Case 8

OPTIONS CASE

General Synergistics is an emerging leader in the development of bioengineering technology.

Since its stock is relatively volatile and draws a large amount of investor interest, the firm has recently been listed on the Chicago Board of Options Exchange (CBOE), and put and call options on the firm's stock are now being traded. The listing has generated a lot of interest among the firm's senior managers, but only a few of them have a good understanding of what options are and how they work. General Synergistics' chief financial officer, Rex Moncrief, plans to hold a seminar on the basics of option theory and valuation. Mr. Moncrief has asked you, a newly hired financial analyst, to make the presentation. To help you get started, Moncrief has supplied you with the following set of questions. See if you can answer them.

1. What is an option?

2. Suppose General Synergistics, which is currently trading at $28, has 9-month put and call options with a striking price of $25. The call option currently sells for $7.50 per share while

the put option costs $2.00 per share.

(1) What is the minimum number of shares in a stock option contract?

(2) Is the call option in or out of the money? What about the put option?

3. Again consider General Synergistics' call option with a $25 striking price. The following

the table contains historical values for this option at different stock prices:

Stock Price Call Option Price

$25 $ 3.00

30 7.50

35 12.00

40 16.50

45 21.00

50 25.50

(1) Create a table that shows (a) stock price, (b) striking price, (c) expiration value, (d) option price, and (e) the premium of option price over expiration value.

4. In 1973, Fischer Black and Myron Scholes developed the Black-Scholes Option Pricing Model (OPM).

(1) What assumptions underlie the OPM?

(2) What is the value of the following call option according to the OPM?

Stock price = $28.00

Exercise price = $25.00

Time to expiration = 9 months

Risk-free rate = 5.0%

Stock return variance = 0.30

5. What impact does each of the following call option parameters have on the value of the option?

(1) Current stock price

(2) Exercise price

(3) Option period

(4) Risk-free rate

(5) Stock return variance

STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .00005 .00005 .00004 .00004 .00004 100004 ,00004 .00001 .00003 .00003 -3.8 .00007 .00007 .00007 .00006 .00006 .00006 .00006 .00005 .00005 .00005 .00011 .00010 .00010 .00010 .00009 .00009 .00008 .00008 .00008 00008 -3.6 .00016 .00015 .00015 .00014 .00014 .00013 .00013 .00012 00012 .00011 -3.5 .00023 .00022 .00022 .00021 .00020 .00019 .00019 ,00018 .00017 .00017 .00034 .00032 .00031 .00030 .00029 .00028 .00027 .00026 .00025 .00024 .00048 .00047 .00045 .00043 .00042 .00040 .00039 ,00038 .00036 .00035 -3.2 .00069 .00066 .0004 .00062 .00060 .00058 .00056 .00054 .00052 .00050 3.1 .00097 .00094 .00090 .00087 .00084 .00082 .00079 .00076 .00074 .00071 -3.0 .00135 .00131 .00126 .00122 .00118 .00114 ,00111 .00107 .00104 .00100 -2.9 .00187 .00181 .00175 .00169 .00164 .00159 .00154 .00149 .00144 .00139 -2.8 .00256 .00248 .00240 .00233 _00226 .00219 .00212 .00205 .00199 .00193 .00347 .00336 .00326 .00317 .00307 .00298 .00289 00280 .00272 .00264 -2.6 00466 .00453 .00440 .00427 .00415 .00402 .00391 .00379 .00368 .00357 -2.5 .00621 .00604 .00587 .00570 .00554 .00539 .00523 ,00508 .00-191 .00480 .00820 .00798 .00776 .00755 .00734 .00714 .00695 .00676 _00657 _00639 .01072 .01044 01017 .00990 .00964 .00939 .00914 .00889 .00866 2008-12 01390 .01355 01321 01287 .01255 012 .01191 .01160 . .01130 01101 -2.1 .01786 .01743 201700 .01659 .01618 .01578 .01539 01500 .01463 01-426 02275 .02222 02169 .02118 02068 02018 .01970 .01923 01876 01831 -1.9 .02872 .02807 .02743 .02680 .02619 .02559 .02500 02442 02385 02330 -1.8 .03593 .03515 .03438 .03362 .03288 .03216 .03144 .03074 .03005 02938 -1.7 .04457 .04363 .04272 .04182 .04093 .04006 .03920 .03836 .03754 .03673 -1.6 05480 .05370 .05262 .05155 05050 .04947 .04846 .04746 .04648 04551 -1.5 .06681 .06552 .06426 .06301 .06178 .06057 .05938 .05821 .05705 .05592 -14 .08076 .07927 .07780 .07636 .07493 ,07353 .07215 .07078 .06944 .06811 -1.3 .09680 .09510 _09342 .09176 09012 08851 .08691 08534 .08379 08226 -1.2 .11507 .11314 11123 .10935 .10749 .10565 .10383 .10204 .10027 _09853 -1.1 .13567 .13350 .13136 .12924 .12714 .12507 .12302 .12100 .11900 11702 -1.0 .15866 .15625 .15386 .15151 .14917 .14686 .14457 .14231 .14007 .13786 -0.9 .18406 .18141 .17879 .17619 .17361 .17106 .16853 .16602 .16354 .16109 -0.8 .21186 20897 20611 20327 20045 .19766 .19189 .19215 .18943 .18673 -0.7 .24196 23885 23576 23270 22965 22663 .22363 .22065 21770 21476 -0,6 27425 27093 26763 26435 26109 25785 25463 25143 24825 24510 .30854 30503 30153 29806 29460 29116 28774 .28434 .28096 27760 .34458 34090 33724 33360 32997 .32636 32276 31918 31561 31207 -0.3 .38209 37828 37448 37070 36693 .36317 35942 35569 35197 34827 -0.2 .42074 .41683 .41294 .40905 .40517 ,40129 .39743 39358 38974 38591 -0.1 46017 .45620 45224 .44828 .44433 44038 .43644 .43251 .42858 .42465 -0.0 .50000 49601 49202 48803 48405 .48006 .47608 .47210 .46812 .46414 .06 .08 1.5 STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. z .00 .01 .02 .03 .04 .05 .07 .09 0.0 .50000 .50399 .50798 .51197 51595 51994 .52392 .52790 53188 .53586 0.1 .53983 .54380 54776 .55172 55567 55962 .56356 56749 57142 57535 0.2 .57926 .58317 .58706 .59095 .59483 .59871 .60257 .60642 .61026 .61409 0.3 .61791 .62172 .62552 .62930 .63307 .63683 .64058 .64431 .64803 .65173 0.4 .65542 .65910 .66276 .66640 .67003 .67364 .67724 .68082 .68439 .68793 0.5 .69146 .69497 .69847 .70194 .70540 .70884 .71226 71566 .71904 72240 0.6 .72575 .72907 .73237 .73565 .73891 .74215 .74537 .74857 .75175 .75490 0.7 .75804 .76115 .76424 .76730 .77035 .77337 .77637 .77935 .78230 .78524 0.8 .78814 .79103 .79389 .79673 .79955 .80234 .80511 .80785 .81057 .81327 0.9 .81594 .81859 .82121 .82381 .82639 .82894 .83147 .83398 .83646 .83891 1.0 .84134 .84375 .84614 .84849 .85083 .85314 .85543 .85769 .85993 .86214 1.1 .86433 .86650 86864 .87076 .87286 .87493 .87698 .87900 .88100 .88298 1.2 .88493 .88686 .88877 .89065 .89251 .89435 .89617 .89796 .89973 .90147 1.3 .90320 .90490 90658 .90824 90988 91149 91309 .91466 91621 91774 1.4 .91924 92073 92220 .92364 92507 .92647 .92785 .92922 93056 .93189 .93319 93448 .93574 93699 93822 93943 .94062 94179 94295 94408 1.6 94520 94630 94738 .94845 94950 95053 .95154 .95254 95352 95449 1.7 .95543 95637 95728 95818 95907 95994 .96080 96164 96246 96327 1.8 .96407 .96485 .96562 .96638 .96712 .96784 .96856 .96926 .96995 97062 1.9 .97128 97193 97257 .97320 97381 97441 .97500 .97558 97615 .97670 2.0 97725 97778 97831 97882 97932 97982 98030 98077 .98124 .98169 2.1 .98214 98257 98300 .98341 98382 .98422 .98461 .98500 .98537 .98574 2.2 .98610 98645 .98679 .98713 .98745 98778 .98809 .98840 .98870 .98899 2.3 .98928 98956 98983 .99010 .99036 .99061 99086 99111 .99134 99158 2.4 .99180 99202 99224 .99245 .99266 .99286 .99305 .99324 99343 99361 2.5 99379 .99396 .99413 99430 99446 99461 99477 .99492 99506 99520 2.6 99534 99547 99560 99573 99585 99598 99609 99621 99632 99643 2.7 99653 99664 99674 .99683 99693 .99702 .99711 .99720 99728 99736 2.8 .99744 99752 99760 99767 .99774 99781 99788 99795 99801 .99807 2.9 .99813 .99819 99825 99831 99836 99841 99846 99851 .99856 99861 3.0 .99865 .99869 99874 .99878 .99882 99886 99889 .99893 99896 99900 3.1 .99903 .99906 -99910 .99913 .99916 .99918 99921 .99924 .99926 99929 3.2 99931 .99934 -99936 99938 99940 99942 .99944 99946 99948 .99950 3.3 .99952 99953 99955 .99957 .99958 99960 -99961 99962 99964 99965 3.4 99966 99968 .99969 .99970 .99971 99972 -99973 .99974 .99975 .99976 3.5 .99977 -99978 .99978 .99979 99980 99981 99981 .99982 99983 99983 3.6 99984 99985 99985 99986 99986 99987 99987 99988 99988 99989 3.7 99989 .99990 .99990 99990 99991 .99991 .99992 99992 99992 99992 3.8 .99993 99993 99993 .99994 99994 .99994 .99994 .99995 99995 .99995 3.9 .99995 -99995 -99996 99996 99996 99996 99996 99996 .99997 99997 STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .00005 .00005 .00004 .00004 .00004 100004 ,00004 .00001 .00003 .00003 -3.8 .00007 .00007 .00007 .00006 .00006 .00006 .00006 .00005 .00005 .00005 .00011 .00010 .00010 .00010 .00009 .00009 .00008 .00008 .00008 00008 -3.6 .00016 .00015 .00015 .00014 .00014 .00013 .00013 .00012 00012 .00011 -3.5 .00023 .00022 .00022 .00021 .00020 .00019 .00019 ,00018 .00017 .00017 .00034 .00032 .00031 .00030 .00029 .00028 .00027 .00026 .00025 .00024 .00048 .00047 .00045 .00043 .00042 .00040 .00039 ,00038 .00036 .00035 -3.2 .00069 .00066 .0004 .00062 .00060 .00058 .00056 .00054 .00052 .00050 3.1 .00097 .00094 .00090 .00087 .00084 .00082 .00079 .00076 .00074 .00071 -3.0 .00135 .00131 .00126 .00122 .00118 .00114 ,00111 .00107 .00104 .00100 -2.9 .00187 .00181 .00175 .00169 .00164 .00159 .00154 .00149 .00144 .00139 -2.8 .00256 .00248 .00240 .00233 _00226 .00219 .00212 .00205 .00199 .00193 .00347 .00336 .00326 .00317 .00307 .00298 .00289 00280 .00272 .00264 -2.6 00466 .00453 .00440 .00427 .00415 .00402 .00391 .00379 .00368 .00357 -2.5 .00621 .00604 .00587 .00570 .00554 .00539 .00523 ,00508 .00-191 .00480 .00820 .00798 .00776 .00755 .00734 .00714 .00695 .00676 _00657 _00639 .01072 .01044 01017 .00990 .00964 .00939 .00914 .00889 .00866 2008-12 01390 .01355 01321 01287 .01255 012 .01191 .01160 . .01130 01101 -2.1 .01786 .01743 201700 .01659 .01618 .01578 .01539 01500 .01463 01-426 02275 .02222 02169 .02118 02068 02018 .01970 .01923 01876 01831 -1.9 .02872 .02807 .02743 .02680 .02619 .02559 .02500 02442 02385 02330 -1.8 .03593 .03515 .03438 .03362 .03288 .03216 .03144 .03074 .03005 02938 -1.7 .04457 .04363 .04272 .04182 .04093 .04006 .03920 .03836 .03754 .03673 -1.6 05480 .05370 .05262 .05155 05050 .04947 .04846 .04746 .04648 04551 -1.5 .06681 .06552 .06426 .06301 .06178 .06057 .05938 .05821 .05705 .05592 -14 .08076 .07927 .07780 .07636 .07493 ,07353 .07215 .07078 .06944 .06811 -1.3 .09680 .09510 _09342 .09176 09012 08851 .08691 08534 .08379 08226 -1.2 .11507 .11314 11123 .10935 .10749 .10565 .10383 .10204 .10027 _09853 -1.1 .13567 .13350 .13136 .12924 .12714 .12507 .12302 .12100 .11900 11702 -1.0 .15866 .15625 .15386 .15151 .14917 .14686 .14457 .14231 .14007 .13786 -0.9 .18406 .18141 .17879 .17619 .17361 .17106 .16853 .16602 .16354 .16109 -0.8 .21186 20897 20611 20327 20045 .19766 .19189 .19215 .18943 .18673 -0.7 .24196 23885 23576 23270 22965 22663 .22363 .22065 21770 21476 -0,6 27425 27093 26763 26435 26109 25785 25463 25143 24825 24510 .30854 30503 30153 29806 29460 29116 28774 .28434 .28096 27760 .34458 34090 33724 33360 32997 .32636 32276 31918 31561 31207 -0.3 .38209 37828 37448 37070 36693 .36317 35942 35569 35197 34827 -0.2 .42074 .41683 .41294 .40905 .40517 ,40129 .39743 39358 38974 38591 -0.1 46017 .45620 45224 .44828 .44433 44038 .43644 .43251 .42858 .42465 -0.0 .50000 49601 49202 48803 48405 .48006 .47608 .47210 .46812 .46414 .06 .08 1.5 STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. z .00 .01 .02 .03 .04 .05 .07 .09 0.0 .50000 .50399 .50798 .51197 51595 51994 .52392 .52790 53188 .53586 0.1 .53983 .54380 54776 .55172 55567 55962 .56356 56749 57142 57535 0.2 .57926 .58317 .58706 .59095 .59483 .59871 .60257 .60642 .61026 .61409 0.3 .61791 .62172 .62552 .62930 .63307 .63683 .64058 .64431 .64803 .65173 0.4 .65542 .65910 .66276 .66640 .67003 .67364 .67724 .68082 .68439 .68793 0.5 .69146 .69497 .69847 .70194 .70540 .70884 .71226 71566 .71904 72240 0.6 .72575 .72907 .73237 .73565 .73891 .74215 .74537 .74857 .75175 .75490 0.7 .75804 .76115 .76424 .76730 .77035 .77337 .77637 .77935 .78230 .78524 0.8 .78814 .79103 .79389 .79673 .79955 .80234 .80511 .80785 .81057 .81327 0.9 .81594 .81859 .82121 .82381 .82639 .82894 .83147 .83398 .83646 .83891 1.0 .84134 .84375 .84614 .84849 .85083 .85314 .85543 .85769 .85993 .86214 1.1 .86433 .86650 86864 .87076 .87286 .87493 .87698 .87900 .88100 .88298 1.2 .88493 .88686 .88877 .89065 .89251 .89435 .89617 .89796 .89973 .90147 1.3 .90320 .90490 90658 .90824 90988 91149 91309 .91466 91621 91774 1.4 .91924 92073 92220 .92364 92507 .92647 .92785 .92922 93056 .93189 .93319 93448 .93574 93699 93822 93943 .94062 94179 94295 94408 1.6 94520 94630 94738 .94845 94950 95053 .95154 .95254 95352 95449 1.7 .95543 95637 95728 95818 95907 95994 .96080 96164 96246 96327 1.8 .96407 .96485 .96562 .96638 .96712 .96784 .96856 .96926 .96995 97062 1.9 .97128 97193 97257 .97320 97381 97441 .97500 .97558 97615 .97670 2.0 97725 97778 97831 97882 97932 97982 98030 98077 .98124 .98169 2.1 .98214 98257 98300 .98341 98382 .98422 .98461 .98500 .98537 .98574 2.2 .98610 98645 .98679 .98713 .98745 98778 .98809 .98840 .98870 .98899 2.3 .98928 98956 98983 .99010 .99036 .99061 99086 99111 .99134 99158 2.4 .99180 99202 99224 .99245 .99266 .99286 .99305 .99324 99343 99361 2.5 99379 .99396 .99413 99430 99446 99461 99477 .99492 99506 99520 2.6 99534 99547 99560 99573 99585 99598 99609 99621 99632 99643 2.7 99653 99664 99674 .99683 99693 .99702 .99711 .99720 99728 99736 2.8 .99744 99752 99760 99767 .99774 99781 99788 99795 99801 .99807 2.9 .99813 .99819 99825 99831 99836 99841 99846 99851 .99856 99861 3.0 .99865 .99869 99874 .99878 .99882 99886 99889 .99893 99896 99900 3.1 .99903 .99906 -99910 .99913 .99916 .99918 99921 .99924 .99926 99929 3.2 99931 .99934 -99936 99938 99940 99942 .99944 99946 99948 .99950 3.3 .99952 99953 99955 .99957 .99958 99960 -99961 99962 99964 99965 3.4 99966 99968 .99969 .99970 .99971 99972 -99973 .99974 .99975 .99976 3.5 .99977 -99978 .99978 .99979 99980 99981 99981 .99982 99983 99983 3.6 99984 99985 99985 99986 99986 99987 99987 99988 99988 99989 3.7 99989 .99990 .99990 99990 99991 .99991 .99992 99992 99992 99992 3.8 .99993 99993 99993 .99994 99994 .99994 .99994 .99995 99995 .99995 3.9 .99995 -99995 -99996 99996 99996 99996 99996 99996 .99997 99997