Today is June 4, 2020. Stock X is selling at $150 per share. The stock has a dividend yield of 5% per year. There is a call option with an August 18, 2020 expiration date and an exercise price of $145, with an implied volatility of 20%. The annual risk free rate is 1%, compounded continuously. Shares and options can only be bought and sold in whole numbers. Requires Normal Probability Table see image june 5th data see image Rebalance the delta-hedged portfolio on June 5, 2020. What are the positions on shares, call options, and risk free asset in this rebalanced portfolio?
Today is June 4, 2020. Stock X is selling at $150 per share. The stock has a dividend yield of 5% per year. There is a call option with an August 18, 2020 expiration date and an exercise price of $145, with an implied volatility of 20%. The annual risk free rate is 1%, compounded continuously. Shares and options can only be bought and sold in whole numbers. Requires Normal Probability Table see image june 5th data see image Rebalance the delta-hedged portfolio on June 5, 2020. What are the positions on shares, call options, and risk free asset in this rebalanced portfolio?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
S3 Q15
Today is June 4, 2020. Stock X is selling at $150 per share. The stock has a dividend yield of 5% per year. There is a call option with an August 18, 2020 expiration date and an exercise price of $145, with an implied volatility of 20%. The annual risk free rate is 1%, compounded continuously. Shares and options can only be bought and sold in whole numbers.
Requires Normal Probability Table see image
june 5th data see image
Rebalance the delta-hedged portfolio on June 5, 2020. What are the positions on shares, call options, and risk free asset in this rebalanced portfolio?
Transcribed Image Text:Normal Probability Table
IZ
0.02
0.04
0.00
0.0 0.5000 0.5040 0.5080 0.5120 0.5160
0.1 0.5398 0.5438 0.5478 0.5517 0.5557
0.2 0.5793 0.5832 0.5871 0.5910 0.5948
0.3 0.6179 0.6217 0.6255 0.6293 0.6331
0.4 0.6554 0.6591 0.6628 0.6664 0.6700
0.5 0.6915 0.6950 0.6985 o.7019 0.7054
0.6 0.7257 0.7291 0.7324 0.7357 0.7389
0.7 0.7580 0.7611 0.7642 0.7673 0.7704
0.8 0.7881 0.7910 0.7939 0.7967 0.7995
0.9 0.8159 0.8186 0.8212 0.8238 0.8264
0.8413 0.8438 0.8461 0.8485 0.8508
1.1 0.8643 0.8665 0.8686 0.8708 0.8729
1.2 0.8849 0.8869 0.8888 0.8907 0.8925
1.3 0.9032 0.9049 0.9066 0.9082 0.9099
1.4 0.9192 0.9207 0.9222 0.9236 0.9251
1.5 0.9332 0.9345 0.9357 0.9370 0.9382
1.6 0.9452
0.01
0.03
0.05
0.5199
0.06
0.5239
0.5596 0.5636
0.6026
0.07
0.5279
0.5675 0.5714 0.5753
0.6064 0.6103 0.6141
0.6443 0.6480 0.6517
0.6808 0.6844 0.6879
0.7157 0.7190 0.7224
0.7486 0.7517 0.7549
0.7794 0.7823 0.7852
0.8078 0.8106 0.8133
0.8340 0.8365 0.8389
0.8577 0.8599 0.8621
0.8790 0.8810
0.8980 0.8997 0.9015
0.9147 0.9162 0.9177
0.9292 0.9306 0.9319
0.9418 0.9429 0.9441
0.9525 0.9535
0.9616 0.9625
0.9693 0.9699 0.9706
0.9756 0.9761
0.9808 0.9812 0.9817
0.08
0.09
0.5319 0.5359
0.5987
0.6368
0.6736
0.6406
0.6772
0.7088 0.7123
0.7422 0.7454
0.7734 0.7764
0.8051
0.8315
0.8554
0.8770
0.8944 0.8962
0.9131
0.9265 0.9279
0.9406
0.9515
0.9608
0.9686
0.9744 0.9750
0.9798 0.9803
0.8023
0.8289
0.8531
0.8749
0.8830
0.9115
0.9394
0.9505
0.9599
0.9678
l0.9463
0.9474 0.9484 0.9495
0.9545
1.7 0.9554 0.9564 0.9573 o.9582 0.9591
1.8 0.9641 0.9649 0.9656 0.9664 0.9671
1.9 0.9713 0.9719 0.9726 0.9732 0.9738
0.9772 0.9778 0.9783 0.9788 0.9793
2.1 0.9821 0.9826 0.9830 0.9834 0.9838
2.2 0.9861 0.9864
2.3 0.9893
2.4 0.9918 0.9920 0.9922 0.9925 0.9927
2.5 0.9938 0.9940 0.9941 0.9943 0.9945
2.6 0.9953 0.9955 0.9956 0.9957 0.9959
2.7 0.9965 0.9966 0.9967 0.9968
2.8 0.9974 0.9975 0.9976 0.9977 0.9977
2.9 0.9981 0.9982 0.9982 o.9983 0.9984
0.9987 0.9987 0.9987 0.9988 0.9988
0.9633
0.9767
12
0.9842
0.9846 0.9850 0.9854 0.9857
0.9868 0.9871 0.9875
0.9896 0.9898 0.9901 0.9904
0.9878 0.9881
0.9909
0.9931
0.9946 0.9948
0.9961
0.9970 0.9971
0.9979
10.9985
0.9989
0.9992
10.9994
0.9884 0.9887 0.9890
0.9911
0.9932 0.9934
0.9949
0.9962
0.9972 0.9973 0.9974
0.9979
0.9985
0.9989
0.9992
0.9995
0.9916
0.9936
0.9951 0.9952
0.9963 0.9964
0.9906
0.9929
0.9913
0.9960
l0.9969
0.9978
0.9984
0.9989
0.9992
0.9980
0.9986
0.9990
0.9993
0.9995
0.9996 0.9996 0.9996
0.9997
0.9981
0.9986
3
3.1 0.9990 0.9991 0.9991
3.2 0.9993 0.9993 0.9994 0.9994 0.9994
3.3 0.9995 0.9995 0.9995
3.4 0.9997 0.9997 0.9997
3.5 0.9998
3.6 0.9998 0.9998 0.9999 0.9999 0.9999
3.7 0.9999 0.9999 0.9999 0.9999 0.9999
3.8 0.9999
3.9 1.0000
4
0.9990
0.9991 0.9992
0.9993
0.9995
0.9997
0.9998
0.9994
0.9996
0.9997
0.9998
0.9999
0.9999
0.9999
1.0000
1.0000
0.9996 0.9996
0.9997 0.9997
0.9998 0.9998
0.9997
0.9998
0.9999
0.9999
0.9999
1.0000
1.0000
0.9997
0.9998 0.9998 0.9998
0.9999 0.9999 0.9999
0.9999
0.9999 0.9999
0.9998 0.9998
0.9999
0.9999
1.0000
1.0000
0.9999
0.9999
1.0000
l0.9999
1.0000
1.0000
0.9999
1.0000
1.0000
0.9999
1.0000
1.0000
1.0000
1.0000 1.0000
1.0000
1.0000
1.0000
Transcribed Image Text:Call Option delta=0.564
Change in Option value with respect to change in stock price represent delta.
Value of Option=0.564 x $152=$85.728
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