PLEASE SHOW ALL WORK

11. Find the current fair price of this European call option given the following information using the Black Scholes options pricing model. You must show all your work via calculations and formula include a snippet/screenshot of your excel sheet calculation of volatility. Your company is DELEK US HOLDINGS INC, and the ticker symbol for your stock is DK. The current stock price is $23.49, and the option's exercise price is $21. Today is March 18th, 2022, and the expiration date is January 20th, 2024. The risk-free rate is 0.92%. You need to obtain the volatility of the stock using daily returns of 1 year (stock returns can be found on Yahoo finance via the Historical Data section of your individual stock). +0 z 0 0.01 0.02 0.03 .50000 .50399 .50798 .51197 +0.1 .53983 .54380 .54776 .55172 +0.2 .57926 .58317 .58706 .59095 +0.3 .61791 .62172 .62552 .62930 +0.4 .65542 .65910 .66276 .66640 +0.5 .69146 .69497 .69847 .70194 +0.6 .72575 .72907 .73237 .73565 +0.7 .75804 .76115 .76424 .76730 +0.8 .78814 .79103 .79389 .79673 +0.9 .81594 .81859 .82121 .82381 +1 .84134 .84375 .84614 .84849 +1.1 .86433 .86650 .86864 .87076 +1.2 .88493 .88686 .88877 .89065 +1.3 90320 .90490 90658 .90824 +1.4 .91924 .92073 .92220 .92364 +1.5 .93319 .93448 93574 .93699 +1.6 .94520 .94630 .94738 .94845 +1.7 .95543 95637 .95728 .95818 +1.8 .96407 .96485 .96562 .96638 +1.9 97128 97193 .97257 .97320 +2 .97725 .97778 97831 .97882 +2.1 .98214 .98257 98300 .98341 +2.2 98610 .98645 .98679 .98713 +2.3 98928 .98956 98983 .99010 +2.4 .99180 .99202 .99224 .99245 +2.5 99379 .99396 .99413 .99430 +2.6 .99534 .99560 .99573 +2.7 .99653 99664 .99674 99683 +2.8 .99744 .99752 .99760 .99767 +2.9 99813 .99819 .99831 +3 .99865 .99869 .99874 99878 +3.1 .99903 .99906 99910 .99913 +3.2 .99934 .99936 .99938 +3.3 99952 .99953 .99955 99957 +3.4 .99966 .99968 .99969 99970 +3.5 .99977 99978 .99978 .99979 +3.6 .99984 99985 .99985 .99986 +3.7 .99989 99990 99990 .99990 +3.8 .99993 .99993 .99993 .99994 +3.9 99995 .99995 .99996 +4 .99997 .99997 .99997 .99997 0.04 .51595 .55567 .59483 .63307 .67003 .70540 .73891 .77035 .79955 .82639 .85083 .87286 .89251 .90988 .92507 .93822 .94950 .95907 .96712 .97381 .97932 .98382 .98745 .99036 .99266 .99446 .99585 99693 .99774 .99836 .99882 .99916 .99940 .99958 .99971 .99980 99986 .99991 .99994 .99996 .99997 0.05 .51994 .55966 .59871 .63683 .67364 .70884 .74215 .77337 .80234 .82894 .85314 .87493 .89435 91149 .92647 .93943 .95053 .95994 .96784 .97441 .97982 .98422 .98778 .99061 .99286 .99461 .99598 .99702 .99781 .99841 .99886 .99918 .99942 .99960 0.06 .52392 .56360 .60257 .64058 .67724 .71226 .74537 .77637 .80511 .83147 .85543 .87698 .89617 .91308 .92785 .94062 .95154 .96080 .96856 .97500 .98030 .98461 .98809 .99086 .99305 .99477 .99609 .99711 .99788 .99846 0.07 .52790 .56749 .60642 .64431 .68082 .71566 .74857 .77935 .80785 .83398 .85769 .87900 .89796 .91466 .92922 .94179 .95254 .96164 .96926 .97558 .98077 .98500 .98840 .99111 .99324 99492 .99621 .99720 .99795 99851 .99893 99924 .99946 .99962 .99974 .99982 .99988 .99992 .99995 .99996 .99998 0.08 .53188 .57142 .61026 .64803 .68439 .71904 .75175 .78230 .81057 .83646 .85993 .88100 .89973 .91621 .93056 .94295 .95352 .96246 .96995 .97615 .98124 .98537 .98870 .99134 .99343 .99506 .99632 .99728 .99801 .99856 .99896 .99926 .99948 .99964 .99975 .99983 .99988 99992 .99995 99997 .99998 0.09 .53586 .57535 .61409 .65173 .68793 .72240 .75490 .78524 .81327 .83891 .86214 .88298 .90147 .91774 .93189 .94408 .95449 .96327 .97062 .97670 .98169 .98574 .98899 .99158 .99361 .99520 .99643 .99736 .99807 .99861 .99900 .99929 .99950 .99965 .99976 .99983 .99989 .99992 .99995 .99997 .99998 .99547 .99825 .99889 .99931 .99972 .99981 .99987 .99991 .99994 .99996 .99997 .99921 .99944 .99961 .99973 .99981 .99987 .99992 .99994 99996 .99998 .99996 11. Find the current fair price of this European call option given the following information using the Black Scholes options pricing model. You must show all your work via calculations and formula include a snippet/screenshot of your excel sheet calculation of volatility. Your company is DELEK US HOLDINGS INC, and the ticker symbol for your stock is DK. The current stock price is $23.49, and the option's exercise price is $21. Today is March 18th, 2022, and the expiration date is January 20th, 2024. The risk-free rate is 0.92%. You need to obtain the volatility of the stock using daily returns of 1 year (stock returns can be found on Yahoo finance via the Historical Data section of your individual stock). +0 z 0 0.01 0.02 0.03 .50000 .50399 .50798 .51197 +0.1 .53983 .54380 .54776 .55172 +0.2 .57926 .58317 .58706 .59095 +0.3 .61791 .62172 .62552 .62930 +0.4 .65542 .65910 .66276 .66640 +0.5 .69146 .69497 .69847 .70194 +0.6 .72575 .72907 .73237 .73565 +0.7 .75804 .76115 .76424 .76730 +0.8 .78814 .79103 .79389 .79673 +0.9 .81594 .81859 .82121 .82381 +1 .84134 .84375 .84614 .84849 +1.1 .86433 .86650 .86864 .87076 +1.2 .88493 .88686 .88877 .89065 +1.3 90320 .90490 90658 .90824 +1.4 .91924 .92073 .92220 .92364 +1.5 .93319 .93448 93574 .93699 +1.6 .94520 .94630 .94738 .94845 +1.7 .95543 95637 .95728 .95818 +1.8 .96407 .96485 .96562 .96638 +1.9 97128 97193 .97257 .97320 +2 .97725 .97778 97831 .97882 +2.1 .98214 .98257 98300 .98341 +2.2 98610 .98645 .98679 .98713 +2.3 98928 .98956 98983 .99010 +2.4 .99180 .99202 .99224 .99245 +2.5 99379 .99396 .99413 .99430 +2.6 .99534 .99560 .99573 +2.7 .99653 99664 .99674 99683 +2.8 .99744 .99752 .99760 .99767 +2.9 99813 .99819 .99831 +3 .99865 .99869 .99874 99878 +3.1 .99903 .99906 99910 .99913 +3.2 .99934 .99936 .99938 +3.3 99952 .99953 .99955 99957 +3.4 .99966 .99968 .99969 99970 +3.5 .99977 99978 .99978 .99979 +3.6 .99984 99985 .99985 .99986 +3.7 .99989 99990 99990 .99990 +3.8 .99993 .99993 .99993 .99994 +3.9 99995 .99995 .99996 +4 .99997 .99997 .99997 .99997 0.04 .51595 .55567 .59483 .63307 .67003 .70540 .73891 .77035 .79955 .82639 .85083 .87286 .89251 .90988 .92507 .93822 .94950 .95907 .96712 .97381 .97932 .98382 .98745 .99036 .99266 .99446 .99585 99693 .99774 .99836 .99882 .99916 .99940 .99958 .99971 .99980 99986 .99991 .99994 .99996 .99997 0.05 .51994 .55966 .59871 .63683 .67364 .70884 .74215 .77337 .80234 .82894 .85314 .87493 .89435 91149 .92647 .93943 .95053 .95994 .96784 .97441 .97982 .98422 .98778 .99061 .99286 .99461 .99598 .99702 .99781 .99841 .99886 .99918 .99942 .99960 0.06 .52392 .56360 .60257 .64058 .67724 .71226 .74537 .77637 .80511 .83147 .85543 .87698 .89617 .91308 .92785 .94062 .95154 .96080 .96856 .97500 .98030 .98461 .98809 .99086 .99305 .99477 .99609 .99711 .99788 .99846 0.07 .52790 .56749 .60642 .64431 .68082 .71566 .74857 .77935 .80785 .83398 .85769 .87900 .89796 .91466 .92922 .94179 .95254 .96164 .96926 .97558 .98077 .98500 .98840 .99111 .99324 99492 .99621 .99720 .99795 99851 .99893 99924 .99946 .99962 .99974 .99982 .99988 .99992 .99995 .99996 .99998 0.08 .53188 .57142 .61026 .64803 .68439 .71904 .75175 .78230 .81057 .83646 .85993 .88100 .89973 .91621 .93056 .94295 .95352 .96246 .96995 .97615 .98124 .98537 .98870 .99134 .99343 .99506 .99632 .99728 .99801 .99856 .99896 .99926 .99948 .99964 .99975 .99983 .99988 99992 .99995 99997 .99998 0.09 .53586 .57535 .61409 .65173 .68793 .72240 .75490 .78524 .81327 .83891 .86214 .88298 .90147 .91774 .93189 .94408 .95449 .96327 .97062 .97670 .98169 .98574 .98899 .99158 .99361 .99520 .99643 .99736 .99807 .99861 .99900 .99929 .99950 .99965 .99976 .99983 .99989 .99992 .99995 .99997 .99998 .99547 .99825 .99889 .99931 .99972 .99981 .99987 .99991 .99994 .99996 .99997 .99921 .99944 .99961 .99973 .99981 .99987 .99992 .99994 99996 .99998 .99996