379 u 17 .1841 S A D 1814 .1788 .1762 .1736 Pr 2000 2119 .2090 .2061 2005 .1611 Ma .1867 M .2420 2389 .1660 .1635 -room Ho .1922 .1894 PA ,2206 D 2578 .2546 .2514 .2483 T 2912 .2877 .2843 2810 2177 2148 S -0.6 2743 .2709 2676 .2451 2000 D .3085 .3050 2776 2033 .2005 P .2327 .2296 2643 2611 F -0.5 .3015 .2981 2946 -0.4 .3372 .3336 .3300 3264 .3228 .3192 .3156 3121 -0.3 3821 3783 .3745 .3707 .3669 3632 3594 3557 3520 .3483 -0.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 3897 .3859 -0.1 .4602 4562 .4522 .4483 4443 .4404 4364 .4325 4286 .4247 -0.0 5000 .4960 4920 4880 4840 .4801 .4761 4721 3446 .3409 4681 .4641 .09 .0301 0901 .0375 0110 COTTO .0582 0571 0143 0170 0100 0239 .0233 0433 0431 .0294 .0367 .0183 0163 .0455 0559 .0571 .0559 .0694 0681 .0681 0823 0995 0985 1170 1170 A-I Assume the following data: Stock price = $45; Exercise price = $52; continuously compounded risk-free rate = 5.4; Continuously compounded variance = 0.18; Expiration = 8 months. Calculate the value of a European call option. Use the Black-Scholes formula. APPENDIX A Z .00 -5.0 .000000287 -4.5 .00000340 -4.0 .0000317 -3.5 000233 Cumulative Probability TABLE A Standard Normal Cumulative Probabilities .00 .01 .02 .03 .04 .05 Z -16 -1.6 -1.5 -1.4 12 -1.3 -1.2 .0003 .0003 .0003 0002 .0003 .0005 .0007 0007 0010 .0010 .0014 -3.4 .0003 .0003 .0003 .0003 .0003 .0003 -3.3 .0005 .0005 0005 .0004 .0004 .0004 .0004 .0004 .0004 -3.2 .0007 .0007 .0006 .0006 .0006 .0006 .0006 0005 .0005 -3.1 .0010 .0009 ,0009 .0009 ,0008 .0008 .0008 .0008 .0007 -3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 -2.9 .0019 .0018 0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 -2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 0021 .0020 -2.7 .0035 0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 0026 -2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 0037 0036 -2.5 ,0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 ,0048 -2.4 ,0082 0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 B .0099 CA .0019 .0064 -0000 COO -2.3 .0107 .0102 .0096 .0094 Co 0122 0144 .0091 .0089 wwww M .0084 www -2.2 0139 0132 0129 0125 104 -2.1 .0154 .0162 .0158 0104 20100 Te 0212 .0207 .0202 0197 -2.0 -1.9 Max .0179 Mirz 0228 0440 -1.1 -1.0 00 -0.9 -0.8 Bien -0.7 0104 40% .0287 0287 .0281 -1.8 .0359 .0351 .0344 0808 0909 0136 20130 0174 STA .0222 0222 LOFT .1357 -1.7 .0446 .0436 .0427 0548 0548 .0537 .0526 .0516 0668 0668 .0655 .0643 0630 0778 .0778 .0764 .0749 0764 .0793 0793 0851 .0951 .0968 LIGI 1121 1151 .1131 .0170 20170 .0217 0217 .0274 Jar .1335 New .1562 0924 0934 uu 1112 .1314 1214 0166 1000 150 .1539 Cumulative probability for z is the area under the standard normal curve to the left of z 2358 ( 0268 .0262 0400 -0204 .0336 .0329 0418 .0409 .0505 .0618 0912 .0918 .06 .1093 1003 .07 .0150 .0146 0130 0146 .0192 .0188 0404 0121 0172 .0256 .0250 .0244 .0322 .0314 .0307 .0401 .0392 .0384 0384 0485 .0475 .0465 0475 0465 .0495 .0485 .0606 .0594 .0721 0721 .0708 .0901 .0885 0869 .0869 0853 .0735 0995 0801 1028 .1075 .1292 .1271 .1251 .1056 .1038 DEL 1220 .1230 w .1446 1000 ICIE 1515 .1711 1685 www SHEE 1977 .1949 Sp .2266 .2236 140 1402 .1492 .1469 .08 0119 0116 MAY .0087 MANI 0113 0115 .0838 1002 1020 .1020 .1003 1310 100 ICON .1210 .1190 900 .1423 .1401 *Dow 123O .1587 .1379 u 17 .1841 S A D 1814 .1788 .1762 .1736 Pr 2000 2119 .2090 .2061 2005 .1611 Ma .1867 M .2420 2389 .1660 .1635 -room Ho .1922 .1894 PA ,2206 D 2578 .2546 .2514 .2483 T 2912 .2877 .2843 2810 2177 2148 S -0.6 2743 .2709 2676 .2451 2000 D .3085 .3050 2776 2033 .2005 P .2327 .2296 2643 2611 F -0.5 .3015 .2981 2946 -0.4 .3372 .3336 .3300 3264 .3228 .3192 .3156 3121 -0.3 3821 3783 .3745 .3707 .3669 3632 3594 3557 3520 .3483 -0.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 3897 .3859 -0.1 .4602 4562 .4522 .4483 4443 .4404 4364 .4325 4286 .4247 -0.0 5000 .4960 4920 4880 4840 .4801 .4761 4721 3446 .3409 4681 .4641 .09 .0301 0901 .0375 0110 COTTO .0582 0571 0143 0170 0100 0239 .0233 0433 0431 .0294 .0367 .0183 0163 .0455 0559 .0571 .0559 .0694 0681 .0681 0823 0995 0985 1170 1170 A-I

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The BlackScholes formula is a widely used model for pricing European call and put optionsIt takes ... View the full answer