Question

11) Using the Black scholes formula calculate the call price based on the following information: Stock price=$100 Strike price=$100 Interest rate= 10% Time to expiration=six months Standard deviation= 30%

Answer 1

All the calculations are shown in the images below:

sol" - Given, stock price, St = $100. and struke puce, Xe = $100. interest rate, r= 10%. Time to expiration, t= 6 months = 1/2 year. Standard deviations 30%. We know Black Scholes G. St. N(di)-x. est. N(de) that famela - wlhere, di On(s) f ( x + 5) xt] de=d, -ts. UE tin years. Nidi), n (de) are Cunmulative disturbilion functions of the standard Nonal distrikietion CT is the premium Step1: Calculating de Substituting all values. di= ln (100) + ( 0.1 + (0-3 » - 0.3x / h = ln (0) + (0.1+0.045) x 2 0 212 = 0+0.0125 0.342. 0. 212

I am attaching normal distribution table of X > 0. The values for N(d₁) and N(d₂) are referred from this table. This table is to be referred as follows:

Values Stepa - Calculating de substituting all values a de=d,- og. Ut = 0.342-(0.3x] 2) = 0.130. N(di) and (ch) values are considered from normal distribuition table ..N(di); N(0:342) = 0.6331. and N (de) = N(0.130) = 0.5517. G = STANld) - x. ert (de) = (100x 0.6331) - (1oox e 0.1x/x 0.5517) 2 63-31 – (100x 0.95120.5517) = 63.31-52.48 = 10.83.8.

For knowing the value of N(d₁) considering d₁ = 0.34, the value of 0.3 is seen from the rows and 0.04 is seen from the columns. The common value is the value of N(d₁).Therefore, N(d₁) = 0.6331.

Similarly, N(d₂) considering d₂ = 0.13, the value of 0.1 is seen from rows and 0.03 is seen from the columns. The common value is the value of N(d₂). Therefore, N(d₂) = 0.5517.

0 1 2 3 4 5 6 7 8 9 00 2000 2040 GOST OTU 160 5199 5239 5279 8319 669 5398 5438 54 5517 557 5596 5636 5675 5714 5753 0. 2 5793 5832 581 5910 026 COCA 6103 6141 0. 36179 6217 6255 63313 6406 6443 6480 6517 655465916628 666 736 6772 6808 68446879 0.5 6915 6950 6985 7019 7054 7088 7123 7157 7190 7224 7257 7291 7324 7357 7389 74227454 7486 7517 7549 7580 7611 7642 7673 7704 7734 7764 779478237852 7881 7910 79397967 79958023 8051 8078 8106 8133 81598186 8212 8238 8264 8289 8315 8340 8365 8389 84138438 8461 8485 8508 8531 8554 8577 8599 8621 8643 8665 8686 8708 87298749 8770 8790 8810 8830 8849 8869 8888 8907 8925 8944 89628980 8997 9015 9032 9049 9066 9082 9099 9115 9131 9147 9162 9177 91929207 9222 9236 9251 9265 9279 9292 9306 9319 1.5 9332 9345 9357 9370 938293949406 9418 94299441 9452 9463 9474 9484 9495 9505 9515 9525 9535 9545 9554 95649573 9582 9591 9599 9608 9616 9625 9633 1. 8 9641 9649 9656 9664 9671 9678 9686 9693 96999706 97139719 9726 9732 9738 9744 9750 9756 9761 9767 2. 0 9772 9778 9783 9788 9793 9798 9803 9808 9812 9817 9821 9826 9830 9834 9838 9842 9846 9850 9854 9857 2. 2 9861 9864 9868 9871 9875 9878 9881 9884 9887 9890 2. 3 9893 9896 9898 9901 9904 9906 9909 9911 9913 9916 2. 4 9918 9920 99229925 9927 9929 9931 9932 99349936 9938 9940 9941 9943 9945 9946 9948 9949 99519952 2. 6 9953 9955 9956 9957 9959 9960 996199629963 9964 2. 7 9965 9966 9967 9968 99699970 9971 99729973 9974 2. 8 9974 9975 9976 9977 9977 9978 997999799980 9981 299981 998299829983 9984 99849985 9985 99869986