You are considering purchasing a call option with a current stock price of $80 and an exercise price of $82, the option has 91 days to maturity (use a 365-day base), the yearly risk-free rate is currently 2% and the volatility for the option is 0.35.

a. Calculate the values of d1 and d2 by hand

b. Calculate the values of a European Call and a European Put Option using the normal distribution table - include your answers for N(d1), N(d2), N(-d2), & N(-d1)

c. Verify that the put-call parity relationship holds for these two options.

d. What initial investment is required for a delta-hedged portfolio (assume one option)?

e. Calculate the overnight profit or loss on the delta-hedged portfolio if the stock price increases to $84 and if it decreases to $76.

d1=tln(S0/K)+(r+2/2)td2=tln(S0/K)+(r2/2)t=d1tc=S0N(d1)KerrN(d2)p=KeertN(d2)S0N(d1)c+KerT=p+S STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline Z & .00 & .01 & .02 & .03 & .04 & .05 & .06 & .07 & .08 & .09 \\ \hline-3.9 & 00005 & 00005 & .00004 & .00004 & .00004 & .00004 & .00004 & .00004 & .00003 & .00003 \\ \hline-3.8 & 00007. & 00007. & 00007. & 00006 & 00006 & 00006 & 00006 & 00005 & 00005 & .00005 \\ \hline-3.7 & 00011 & 00010. & 00010. & 00010. & 00009 & 00009 & 00008 & 00008 & 00008 & .00008 \\ \hline-3.6 & 00016 & 00015 & 00015 & .00014 & .00014 & .00013 & .00013 & .00012 & .00012 & .00011 \\ \hline-3.5 & .00023 & .00022 & .00022 & .00021 & .00020 & .00019 & .00019 & .00018 & .00017 & .00017 \\ \hline-3.4 & .00034 & .00032 & .00031 & .00030 & 00029 & .00028 & .00027 & 00026 & .00025 & .00024 \\ \hline-3.3 & .00048. & .00047 & 00045 & 00043 & . 00042 & 00040. & .00039. & 00038 & .00036. & .00035 \\ \hline-3.2 & .00069. & .00066 & .00064 & .00062 & 00060 & .00058 & .00056. & .00054 & .00052 & .00050 \\ \hline-3.1 & .00097. & .00094. & 00090. & 00087. & 00084 & .00082 & 00079. & .00076. & 00074 & .00071 \\ \hline-3.0 & .00135 & .00131 & .00126 & .00122 & .00118 & .00114 & .00111 & .00107 & .00104 & .00100 \\ \hline-2.9 & .00187 & .00181 & .00175 & .00169 & .00164 & .00159. & .00154 & .00149. & .00144 & .00139 \\ \hline-2.8 & .00256. & .00248 & 00240. & .00233 & .00226. & .00219. & . 00212 & .00205. & 00199. & .00193. \\ \hline-2.7 & .00347 & .00336. & .00326. & .00317. & 00307. & 00298 & 00289 & 00280 & . 00272 & .00264 \\ \hline-2.6 & .00466. & .00453 & 00440. & .00427. & .00415. & .00402 & 00391 & .00379. & 00368 & .00357 \\ \hline-2.5 & .00621 & .00604 & .00587 & .00570 & .00554 & .00539 & .00523 & .00508 & .00494 & .00480 \\ \hline-2.4 & .00820 & .00798 & 00776 & .00755 & .00734 & .00714 & 00695 & 00676 & 00657 & 00639 \\ \hline-2.3 & .01072 & .01044 & .01017 & .00990 & .00964 & .00939 & .00914 & .00889 & .00866 & .00842 \\ \hline-2.2 & 01390. & 01355 & .01321 & 01287. & 01255 & 01222 & 01191 & 01160 & 01130 & 01101 \\ \hline-2.1 & 01786 & 01743 & 01700 & 01659 & 01618 & 01578 & 01539 & 01500 & 01463 & .01426 \\ \hline-2.0 & .02275 & .02222 & .02169 & .02118 & .02068 & .02018 & .01970 & .01923 & .01876 & .01831 \\ \hline-1.9 & .02872 & 02807 & .02743 & .02680 & 02619 & 02559 & .02500 & .02442 & .02385 & .02330 \\ \hline-1.8 & .03593 & .03515 & .03438 & .03362 & .03288 & .03216 & .03144 & .03074 & .03005 & .02938 \\ \hline-1.7 & .04457. & .04363 & .04272 & .04182 & .04093. & 04006. & 03920. & .03836 & 03754 & .03673 \\ \hline-1.6 & .05480 & .05370 & .05262 & .05155 & .05050 & .04947 & .04846 & .04746 & .04648 & 04551 \\ \hline-1.5 & .06681 & .06552 & .06426 & .06301 & .06178 & .06057 & .05938 & .05821 & .05705 & .05592 \\ \hline-1.4 & 08076 & 07927. & 07780 & 07636 & .07493 & .07353 & 07215 & 07078 & .06944. & .06811 \\ \hline-1.3 & .09680 & .09510 & .09342 & .09176 & .09012 & .08851 & .08691 & .08534 & .08379 & .08226 \\ \hline-1.2 & 11507 & .11314 & .11123 & 10935 & 10749 & 10565 & .10383 & 10204 & 10027 & 09853 \\ \hline-1.1 & 13567. & .13350 & 13136 & 12924 & 12714 & 12507 & 12302 & 12100 & 11900. & .11702 \\ \hline-1.0 & .15866 & .15625 & .15386 & .15151 & .14917 & .14686 & .14457 & .14231 & .14007 & .13786 \\ \hline-0.9 & .18406 & . 18141 & 17879. & 17619. & . 17361 & . 17106 & .16853 & .16602 & .16354 & .16109 \\ \hline-0.8 & 21186 & 20897. & 20611 & 20327 & 20045 & 19766 & 19489 & .19215. & 18943 & .18673 \\ \hline-0.7 & 24196. & 23885 & 23576 & 23270 & 22965. & .22663 & .22363 & 22065 & 21770 & .21476 \\ \hline-0.6 & 27425 & 27093 & 26763 & 26435 & 26109 & 25785 & .25463 & .25143 & 24825 & .24510 \\ \hline-0.5 & .30854 & .30503 & .30153 & .29806 & .29460 & .29116 & .28774 & .28434 & .28096 & .27760 \\ \hline-0.4 & .34458 & .34090 & .33724 & .33360 & .32997 & .32636 & .32276 & .31918 & .31561 & .31207 \\ \hline-0.3 & .38209 & .37828 & .37448 & .37070 & .36693 & .36317 & .35942 & .35569 & .35197 & .34827 \\ \hline-0.2 & .42074 & .41683 & 41294 & 40905 & .40517 & 40129 & .39743 & .39358 & .38974 & .38591 \\ \hline-0.1 & 46017 & .45620 & .45224 & .44828 & .44433 & .44038 & .43644 & .43251 & .42858 & .42465 \\ \hline-0.0 & .50000 & .49601 & .49202 & .48803 & .48405 & .48006 & .47608 & .47210 & .46812 & .46414 \\ \hline \end{tabular} STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline Z & .00 & .01 & .02 & .03 & .04 & .05 & .06 & .07 & .08 & .09 \\ \hline 0.0 & .50000 & .50399 & .50798 & .51197 & .51595 & .51994 & .52392 & .52790 & .53188 & .53586 \\ \hline 0.1 & .53983 & .54380 & .54776 & .55172 & .55567 & .55962 & .56356 & .56749 & .57142 & .57535 \\ \hline 0.2 & .57926 & .58317 & .58706 & .59095 & .59483 & .59871 & 60257 & .60642 & 61026 & 61409 \\ \hline 0.3 & 61791 & 62172 & 62552 & 62930 & 63307 & 63683 & 64058 & 64431 & 64803 & 65173 \\ \hline 0.4 & .65542 & 65910 & .66276 & 66640 & .67003 & .67364 & .67724 & .68082 & 68439 & 68793 \\ \hline 0.5 & 69146 & 69497 & 69847 & .70194 & .70540 & .70884 & .71226 & .71566 & .71904 & .72240 \\ \hline 0.6 & .72575 & .72907 & .73237 & .73565 & .73891 & .74215 & .74537 & .74857 & .75175 & .75490 \\ \hline 0.7 & .75804 & .76115 & .76424 & .76730 & .77035 & .77337 & .77637 & .77935 & .78230 & .78524 \\ \hline 0.8 & .78814 & .79103 & .79389 & .79673 & 79955 & .80234 & .80511 & .80785 & .81057 & .81327 \\ \hline 0.9 & .81594 & .81859 & .82121 & .82381 & .82639 & .82894 & .83147 & .83398 & .83646 & .83891 \\ \hline 1.0 & .84134 & .84375 & .84614 & .84849 & .85083 & .85314 & .85543 & .85769 & .85993 & .86214 \\ \hline 1.1 & .86433 & .86650 & .86864 & .87076 & .87286 & .87493 & .87698 & .87900 & .88100 & .88298 \\ \hline 1.2 & .88493 & .88686 & 88877 & .89065 & .89251 & .89435 & .89617 & 89796 & 89973 & 90147. \\ \hline 1.3 & .90320 & 90490 & 90658 & .90824 & 90988 & 91149. & 91309 & 91466 & .91621 & 91774 \\ \hline 1.4 & .91924 & .92073 & .92220 & .92364 & .92507 & .92647 & .92785 & .92922 & .93056 & .93189 \\ \hline 1.5 & 93319 & .93448 & .93574 & .93699 & .93822 & 93943 & .94062 & 94179 & 94295 & 94408 \\ \hline 1.6 & .94520 & .94630 & .94738 & .94845 & 94950 & .95053 & .95154 & .95254 & .95352 & 95449. \\ \hline 1.7 & .95543 & .95637 & .95728 & .95818 & .95907 & .95994 & .96080 & .96164 & 96246 & 96327 \\ \hline 1.8 & 96407. & .96485 & 96562 & .96638 & 96712. & 96784 & 96856 & 96926 & 96995. & 97062 \\ \hline 1.9 & .97128 & .97193 & .97257 & .97320 & .97381 & .97441 & .97500 & .97558 & .97615 & .97670 \\ \hline 2.0 & .97725 & .97778 & .97831 & .97882 & 97932 & 97982 & .98030 & 98077 & 98124 & 98169 \\ \hline 2.1 & 98214 & .98257 & 98300 & 98341 & .98382 & 98422 & .98461 & .98500 & 98537 & .98574 \\ \hline 2.2 & 98610 & .98645 & 98679 & .98713 & 98745. & 98778 & 98809 & 98840 & 98870 & 98899 \\ \hline 2.3 & 98928. & .98956 & 98983. & 99010 & 99036. & 99061. & 99086 & 99111 & 99134. & 99158. \\ \hline 2.4 & .99180 & .99202 & .99224. & .99245 & .99266 & .99286 & .99305 & .99324 & .99343 & .99361 \\ \hline 2.5 & 99379 & 99396 & 99413 & .99430 & 99446. & 99461 & 99477 & 99492 & 99506 & 99520 \\ \hline 2.6 & 99534. & .99547 & 99560. & .99573 & 99585. & 99598. & 99609 & 99621 & 99632. & 99643. \\ \hline 2.7 & .99653 & .99664 & 99674 & 99683. & 99693. & 99702. & .99711 & 99720. & 99728. & 99736. \\ \hline 2.8 & 99744. & .99752 & .99760 & .99767. & 99774 & 99781. & .99788 & 99795 & 99801. & 99807 \\ \hline 2.9 & .99813 & .99819 & .99825 & .99831 & .99836 & .99841 & .99846 & .99851 & .99856 & .99861 \\ \hline 3.0 & .99865 & .99869 & 99874 & .99878 & 99882 & 99886 & 99889 & 99893 & 99896 & 99900. \\ \hline 3.1 & 99903 & 99906 & 99910. & 99913. & 99916. & 99918. & 99921 & 99924 & 99926. & 99929. \\ \hline 3.2 & 99931. & 99934 & 99936. & 99938 & 99940. & 99942. & 99944 & 99946. & 99948. & 99950. \\ \hline 3.3 & 99952. & .99953 & 99955. & 99957. & 99958. & 99960. & 99961. & 99962. & 99964. & 99965. \\ \hline 3.4 & .99966 & .99968 & .99969 & .99970 & 99971 & .99972 & .99973 & \begin{tabular}{l} 99974 \\ \end{tabular} & .99975 & .99976 \\ \hline 3.5 & 99977. & 99978 & 99978. & 99979. & 99980. & 99981. & 99981 & 99982 & 99983 & 99983. \\ \hline 3.6 & 99984. & 99985 & 99985. & 99986. & 99986. & 99987. & 99987. & 99988. & 99988. & 99989. \\ \hline 3.7 & 99989 & 99990 & .99990. & 99990. & 99991 & 99991. & 99992 & 99992 & 99992. & 99992 \\ \hline 3.8 & 99993. & 99993 & 99993. & 99994. & 99994. & 99994. & 99994. & 99995. & 99995. & 99995. \\ \hline 3.9 & .99995 & 99995 & .99996 & 99996. & 99996 & .99996 & 99996 & 99996 & 99997 & 99997 \\ \hline \end{tabular}