23Black-Scholes Model V3

7/29/2019 23Black-Scholes Model V3

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Black-Scholes Option Pricing Model copyright THC 2003. All rights reserved by Tho

reference number 9 classificatio 40401

Version V3 level basic Instructions

publication date Jul-03 1. The risk source of both the call an

author Hanyang Financial Engineering Lab. 2. Enter the option descriptions

affiliation Hanyang University input option terms and conditi

email address [email protected] output option price and the senlast revised date Jan-04

references Black, F. and M. Scholes, 1973, The Pricing of Options and Corporate Lia

Ch. 4 of "The Oxford Guide to Financial Modeling" by Thomas S.Y. Ho an

Descriptions

financial model class equity options

issuer/modeler market participants

model type continuous time model

risk sources stock price

risk distribution lognormal

economic assumptions perfect capital market

technical assumptions continuous compounding interest rate

key words the law of one price, no abitrage condition, dynamic hedging, hedge ratio,

Links

data N/A

financial models

Inputs

Stock Price(S) 100

Strike Price(K) 100

Time to expiration(T) 1

Stock volitility() 0.2

Risk-free rate(r) 0.04

Dividend yields N/A

Outputs

Call Put

Price 9.92505 6.00400 C = S* N(d1) - Ke-rT

N(d2)

(Delta) 0.61791 -0.38209 P = -S* N(-d1) + Ke-rT

N(-d2)

(Gamma) 0.01907 0.01907

v (Vega) 38.13878 38.13878

(Theta) -5.88852 -2.04536

(Rho) 51.86609 -44.21286

(Omega) 6.22577 -6.36390

Interim Calcuations

Step 1 Calculate call price and put price.

d1 0.3

d2 0.1

2

1

ln2

SR T

Kd

2 1d d
mailto:[email protected]:[email protected]


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Step 2 Calculate option greeks.

Step 3 Show the performance profile of option greeks.

Stock Price 50 51 52 53 54 55

Delta 0.0008 0.0011 0.0015 0.0020 0.0027 0.0036

Gamma 0.0003 0.0004 0.0005 0.0006 0.0008 0.0010

Vega 0.1329 0.1846 0.2523 0.3397 0.4508 0.5901

Theta -0.0148 -0.0206 -0.0282 -0.0380 -0.0506 -0.0664

Rho 0.0367 0.0523 0.0733 0.1013 0.1381 0.1855

v (Vega)

(Omega)

(Theta)

(Rho)

Call

(Delta)

(Gamma)

1( )

CN d

S

P

S

1

2

( )( )

2

rTS N dCr K e N d

t T

P

t

1'( )N d

S S T

S S

1( )S T N d S T

2( )

rTK T e N d K T

1( )

C S SN d

S C C

P

S

0.00.10.20.30.40.5

0.60.70.80.91.0

50

58

66

74

82

90

98

106

114

122

130

138

146

Stock Price

Delta of European Call Option

Delta

0.000

0.005

0.010

0.015

0.020

0.025

50

58

66

74

82

90

98

106

114

122

130

138

Stock Price

Gamma of European Call Option

Gamma


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mas Ho Company, New York, NY. USA www. thomasho.com [email protected]

put options and the underlying asset is the same.

ns

itivities

ilities, Journal of Political Economy , Vol.81, 637-654.

d Sang Bin Lee, 2004, Oxford University Press

greeks

T


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56 57 58 59 60 61 62 63

0.0047 0.0060 0.0077 0.0097 0.0121 0.0149 0.0183 0.0222

0.0012 0.0015 0.0018 0.0022 0.0026 0.0031 0.0036 0.0042

0.7624 0.9729 1.2269 1.5297 1.8868 2.3031 2.7837 3.3327

-0.0861 -0.1102 -0.1394 -0.1744 -0.2158 -0.2644 -0.3207 -0.3853

0.2462 0.3226 0.4179 0.5353 0.6784 0.8511 1.0574 1.3015

Put

1( ) 1d

1

2

( )( )

2

rTS N d

r K e N d

T

1'( )N d

T

1( )N d

2( )

rTe N d

1( ) 1S

N dP

146

0.00005.0000

10.000015.000020.0000

25.000030.000035.000040.000045.0000

50

58

66

74

82

90

98

106

114

122

130

138

146

Stock Price

Vega of European Call Option

Vega

(7.0)

(6.0)

(5.0)

(4.0)(3.0)

(2.0)

(1.0)

0.0

50

58

66

74

82

90

st

Theta of Euro

Theta


5/148


6/148

64 65 66 67 68 69 70 71

0.0267 0.0319 0.0377 0.0443 0.0517 0.0599 0.0690 0.0789

0.0048 0.0055 0.0062 0.0070 0.0078 0.0086 0.0095 0.0104

3.9540 4.6504 5.4240 6.2757 7.2057 8.2125 9.2939 10.4461

-0.4589 -0.5419 -0.6346 -0.7373 -0.8503 -0.9735 -1.1068 -1.2500

1.5879 1.9208 2.3048 2.7440 3.2428 3.8050 4.4342 5.1337

98

106

114

122

130

138

146

ck Price

pean Call Option

0.0

20.0

40.0

60.0

80.0

100.0

50

57

64

71

78

85

92

99

106

113

120

127

134

141

148

Stock Price

Rho of European Call Option

Rho


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8/148

72 73 74 75 76 77 78 79

0.0897 0.1014 0.1140 0.1275 0.1418 0.1570 0.1730 0.1898

0.0113 0.0121 0.0130 0.0139 0.0148 0.0156 0.0164 0.0172

11.6645 12.9430 14.2746 15.6514 17.0646 18.5046 19.9614 21.4244

-1.4027 -1.5645 -1.7347 -1.9125 -2.0971 -2.2876 -2.4829 -2.6819

5.9063 6.7544 7.6798 8.6837 9.7668 10.9290 12.1697 13.4876


9/148


10/148

80 81 82 83 84 85 86 87

0.2073 0.2255 0.2444 0.2638 0.2837 0.3041 0.3249 0.3459

0.0179 0.0185 0.0191 0.0197 0.0202 0.0206 0.0209 0.0212

22.8829 24.3261 25.7432 27.1238 28.4577 29.7353 30.9477 32.0866

-2.8835 -3.0865 -3.2896 -3.4918 -3.6918 -3.8884 -4.0806 -4.2674

14.8809 16.3470 17.8830 19.4852 21.1495 22.8714 24.6461 26.4682


11/148


12/148

88 89 90 91 92 93 94 95

0.3672 0.3887 0.4103 0.4319 0.4535 0.4749 0.4963 0.5174

0.0214 0.0215 0.0216 0.0216 0.0215 0.0214 0.0212 0.0210

33.1446 34.1153 34.9931 35.7734 36.4527 37.0284 37.4989 37.8636

-4.4478 -4.6208 -4.7859 -4.9421 -5.0890 -5.2260 -5.3528 -5.4690

28.3323 30.2327 32.1635 34.1189 36.0927 38.0791 40.0723 42.0665


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14/148

96 97 98 99 100 101 102 103

0.5382 0.5587 0.5789 0.5986 0.6179 0.6367 0.6551 0.6728

0.0207 0.0203 0.0200 0.0195 0.0191 0.0186 0.0181 0.0175

38.1228 38.2776 38.3299 38.2826 38.1388 37.9026 37.5784 37.1711

-5.5745 -5.6692 -5.7530 -5.8261 -5.8885 -5.9406 -5.9825 -6.0148

44.0561 46.0359 48.0006 49.9455 51.8661 53.7581 55.6176 57.4411


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16/148

104 105 106 107 108 109 110 111

0.6901 0.7068 0.7229 0.7384 0.7533 0.7676 0.7813 0.7944

0.0170 0.0164 0.0158 0.0152 0.0146 0.0140 0.0134 0.0128

36.6859 36.1284 35.5044 34.8196 34.0801 33.2918 32.4606 31.5923

-6.0376 -6.0516 -6.0571 -6.0546 -6.0448 -6.0280 -6.0050 -5.9761

59.2254 60.9677 62.6654 64.3165 65.9191 67.4716 68.9730 70.4223


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18/148

112 113 114 115 116 117 118 119

0.8069 0.8189 0.8302 0.8411 0.8513 0.8610 0.8702 0.8790

0.0122 0.0117 0.0111 0.0105 0.0100 0.0095 0.0090 0.0085

30.6927 29.7672 28.8212 27.8598 26.8876 25.9093 24.9291 23.9510

-5.9420 -5.9032 -5.8603 -5.8136 -5.7638 -5.7113 -5.6565 -5.6000

71.8190 73.1627 74.4533 75.6910 76.8760 78.0091 79.0908 80.1220


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20/148

120 121 122 123 124 125 126 127

0.8872 0.8949 0.9022 0.9091 0.9155 0.9216 0.9272 0.9326

0.0080 0.0075 0.0071 0.0067 0.0062 0.0059 0.0055 0.0051

22.9784 22.0149 21.0634 20.1265 19.2068 18.3063 17.4270 16.5703

-5.5420 -5.4830 -5.4233 -5.3632 -5.3031 -5.2432 -5.1837 -5.1249

81.1038 82.0373 82.9236 83.7642 84.5604 85.3137 86.0254 86.6973


21/148


22/148

128 129 130 131 132 133 134 135

0.9375 0.9422 0.9465 0.9505 0.9543 0.9578 0.9611 0.9641

0.0048 0.0045 0.0042 0.0039 0.0036 0.0034 0.0031 0.0029

15.7376 14.9301 14.1485 13.3937 12.6660 11.9658 11.2932 10.6482

-5.0670 -5.0101 -4.9544 -4.9000 -4.8471 -4.7956 -4.7458 -4.6976

87.3307 87.9273 88.4886 89.0161 89.5115 89.9762 90.4117 90.8195


23/148


24/148

136 137 138 139 140 141 142 143

0.9669 0.9695 0.9720 0.9742 0.9763 0.9782 0.9800 0.9816

0.0027 0.0025 0.0023 0.0022 0.0020 0.0018 0.0017 0.0016

10.0307 9.4405 8.8770 8.3400 7.8289 7.3431 6.8819 6.4447

-4.6511 -4.6063 -4.5633 -4.5221 -4.4825 -4.4447 -4.4087 -4.3743

91.2009 91.5575 91.8904 92.2012 92.4909 92.7608 93.0120 93.2458


25/148


26/148

144 145 146 147 148 149 150

0.9831 0.9845 0.9858 0.9870 0.9881 0.9891 0.9900

0.0015 0.0013 0.0012 0.0011 0.0010 0.0010 0.0009

6.0306 5.6390 5.2690 4.9198 4.5905 4.2805 3.9887

-4.3416 -4.3105 -4.2810 -4.2530 -4.2265 -4.2015 -4.1779

93.4631 93.6649 93.8523 94.0261 94.1872 94.3365 94.4748


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Version 1.0 level basic Instructions







Descriptions

financial model class equity options: the Black-Scholes model








Links

data N/A

financial models

Inputs

Stock Price (S) 100

Mean () 0.15

Volitility () 0.10

time increment (t) 0.004

Outputs

average of stock return -0.000315

0.00058

variance of stock return 3.758E-05

annualized var 0.009395

annualized std. 0.0969278

max return 0.0176123

min return -0.016722

max price 106.27154

min price 91.101883

Interim Calcuations

time Z stock price stock return exp(return)

0 100

1 -0.441778 99.77884 -0.002214 0.9977884

2 1.0650047 100.51147 0.0073157 1.0073425

3 1.3170848 101.41102 0.00891 1.0089498

90

92

94

96

98

100

102

104

106

108

0 50 100 150 200

Stock

Price

Day

Simulated Stock Price Path


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4 0.3237642 101.67785 0.0026277 1.0026311

5 -1.502613 100.77458 -0.008923 0.9911163

6 0.8786537 101.39494 0.0061371 1.006156

7 -0.564692 101.09208 -0.002991 0.997013

8 0.1378658 101.23896 0.0014519 1.001453

9 0.5404524 101.64454 0.0039981 1.0040061

10 0.6559503 102.12631 0.0047286 1.0047398

11 0.1863918 102.3061 0.0017588 1.0017604

12 -0.011207 102.3582 0.0005091 1.0005092

13 -0.660891 101.99039 -0.0036 0.9964066

14 0.3455284 102.27281 0.0027653 1.0027691

15 -0.420621 102.06028 -0.00208 0.9979219

16 0.6767721 102.55753 0.0048603 1.0048721

17 -0.539302 102.26762 -0.002831 0.9971732

18 0.7624112 102.82155 0.0054019 1.0054165

19 -1.433418 101.95273 -0.008486 0.9915502

20 -0.934497 101.41074 -0.00533 0.9946839

21 0.5106779 101.79783 0.0038098 1.0038171

22 0.7357755 102.33198 0.0052335 1.0052472

23 1.1852762 103.16179 0.0080763 1.008109

24 -0.450482 102.92798 -0.002269 0.9977335

25 0.7881374 103.50233 0.0055646 1.0055801

26 -1.195062 102.78258 -0.006978 0.9930461

27 -0.635221 102.42987 -0.003437 0.9965684

28 -1.190233 101.72068 -0.006948 0.9930764

29 -2.002525 100.49878 -0.012085 0.9879876

30 -0.394685 100.30639 -0.001916 0.9980856

31 -0.222639 100.22336 -0.000828 0.9991723

32 -1.148258 99.555878 -0.006682 0.9933401

33 0.5046741 99.932095 0.0037718 1.003779

34 -1.604585 98.980476 -0.009568 0.9904773

35 0.5570814 99.387457 0.0041033 1.0041117

36 -0.77423 98.959359 -0.004317 0.9956926

37 0.401144 99.268303 0.0031171 1.003121938 0.738587 99.790955 0.0052512 1.005265

39 0.6410346 100.25449 0.0046343 1.004645

40 0.3907189 100.56084 0.0030511 1.0030558

41 0.4826381 100.92679 0.0036325 1.0036391

42 -1.483954 100.042 -0.008805 0.9912333

43 0.1826561 100.21574 0.0017352 1.0017367

44 -0.571704 99.91197 -0.003036 0.9969688

45 -0.179391 99.856577 -0.000555 0.9994456

46 0.9245991 100.50049 0.0064277 1.0064484

47 0.4090327 100.81927 0.003167 1.003172

48 -1.351741 100.01902 -0.007969 0.9920625

49 0.0376849 100.10091 0.0008183 1.0008187

50 2.6930502 101.87953 0.0176123 1.017768451 -1.709577 100.84239 -0.010232 0.9898199

52 0.2454397 101.05764 0.0021323 1.0021346

53 1.0116287 101.7653 0.0069781 1.0070025

54 1.3201861 102.67809 0.0089296 1.0089696

55 -0.73137 102.26354 -0.004046 0.9959626

56 -0.151239 102.22504 -0.000377 0.9996236

57 0.229702 102.43305 0.0020328 1.0020348


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58 -0.429496 102.21445 -0.002136 0.9978659

59 -0.08444 102.21914 4.596E-05 1.000046

60 0.3540674 102.50774 0.0028193 1.0028233

61 1.6620652 103.65107 0.0110918 1.0111536

62 -0.233709 103.55802 -0.000898 0.9991023

63 0.5219533 103.96072 0.0038811 1.0038887

64 0.8616735 104.58947 0.0060297 1.0060479

65 -0.963419 104.01443 -0.005513 0.994502

66 0.4227945 104.35344 0.003254 1.0032593

67 -1.656913 103.32552 -0.009899 0.9901496

68 1.353078 104.274 0.0091376 1.0091795

69 1.0498843 105.02958 0.0072201 1.0072462

70 -0.910497 104.4871 -0.005178 0.9948349

71 -2.286633 103.04663 -0.013882 0.986214

72 0.7432163 103.59221 0.0052805 1.0052945

73 -0.981586 103.01082 -0.005628 0.9943877

74 -0.819737 102.5376 -0.004604 0.9954061

75 -0.793261 102.08365 -0.004437 0.9955728

76 1.3008662 102.98671 0.0088074 1.0088463

77 0.9538508 103.66999 0.0066127 1.0066346

78 -0.963298 103.10008 -0.005512 0.9945027

79 2.4409383 104.76482 0.0160178 1.0161468

80 1.4768602 105.80931 0.0099205 1.0099699

81 0.2508841 106.03882 0.0021667 1.0021691

82 -0.016562 106.08923 0.0004753 1.0004754

83 0.1797798 106.27154 0.001717 1.0017185

84 -0.988171 105.67072 -0.00567 0.9943463

85 -1.292533 104.87122 -0.007595 0.9924341

86 -1.129963 104.18484 -0.006567 0.993455

87 -1.145304 103.49291 -0.006664 0.9933586

88 0.0665648 103.59655 0.001001 1.0010015

89 0.4335266 103.94126 0.0033219 1.0033274

90 -0.949519 103.37888 -0.005425 0.9945894

91 0.0403634 103.46526 0.0008353 1.000835692 0.0159503 103.53573 0.0006809 1.0006811

93 -0.890191 103.01419 -0.00505 0.9949627

94 0.0351588 103.09688 0.0008024 1.0008027

95 1.7700222 104.31798 0.0117746 1.0118442

96 -0.752018 103.88323 -0.004176 0.9958325

97 -0.193636 103.81629 -0.000645 0.9993555

98 1.4359875 104.82422 0.009662 1.0097088

99 -0.125133 104.80206 -0.000211 0.9997886

100 -0.357979 104.62572 -0.001684 0.9983174

101 1.5695514 105.73078 0.0105067 1.0105621

102 -0.1408 105.69796 -0.00031 0.9996896

103 -1.024473 105.07625 -0.005899 0.994118

104 -2.339912 103.59275 -0.014219 0.9858817105 -1.291298 102.80978 -0.007587 0.9924418

106 0.0707814 102.91549 0.0010277 1.0010282

107 0.3345053 103.19328 0.0026956 1.0026992

108 -0.823488 102.71678 -0.004628 0.9953825

109 -1.014696 102.11892 -0.005838 0.9941795

110 0.9484393 102.79292 0.0065785 1.0066001

111 -1.193346 102.07921 -0.006967 0.9930568


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112 -0.864673 101.5814 -0.004889 0.9951233

113 -1.692993 100.55783 -0.010127 0.9899237

114 -1.994631 99.354857 -0.012035 0.988037

115 0.3677837 99.644009 0.0029061 1.0029103

116 -0.974183 99.089418 -0.005581 0.9944343

117 0.9107293 99.719636 0.00634 1.0063601

118 0.2593401 99.941281 0.0022202 1.0022227

119 -0.474661 99.699514 -0.002422 0.9975809

120 0.1856915 99.874582 0.0017544 1.001756

121 -0.517225 99.606159 -0.002691 0.9973124

122 -2.139313 98.324555 -0.01295 0.9871333

123 -0.004858 98.378578 0.0005493 1.0005494

124 0.5604807 98.785207 0.0041248 1.0041333

125 -2.735651 97.147077 -0.016722 0.9834173

126 -1.347557 96.378523 -0.007943 0.9920888

127 -0.91514 95.877902 -0.005208 0.9948057

128 0.5091101 96.242921 0.0037999 1.0038071

129 0.7931567 96.783042 0.0055964 1.0056121

130 -1.241826 96.081596 -0.007274 0.9927524

131 -0.376474 95.908706 -0.001801 0.9982006

132 0.0018736 95.965486 0.0005918 1.000592

133 -0.354801 95.805937 -0.001664 0.9983374

134 -0.02758 95.8448 0.0004056 1.0004056

135 0.3097693 96.088474 0.0025392 1.0025424

136 -0.689524 95.725856 -0.003781 0.9962262

137 -1.24697 95.028981 -0.007307 0.9927201

138 -0.154644 94.991162 -0.000398 0.999602

139 1.0955796 95.707141 0.0075091 1.0075373

140 -0.464496 95.481755 -0.002358 0.997645

141 -0.648756 95.145956 -0.003523 0.9964831

142 -0.016104 95.191461 0.0004782 1.0004783

143 -0.793575 94.769841 -0.004439 0.9955708

144 0.1947274 94.941678 0.0018116 1.0018132

145 -2.404959 93.562765 -0.01463 0.9854762146 -0.327152 93.423546 -0.001489 0.998512

147 -1.03239 92.869381 -0.005949 0.9940683

148 -0.897605 92.397234 -0.005097 0.994916

149 0.0600494 92.485958 0.0009598 1.0009602

150 -2.009965 91.370685 -0.012132 0.9879412

151 1.8393803 92.493462 0.0122133 1.0122881

152 -0.385193 92.321937 -0.001856 0.9981455

153 -0.153638 92.285783 -0.000392 0.9996084

154 -0.559138 92.013361 -0.002956 0.9970481

155 -0.241184 91.926414 -0.000945 0.9990551

156 0.0734667 92.022495 0.0010446 1.0010452

157 0.9658561 92.64006 0.0066886 1.006711

158 -1.362114 91.898702 -0.008035 0.9919974159 0.6476239 92.32942 0.0046759 1.0046869

160 -0.522655 92.078113 -0.002726 0.9972782

161 -0.709063 91.719295 -0.003905 0.9961031

162 0.0346995 91.79265 0.0007995 1.0007998

163 -1.270621 91.110779 -0.007456 0.9925716

164 0.1299918 91.238619 0.0014021 1.0014031

165 0.547725 91.608345 0.0040441 1.0040523


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166 0.7667154 92.107052 0.0054291 1.0054439

167 -0.579739 91.823193 -0.003087 0.9969182

168 -1.091685 91.244297 -0.006324 0.9936955

169 -0.103803 91.237317 -7.65E-05 0.9999235

170 -0.326587 91.101883 -0.001486 0.9985156

171 1.0645999 91.770564 0.0073131 1.0073399

172 0.4256412 92.071328 0.003272 1.0032774

173 -1.039587 91.521019 -0.005995 0.994023

174 -0.298152 91.4016 -0.001306 0.9986952

175 1.1495899 92.121986 0.0078506 1.0078815

176 0.1524768 92.264364 0.0015443 1.0015455

177 -0.528892 92.009605 -0.002765 0.9972388

178 -0.365902 91.850183 -0.001734 0.9982673

179 1.2313103 92.621963 0.0083675 1.0084026

180 -1.41009 91.852874 -0.008338 0.9916965

181 1.2141845 92.614645 0.0082592 1.0082934

182 0.2973525 92.842815 0.0024606 1.0024637

183 0.3619789 93.109597 0.0028694 1.0028735

184 -0.238429 93.023235 -0.000928 0.9990725

185 0.458964 93.347776 0.0034827 1.0034888

186 -0.158284 93.308478 -0.000421 0.999579

187 -1.104545 92.712677 -0.006406 0.9936147

188 0.0271984 92.782425 0.000752 1.0007523

189 -0.630454 92.466822 -0.003407 0.9965985

190 2.4424662 93.960775 0.0160275 1.0161566

191 -0.153948 93.923794 -0.000394 0.9996064

192 1.3673571 94.794527 0.0092279 1.0092706

193 -0.199095 94.730166 -0.000679 0.999321

194 -0.055758 94.751706 0.0002274 1.0002274

195 1.6121157 95.778263 0.0107759 1.0108342

196 -2.245743 94.482293 -0.013623 0.9864691

197 0.6246796 94.911347 0.0045308 1.0045411

198 -0.508501 94.661486 -0.002636 0.9973674

199 -0.251121 94.566094 -0.001008 0.9989923200 -1.140602 93.940837 -0.006634 0.9933882

201 -1.381518 93.177634 -0.008157 0.9918757

202 0.8225231 93.717956 0.0057821 1.0057988

203 -0.09527 93.715844 -2.25E-05 0.9999775

204 1.4807392 94.652499 0.009945 1.0099946

205 2.5392728 96.240672 0.0166398 1.016779

206 -0.682555 95.881705 -0.003737 0.9962701

207 -1.304797 95.14889 -0.007672 0.9923571

208 -0.240871 95.059169 -0.000943 0.999057

209 -0.296793 94.935949 -0.001297 0.9987038

210 0.947241 95.561816 0.0065709 1.0065925

211 0.1678973 95.718845 0.0016419 1.0016432

212 2.2773202 97.163802 0.014983 1.0150958213 0.6441383 97.617046 0.0046539 1.0046647

214 -1.056947 97.022936 -0.006105 0.9939139

215 -0.486854 96.780766 -0.002499 0.997504

216 -1.459994 95.946857 -0.008654 0.9913835

217 -0.605729 95.635443 -0.003251 0.9967543

218 1.5993419 96.663766 0.0106951 1.0107525

219 -0.01771 96.709014 0.000468 1.0004681


32/148

220 -0.019088 96.753441 0.0004593 1.0004594

221 -1.734857 95.753166 -0.010392 0.9896616

222 0.9308337 96.374419 0.0064671 1.0064881

223 -0.070629 96.387267 0.0001333 1.0001333

224 -0.888599 95.902698 -0.00504 0.9949727

225 0.3244099 96.155422 0.0026317 1.0026352

226 -0.349347 95.998868 -0.001629 0.9983719

227 -1.712551 95.019798 -0.010251 0.9898012

228 0.4212063 95.328537 0.0032439 1.0032492

229 -0.392371 95.147436 -0.001902 0.9981002

230 0.2409479 95.347826 0.0021039 1.0021061

231 0.4046285 95.647602 0.0031391 1.003144

232 -0.161538 95.605368 -0.000442 0.9995584

233 0.164174 95.760215 0.0016183 1.0016196

234 -0.828438 95.315057 -0.00466 0.9953513

235 -0.155418 95.276658 -0.000403 0.9995971

236 -1.313811 94.543078 -0.007729 0.9923005

237 -1.193814 93.886372 -0.00697 0.9930539

238 -0.331836 93.743893 -0.001519 0.9984824

239 -0.583364 93.452848 -0.00311 0.9968953

240 -1.027579 92.901336 -0.005919 0.9940985

241 -0.289845 92.784991 -0.001253 0.9987476

242 0.4260596 93.089326 0.0032746 1.00328

243 0.7991434 93.615293 0.0056342 1.0056501

244 -0.429245 93.415657 -0.002135 0.9978675

245 -1.48857 92.594008 -0.008835 0.9912044

246 1.2685655 93.394041 0.0086031 1.0086402

247 -0.353498 93.239535 -0.001656 0.9983457

248 -0.096192 93.23689 -2.84E-05 0.9999716

249 -1.090575 92.649731 -0.006317 0.9937025

250 -0.453786 92.437807 -0.00229 0.9977126

92.437807


33/148



ns

itivities



greeks

bins frequency bins frequency

-0.04 0 73 0

-0.038 0 74 0

-0.036 0 75 0

stock return stock price

250 300

0

5

10

15

2025

30

35

40

-0.

040

-0.

036

-0.

032

-0.

028

-0.

024

-0.

020

-0.

016

-0.

012

-0.

008

-0.

004

0.

000

0.

004

0.

008

0.

012

0.

016

0.

020

0.

024

0.

028

0.

032

0.

036

frequen

cy

stock return

distribution of stock return


34/148

-0.034 0 76 0

-0.032 0 77 0

-0.03 0 78 0

-0.028 0 79 0

-0.026 0 80 0

-0.024 0 81 0

-0.022 0 82 0

-0.02 0 83 0

-0.018 1 84 0

-0.016 2 85 0

-0.014 6 86 0

-0.012 4 87 0

-0.01 10 88 0

-0.008 21 89 0

-0.006 26 90 0

-0.004 27 91 0

-0.002 36 92 17

2.082E-17 31 93 27

0.002 30 94 21

0.004 18 95 13

0.006 15 96 31

0.008 12 97 13

0.01 5 98 4

0.012 1 99 5

0.014 1 100 17

0.016 4 101 16

0.018 0 102 15

0.02 0 103 28

0.022 0 104 23

0.024 0 105 12

0.026 0 106 6

0.028 0 107 3

0.03 0 108 0

0.032 00.034 0

0.036 0

0.038 0

0.04 0


35/148


36/148


37/148


38/148


39/148

0.

040

0

5

10

15

2025

30

35

73 75 77 79 81 83 85 87 89 91 93 95 97 99 101103105107

stock price

distribution of stock price


40/148






affiliation Hanyang University 3. Use "data-table" to generate the p

email address [email protected] input option terms and conditilast revised date Jan-04 output option price and the sen



Descriptions









Links

data N/A

financial models

Inputs

Stock Price (S) 100

Strike Price (K) 100

Time to expiration (T) 1

Stock volitility () 0.2

Risk-free rate (r) 0.04

Dividend yields () 0.01

Outputs

Call Put

Price 9.3197 6.3937 C = S*N(d1) - Ke

-rTN(d2)

(Delta) 0.5927 -0.3973 P = -S*N(-d1) + Ke

-rTN(-d2)

(Gamma) 0.0191 0.0191 S*= S e

-T

v (Vega) 38.2821 38.2821

(Theta) -5.2337 -2.3806

(Rho) 49.9552 -46.1238

(Omega) 6.3601 -6.2139

ensitivity to dividend yield (f/ -59.27491 39.730074

Interim Calcuations


d1 0.2500

d2 0.0500

21

ln 2S K r T d

T

2 1d d


41/148

Step 2 Calculate option greeks.

Step 3 Show the performance profile of option greeks.

Stock Price 50 51 52 53 54

Delta 0.5927 0.0006 0.0009 0.0013 0.0017 0.0023

Gamma 0.0191 0.0002 0.0003 0.0004 0.0005 0.0007

Vega 38.2821 0.1122 0.1566 0.2151 0.2909 0.3879

Theta -5.2337 -0.0121 -0.0169 -0.0233 -0.0316 -0.0422

Rho 49.9552 0.0306 0.0438 0.0617 0.0856 0.1171

(Omega) 6.3601 19.5637 19.1222 18.6913 18.2706 17.8597

ensitivity to dividend yield (f/ -59.2749 -0.0322 -0.0462 -0.0651 -0.0905 -0.1241

Call

(Delta)

(Gamma)

v (Vega)

sensitivity to dividend yield C/ = -TSe-T

N(d1) P/ =

(Omega)

(Theta)

(Rho)

1( )TC

e N dS

Pe

S

1

1 2

( )( ) ( )

2

T

T rTSe N d C

Se N d rKe N d t T

P

t

1'( )T N d

eS S T

e

S

1( )

TCSe T N d

P

2( )rTC

K Te N d r

P

1( )

C S STN d

S C Ce

P S

S P

0.10.20.30.40.50.60.70.80.91.0

Delta of European Call Option

Delta 0.005

0.010

0.015

0.020

0.025

Gamma of European Call Option

Gamma


42/148

.

50

58

66

74

82

90

98

106

114

122

130

138

146

Stock Price

.

50

58

66

74

82

90

98

106

114

122

130

138

Stock Price

0

5

10

15

20

25

30

35

40

45

50

58

66

74

82

90

98

106

114

122

130

138

146

Stock Price

Vega of European Call Option

Vega

(6.0)

(5.0)

(4.0)

(3.0)

(2.0)

(1.0)

0.0

50

58

66

74

82

90

98

106

114

122

130

138

stock Price

Theta of European Call Option

Theta

0.010.020.030.040.050.060.070.080.090.0

100.0

5

0

5

8

6

6

7

4

8

2

9

0

9

8

10

6

11

4

12

2

13

0

13

8

14

6

Stock Price

Rho of European Call Option

Rho

0

5

10

15

20

25

50 70 90 110 130Stock Price

(Omega)

(Omega)

-160

-140

-120

-100

-80

-60

-40

-20

050 100 150

Stock Price

sensitivity to dividend yield (f/)

sensitivity to

dividend yield

(f/)


43/148



rformance profiles of the option greeks

nsitivities



greeks

T


44/148

55 56 57 58 59 60 61 62

0.0030 0.0040 0.0052 0.0066 0.0084 0.0105 0.0130 0.0160

0.0008 0.0011 0.0013 0.0016 0.0019 0.0023 0.0027 0.0032

0.5101 0.6620 0.8486 1.0747 1.3457 1.6668 2.0431 2.4794

-0.0557 -0.0724 -0.0930 -0.1181 -0.1482 -0.1840 -0.2261 -0.2751

0.1581 0.2106 0.2772 0.3605 0.4635 0.5897 0.7426 0.9259

17.4584 17.0665 16.6835 16.3093 15.9436 15.5861 15.2367 14.8952

-0.1677 -0.2237 -0.2948 -0.3840 -0.4945 -0.6301 -0.7947 -0.9926

Put

TSe-T

N(-d1)

1( ) 1T N d

1

1 2

( )( ) ( )

2

T

T rTe N d

Se N d rKe N d

T

1'( )T N d

S T

1( )

Te T N d

2( )

rTK Te N d

1( ) 1T S

e N dP


45/148

146

146

150


46/148


47/148

63 64 65 66 67 68 69 70

0.0195 0.0235 0.0282 0.0335 0.0395 0.0462 0.0537 0.0620

0.0038 0.0043 0.0050 0.0056 0.0063 0.0071 0.0079 0.0087

2.9803 3.5498 4.1913 4.9072 5.6992 6.5680 7.5131 8.5330

-0.3315 -0.3959 -0.4688 -0.5505 -0.6413 -0.7413 -0.8508 -0.9695

1.1438 1.4004 1.6999 2.0466 2.4448 2.8986 3.4120 3.9887

14.5613 14.2349 13.9158 13.6038 13.2987 13.0005 12.7089 12.4238

-1.2282 -1.5062 -1.8315 -2.2090 -2.6436 -3.1402 -3.7034 -4.3378


48/148


49/148


50/148

71 72 73 74 75 76 77 78

0.0711 0.0811 0.0919 0.1036 0.1162 0.1296 0.1439 0.1589

0.0095 0.0104 0.0113 0.0121 0.0130 0.0138 0.0147 0.0155

9.6250 10.7852 12.0086 13.2892 14.6200 15.9929 17.3993 18.8297

-1.0973 -1.2340 -1.3790 -1.5319 -1.6920 -1.8584 -2.0304 -2.2070

4.6321 5.3452 6.1308 6.9909 7.9271 8.9405 10.0315 11.2000

12.1451 11.8726 11.6062 11.3458 11.0914 10.8426 10.5996 10.3621

-5.0477 -5.8369 -6.7088 -7.6666 -8.7126 -9.8488 -11.0765 -12.3963


51/148


52/148


53/148

79 80 81 82 83 84 85 86

0.1748 0.1914 0.2087 0.2267 0.2453 0.2644 0.2840 0.3040

0.0162 0.0170 0.0177 0.0183 0.0189 0.0194 0.0198 0.0202

20.2742 21.7226 23.1645 24.5893 25.9866 27.3463 28.6587 29.9145

-2.3871 -2.5698 -2.7538 -2.9380 -3.1214 -3.3027 -3.4809 -3.6550

12.4452 13.7658 15.1598 16.6246 18.1573 19.7543 21.4114 23.1244

10.1300 9.9033 9.6819 9.4656 9.2544 9.0482 8.8469 8.6504

-13.8083 -15.3119 -16.9059 -18.5884 -20.3571 -22.2088 -24.1401 -26.1470


54/148


55/148


56/148

87 88 89 90 91 92 93 94

0.3244 0.3451 0.3660 0.3871 0.4082 0.4294 0.4505 0.4716

0.0205 0.0208 0.0210 0.0211 0.0212 0.0212 0.0211 0.0210

31.1051 32.2228 33.2603 34.2115 35.0711 35.8349 36.4993 37.0620

-3.8238 -3.9865 -4.1422 -4.2901 -4.4295 -4.5598 -4.6805 -4.7912

24.8882 26.6979 28.5481 30.4331 32.3474 34.2852 36.2406 38.2079

8.4586 8.2715 8.0889 7.9108 7.7372 7.5679 7.4028 7.2419

-28.2251 -30.3695 -32.5752 -34.8368 -37.1488 -39.5053 -41.9007 -44.3291


57/148


58/148


59/148

95 96 97 98 99 100 101 102

0.4925 0.5131 0.5336 0.5537 0.5734 0.5927 0.6117 0.6301

0.0208 0.0205 0.0203 0.0199 0.0196 0.0191 0.0187 0.0182

37.5216 37.8775 38.1299 38.2801 38.3300 38.2821 38.1397 37.9067

-4.8916 -4.9814 -5.0605 -5.1288 -5.1865 -5.2337 -5.2705 -5.2971

40.1815 42.1557 44.1253 46.0850 48.0298 49.9552 51.8566 53.7301

7.0851 6.9324 6.7836 6.6386 6.4975 6.3601 6.2264 6.0963

-46.7847 -49.2618 -51.7547 -54.2580 -56.7665 -59.2749 -61.7786 -64.2730


60/148


61/148


62/148

103 104 105 106 107 108 109 110

0.6481 0.6655 0.6825 0.6988 0.7146 0.7299 0.7445 0.7586

0.0177 0.0172 0.0166 0.0161 0.0155 0.0149 0.0144 0.0138

37.5875 37.1866 36.7092 36.1607 35.5466 34.8727 34.1446 33.3682

-5.3141 -5.3216 -5.3202 -5.3102 -5.2923 -5.2668 -5.2343 -5.1954

55.5718 57.3782 59.1464 60.8735 62.5570 64.1950 65.7855 67.3271

5.9697 5.8466 5.7268 5.6103 5.4971 5.3871 5.2801 5.1762

-66.7538 -69.2172 -71.6594 -74.0772 -76.4675 -78.8278 -81.1555 -83.4488


63/148


64/148


65/148

111 112 113 114 115 116 117 118

0.7721 0.7850 0.7974 0.8092 0.8204 0.8311 0.8412 0.8508

0.0132 0.0126 0.0121 0.0115 0.0109 0.0104 0.0099 0.0094

32.5492 31.6934 30.8061 29.8929 28.9588 28.0088 27.0477 26.0799

-5.1506 -5.1005 -5.0455 -4.9862 -4.9232 -4.8570 -4.7880 -4.7166

68.8186 70.2592 71.6482 72.9853 74.2704 75.5035 76.6851 77.8155

5.0752 4.9771 4.8819 4.7894 4.6996 4.6124 4.5278 4.4457

-85.7057 -87.9249 -90.1052 -92.2457 -94.3456 -96.4045 -98.4222 -100.3987


66/148


67/148


68/148

119 120 121 122 123 124 125 126

0.8600 0.8686 0.8767 0.8844 0.8917 0.8985 0.9049 0.9109

0.0089 0.0084 0.0079 0.0075 0.0070 0.0066 0.0062 0.0058

25.1095 24.1404 23.1762 22.2201 21.2752 20.3441 19.4293 18.5329

-4.6434 -4.5688 -4.4931 -4.4167 -4.3400 -4.2632 -4.1866 -4.1106

78.8955 79.9258 80.9075 81.8416 82.7292 83.5717 84.3704 85.1265

4.3660 4.2887 4.2137 4.1410 4.0704 4.0019 3.9355 3.8711

-102.3341 -104.2288 -106.0832 -107.8978 -109.6736 -111.4111 -113.1115 -114.7756


69/148


70/148


71/148

127 128 129 130 131 132 133 134

0.9166 0.9219 0.9268 0.9315 0.9358 0.9399 0.9436 0.9472

0.0055 0.0051 0.0048 0.0045 0.0042 0.0039 0.0036 0.0034

17.6567 16.8023 15.9712 15.1644 14.3829 13.6274 12.8983 12.1962

-4.0353 -3.9609 -3.8877 -3.8158 -3.7453 -3.6763 -3.6090 -3.5434

85.8417 86.5173 87.1549 87.7559 88.3219 88.8543 89.3548 89.8246

3.8087 3.7481 3.6894 3.6325 3.5773 3.5238 3.4718 3.4215

-116.4045 -117.9994 -119.5614 -121.0916 -122.5912 -124.0615 -125.5037 -126.9190


72/148


73/148


74/148

135 136 137 138 139 140 141 142

0.9504 0.9535 0.9563 0.9589 0.9614 0.9637 0.9658 0.9677

0.0032 0.0029 0.0027 0.0025 0.0024 0.0022 0.0020 0.0019

11.5210 10.8729 10.2518 9.6575 9.0897 8.5480 8.0318 7.5407

-3.4796 -3.4177 -3.3576 -3.2995 -3.2433 -3.1889 -3.1365 -3.0860

90.2654 90.6785 91.0653 91.4273 91.7656 92.0816 92.3766 92.6516

3.3727 3.3254 3.2795 3.2350 3.1918 3.1499 3.1093 3.0699

-128.3086 -129.6737 -131.0154 -132.3350 -133.6335 -134.9121 -136.1717 -137.4135


75/148


76/148


77/148

143 144 145 146 147 148 149 150

0.9695 0.9712 0.9727 0.9741 0.9754 0.9766 0.9778 0.9788

0.0017 0.0016 0.0015 0.0014 0.0013 0.0012 0.0011 0.0010

7.0740 6.6311 6.2112 5.8136 5.4375 5.0823 4.7470 4.4308

-3.0373 -2.9905 -2.9455 -2.9022 -2.8606 -2.8206 -2.7823 -2.7455

92.9080 93.1467 93.3688 93.5754 93.7673 93.9456 94.1110 94.2644

3.0316 2.9945 2.9585 2.9236 2.8897 2.8567 2.8248 2.7937

-138.6385 -139.8475 -141.0416 -142.2216 -143.3883 -144.5426 -145.6853 -146.8170


78/148










Descriptions









Links

data N/A

financial models

Inputs

Stock Price (S) 27.43

Strike Price (K) 27.5



bid price: PV(100) 97.40625


Dividend schedule (T) quarterly 0.25 0.5 0.75 1Dividend amount 0.16 0.16 0.16 0.16 0.16

PV(Div.) 0.6295909 0.1589523 0.1579114 0.1568773 0.15585

Div. Adjusted Stock Price (S*) 26.800409

Outputs

2.14111 2.12742

0 2.49611 1.85283

0.16 2.14111 2.12742

Dividend Call Put

Call Put C = S*N(d1) - Ke

-rTN(d2)

European Option Price 2.14111 2.12742 P = -S*N(-d1) + Ke

-rTN(-d2)

Interim Calcuations


d1 0.1025548

d2 -0.097445

* 21

ln 2S K r T d

T


79/148

2 1d d T


80/148



ns

itivities



greeks


81/148


82/148


83/148










Descriptions









Links

data N/A

financial models

Inputs

Stock Price (S) 27.29

Strike Price (K) 30

Time to expiration (T) 0.1360

Stock volitility () 0.2231 Changing cell for solver


Dividend schedule (T) quarterly 0.25 0.5 0.75

Dividend amount 0 0 0 0PV(Div.) 0 0 0 0

Div. Adjusted Stock Price (S*) 27.29

Option premium (market value) 0.15

Outputs

Call Put C = S*N(d1) - Ke

-rTN(d2)

European Option Price 0.15 2.83 P = -S*N(-d1) + Ke

-rTN(-d2)

(market value - BSOPM)2 4.572E-13 Target cell for solver

Interim Calcuations


d1 -1.095529

d2 -1.177806

* 21

2 1

ln 2S K r T d

T

d d T


84/148

Historical volatility for the last 34 days

daily average -0.000617

daily standard deviation 0.0101464

annual average -0.154241

annual standard deviation 0.1604282

Date Open High Low Close Volume Adj. Close*

3-Feb-04 27.4 27.55 27.18 27.29 47993800 27.29

2-Feb-04 27.61 27.8 27.24 27.4 62891800 27.4

30-Jan-04 27.84 27.9 27.55 27.65 40528700 27.65

29-Jan-04 27.81 27.95 27.57 27.91 63748400 27.91

28-Jan-04 28.3 28.44 27.47 27.71 71336000 27.71

27-Jan-04 28.64 28.72 28.22 28.25 63196200 28.25

26-Jan-04 28.49 28.83 28.32 28.8 58299600 28.8

23-Jan-04 28.28 28.76 28.22 28.48 127259104 28.48

22-Jan-04 28.36 28.44 27.94 28.01 78425200 28.01

21-Jan-04 28.13 28.3 27.85 28.3 53570600 28.3

20-Jan-04 27.98 28.2 27.93 28.1 63068500 28.1

16-Jan-04 27.71 27.88 27.53 27.81 63983400 27.81

15-Jan-04 27.55 27.72 27.42 27.54 58504100 27.54

14-Jan-04 27.52 27.73 27.47 27.7 43907000 27.7

13-Jan-04 27.55 27.64 27.26 27.43 51555900 27.43

12-Jan-04 27.67 27.73 27.35 27.57 55845200 27.57

9-Jan-04 28.03 28.06 27.59 27.66 67079900 27.66

8-Jan-04 28.39 28.48 28 28.16 58810800 28.16

7-Jan-04 28.17 28.31 28.01 28.21 54298200 28.21

6-Jan-04 28.19 28.28 28.07 28.24 46950800 28.24

5-Jan-04 27.73 28.18 27.72 28.14 67333696 28.14

2-Jan-04 27.58 27.77 27.33 27.45 44487700 27.45

31-Dec-03 27.42 27.55 27.23 27.37 42198900 27.37

30-Dec-03 27.41 27.55 27.4 27.52 34406600 27.5229-Dec-03 27.21 27.53 27.16 27.46 40426700 27.46

26-Dec-03 27.05 27.25 27 27.21 12076900 27.21

24-Dec-03 27.14 27.16 27 27.04 19924200 27.04

23-Dec-03 27.17 27.34 27.01 27.15 39609000 27.15

22-Dec-03 27.16 27.43 26.97 27.18 43894800 27.18

19-Dec-03 27.49 27.55 27.19 27.36 76856400 27.36

18-Dec-03 27.1 27.45 27.05 27.4 61177800 27.4

17-Dec-03 27.04 27.08 26.85 27.04 53712300 27.04

16-Dec-03 26.83 27.16 26.77 27.06 73978000 27.06

15-Dec-03 27.05 27.1 26.68 26.74 88860600 26.74

2

( ) ( ) exp

~ (0,1)

ln ( ) ( )

ln ( ) ( )

S t t S t t e t

e N

E S t t S t t

Var S t t S t t


85/148



ns

itivities



greeks

1

00


86/148

0.0040227

0.0090827

0.0093593

-0.007192

0.0193001

0.0192819

-0.011173

-0.01664

0.0103002

-0.007092

-0.010374

-0.009756

0.0057929

-0.009795

0.0050909

0.0032591

0.0179152

0.001774

0.0010629

-0.003547

-0.024826

-0.002919

0.0054655-0.002183

-0.009146

-0.006267

0.0040598

0.0011044

0.0066007

0.0014609

-0.013226

0.0007394

-0.011896


87/148


88/148






affiliation Hanyang University 3. Use "data-table" to generate the p

email address [email protected] input option terms and conditilast revised date Jan-04 output option price and the sen



Descriptions









Links

data N/A

financial models

Inputs

Stock Price (S) 100






Outputs

Call Put

Price 4.8444 3.1226

(Delta) 0.5846 -0.4079

(Gamma) 0.0386 0.0386

v (Vega) 19.3032 19.3032

(Theta) -11.3291 -4.5536

(Rho) 13.4041 -10.9786

(Omega) 12.0677 -13.0634

ensitivity to dividend yield (f/ -14.61523 10.197969

Interim Calcuations

d1 0.2250

d2 0.1250

Option Value

stock price 50 51 52 53 54

long call 4.8444 6.982E-12 2.787E-11 1.044E-10 3.683E-10 1.227E-09

P S

21

ln 2S K r T d

T

2 1

d d T

1 2( ) ( )

T rTC S e N d K e N d


89/148

short call -4.8444 -6.98E-12 -2.79E-11 -1.04E-10 -3.68E-10 -1.23E-09

covered call 95.1556 50 51 52 53 54

long put 3.1226 47.904588 46.91206 45.919532 44.927004 43.934476

short put -3.1226 -47.90459 -46.91206 -45.91953 -44.927 -43.93448

protective put 103.1226 97.904588 97.91206 97.919532 97.927004 97.934476

straddle 7.9670 47.904588 46.91206 45.919532 44.927004 43.934476

3.1226 50 51 52 53 54

put (K=90) 90.0000 38.151489 37.158961 36.166433 35.173905 34.181378

strangle 38.151489 37.158961 36.166433 35.173905 34.181378

Intrinsic Value

long call 0 0 0 0 0

short call 0 0 0 0 0

covered call 50 51 52 53 54

long put 50 49 48 47 46

short put -50 -49 -48 -47 -46

protective put 100 100 100 100 100

straddle 50 49 48 47 46

strangle 40 39 38 37 36

Profit Diagram

stock price 50 51 52 53 54

long call -4.844417 -4.844417 -4.844417 -4.844417 -4.844417

short call 4.844417 4.844417 4.844417 4.844417 4.844417

covered call -45.15558 -44.15558 -43.15558 -42.15558 -41.15558

long put 46.877397 45.877397 44.877397 43.877397 42.877397

short put -46.8774 -45.8774 -44.8774 -43.8774 -42.8774

protective put -3.122603 -3.122603 -3.122603 -3.122603 -3.122603

straddle 42.03298 41.03298 40.03298 39.03298 38.03298

strangle 34.662336 33.662336 32.662336 31.662336 30.662336

-60

-40

-20

0

20

40

60

0 50 100 150 200Profit/Loss

Stock Price

Profit Diagram

long call

short call

covered call

long put

short put

protective put

straddle

strangle


90/148

rate of return

stock price 100 101 102 103 104 105

long stock 0 0.01 0.02 0.03 0.04 0.0

long call 0 0.1246156 0.2569039 0.3965157 0.5430543 0.6960

covered call 0 0.0041649 0.0079391 0.0113405 0.0143893 0.0171

0

10

20

30

40

50

60

50 70 90 110 130 150

stock price

long call

long call

-60

-50

-40

-30

-20

-10

050 70 90 110 130

stock price

short call

short call

0

20

40

60

80

100

120

50 100 150

stock price

covered call

covered call

0

10

20

30

40

50

60

50 100stock price

long put

-60

-50

-40

-30

-20

-10

050 100 150

stock price

short put

short

0

50

100

150

200

50 100

stock price

protective put

protect

0

10

20

30

40

50

60

50 100 150stock price

straddle

strad

0

10

20

30

40

50

60

50 100stock price

strangle


91/148

0

0.02

0.04

0.06

0.08

0.1

0.12

95 100 105 110 115

Rate of Return

long stock

covered call

protective put

0

0.2

0.4

0.6

0.8

1

1.2

1.41.6

1.8

95 100 105

Rate of Ret


92/148



rformance profiles of the profit diagrams.

nsitivities



greeks

55 56 57 58 59 60 61 62

3.869E-09 1.158E-08 3.301E-08 8.975E-08 2.333E-07 5.809E-07 1.388E-06 3.191E-06

1 2( ) ( )

T rTe N d K e N d


93/148

-3.87E-09 -1.16E-08 -3.3E-08 -8.97E-08 -2.33E-07 -5.81E-07 -1.39E-06 -3.19E-06

55 56 57 58 59 59.999999 60.999999 61.999997

42.941948 41.94942 40.956892 39.964364 38.971836 37.979308 36.986781 35.994255

-42.94195 -41.94942 -40.95689 -39.96436 -38.97184 -37.97931 -36.98678 -35.99425

97.941948 97.94942 97.956892 97.964364 97.971836 97.979308 97.986781 97.994255

42.941948 41.94942 40.956892 39.964364 38.971836 37.979309 36.986783 35.994258

55 56 57 58 59 60 61 62

33.18885 32.196324 31.203801 30.211284 29.218778 28.226296 27.233859 26.241502

33.18885 32.196324 31.203801 30.211284 29.218778 28.226297 27.23386 26.241505

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

55 56 57 58 59 60 61 62

45 44 43 42 41 40 39 38

-45 -44 -43 -42 -41 -40 -39 -38

100 100 100 100 100 100 100 100

45 44 43 42 41 40 39 38

35 34 33 32 31 30 29 28

55 56 57 58 59 60 61 62

-4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417

4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417

-40.15558 -39.15558 -38.15558 -37.15558 -36.15558 -35.15558 -34.15558 -33.15558

41.877397 40.877397 39.877397 38.877397 37.877397 36.877397 35.877397 34.877397

-41.8774 -40.8774 -39.8774 -38.8774 -37.8774 -36.8774 -35.8774 -34.8774

-3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603

37.03298 36.03298 35.03298 34.03298 33.03298 32.03298 31.03298 30.03298

29.662336 28.662336 27.662336 26.662336 25.662336 24.662336 23.662336 22.662336


94/148

106 107 108 109 110

0.06 0.07 0.08 0.09 0.1

0.8551562 1.0197897 1.1895113 1.3638489 1.5423425

0.0195182 0.0216457 0.0235142 0.0251477 0.0265696

0.0406076 0.0484141 0.0564596 0.064722 0.0731796

-50

-40

-30

-20-10

0

10

20

30

40

50

0 50 100 150 200profit/loss

stock price

ro agram

long call

short call

-60

-40

-20

0

20

40

60

0 50 100

-60

-40

-200

20

40

60

0 50 100 150 200Profit/Loss

Stock Price

Profit Diagram

covered call

protective put

-20

-10

0

10

20

30

40

50

0 50 100

Profit Diagram


95/148

110 115

urn

long

call


96/148

63 64 65 66 67 68 69 70

7.066E-06 1.51E-05 3.117E-05 6.228E-05 0.0001206 0.0002267 0.0004141 0.0007358


97/148

-7.07E-06 -1.51E-05 -3.12E-05 -6.23E-05 -0.000121 -0.000227 -0.000414 -0.000736

62.999993 63.999985 64.999969 65.999938 66.999879 67.999773 68.999586 69.999264

35.001731 34.009211 33.016699 32.024202 31.031732 30.03931 29.046969 28.054763

-35.00173 -34.00921 -33.0167 -32.0242 -31.03173 -30.03931 -29.04697 -28.05476

98.001731 98.009211 98.016699 98.024202 98.031732 98.03931 98.046969 98.054763

35.001738 34.009226 33.01673 32.024264 31.031853 30.039537 29.047384 28.055499

63 64 65 66 67 68 69 70

25.249287 24.257313 23.265734 22.274784 21.284803 20.296276 19.309865 18.326458

25.249294 24.257328 23.265765 22.274846 21.284924 20.296502 19.310279 18.327194

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

63 64 65 66 67 68 69 70

37 36 35 34 33 32 31 30

-37 -36 -35 -34 -33 -32 -31 -30

100 100 100 100 100 100 100 100

37 36 35 34 33 32 31 30

27 26 25 24 23 22 21 20

63 64 65 66 67 68 69 70

-4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417

4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417

-32.15558 -31.15558 -30.15558 -29.15558 -28.15558 -27.15558 -26.15558 -25.15558

33.877397 32.877397 31.877397 30.877397 29.877397 28.877397 27.877397 26.877397

-33.8774 -32.8774 -31.8774 -30.8774 -29.8774 -28.8774 -27.8774 -26.8774

-3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603

29.03298 28.03298 27.03298 26.03298 25.03298 24.03298 23.03298 22.03298

21.662336 20.662336 19.662336 18.662336 17.662336 16.662336 15.662336 14.662336


98/148

150 200

long put

short put

150 200

straddle

strangle


99/148


100/148

71 72 73 74 75 76 77 78

0.0012734 0.002149 0.0035401 0.005698 0.0089697 0.0138224 0.0208702 0.0309009


101/148

-0.001273 -0.002149 -0.00354 -0.005698 -0.00897 -0.013822 -0.02087 -0.030901

70.998727 71.997851 72.99646 73.994302 74.99103 75.986178 76.97913 77.969099

27.062773 26.07112 25.079983 24.089613 23.100357 22.112681 21.127201 20.144704

-27.06277 -26.07112 -25.07998 -24.08961 -23.10036 -22.11268 -21.1272 -20.1447

98.062773 98.07112 98.079983 98.089613 98.100357 98.112681 98.127201 98.144704

27.064046 26.073269 25.083523 24.095311 23.109326 22.126504 21.148071 20.175605

71 72 73 74 75 76 77 78

17.347204 16.373549 15.407271 14.450489 13.505664 12.575585 11.66332 10.772159

17.348477 16.375698 15.410811 14.456187 13.514634 12.589407 11.68419 10.80306

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

71 72 73 74 75 76 77 78

29 28 27 26 25 24 23 22

-29 -28 -27 -26 -25 -24 -23 -22

100 100 100 100 100 100 100 100

29 28 27 26 25 24 23 22

19 18 17 16 15 14 13 12

71 72 73 74 75 76 77 78

-4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417

4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417

-24.15558 -23.15558 -22.15558 -21.15558 -20.15558 -19.15558 -18.15558 -17.15558

25.877397 24.877397 23.877397 22.877397 21.877397 20.877397 19.877397 18.877397

-25.8774 -24.8774 -23.8774 -22.8774 -21.8774 -20.8774 -19.8774 -18.8774

-3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603

21.03298 20.03298 19.03298 18.03298 17.03298 16.03298 15.03298 14.03298

13.662336 12.662336 11.662336 10.662336 9.6623364 8.6623364 7.6623364 6.6623364


102/148


103/148


104/148

79 80 81 82 83 84 85 86

0.0449024 0.0640857 0.0899027 0.1240561 0.1684998 0.2254284 0.2972537 0.386569


105/148

-0.044902 -0.064086 -0.089903 -0.124056 -0.1685 -0.225428 -0.297254 -0.386569

78.955098 79.935914 80.910097 81.875944 82.8315 83.774572 84.702746 85.613431

19.166177 18.192833 17.226122 16.267747 15.319662 14.384063 13.46336 12.560147

-19.16618 -18.19283 -17.22612 -16.26775 -15.31966 -14.38406 -13.46336 -12.56015

98.166177 98.192833 98.226122 98.267747 98.319662 98.384063 98.46336 98.560147

19.21108 18.256918 17.316024 16.391803 15.488162 14.609491 13.760614 12.946716

79 80 81 82 83 84 85 86

9.9055333 9.0669177 8.2597228 7.487184 6.7522515 6.0574901 5.4049928 4.7963151

9.9504357 9.1310034 8.3496256 7.6112401 6.9207513 6.2829185 5.7022465 5.1828841

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

79 80 81 82 83 84 85 86

21 20 19 18 17 16 15 14

-21 -20 -19 -18 -17 -16 -15 -14

100 100 100 100 100 100 100 100

21 20 19 18 17 16 15 14

11 10 9 8 7 6 5 4

79 80 81 82 83 84 85 86

-4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417

4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417

-16.15558 -15.15558 -14.15558 -13.15558 -12.15558 -11.15558 -10.15558 -9.155583

17.877397 16.877397 15.877397 14.877397 13.877397 12.877397 11.877397 10.877397

-17.8774 -16.8774 -15.8774 -14.8774 -13.8774 -12.8774 -11.8774 -10.8774

-3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603

13.03298 12.03298 11.03298 10.03298 9.0329803 8.0329803 7.0329803 6.0329803

5.6623364 4.6623364 3.6623364 2.6623364 1.6623364 0.6623364 -0.337664 -1.337664


106/148


107/148


108/148

87 88 89 90 91 92 93 94

0.4961015 0.6286538 0.7870381 0.9740036 1.1921635 1.4439233 1.7314136 2.0564324


109/148

-0.496101 -0.628654 -0.787038 -0.974004 -1.192164 -1.443923 -1.731414 -2.056432

86.503899 87.371346 88.212962 89.025996 89.807836 90.556077 91.268586 91.943568

11.677152 10.817176 9.9830324 9.1774698 8.4031017 7.6623334 6.9572957 6.2897865

-11.67715 -10.81718 -9.983032 -9.17747 -8.403102 -7.662333 -6.957296 -6.289786

98.677152 98.817176 98.983032 99.17747 99.403102 99.662333 99.957296 100.28979

12.173253 11.44583 10.77007 10.151473 9.5952652 9.1062567 8.6887092 8.3462189

87 88 89 90 91 92 93 94

4.2324311 3.7137154 3.2399478 2.8103425 2.4235951 2.0779471 1.7712599 1.5010965

4.7285326 4.3423692 4.0269859 3.784346 3.6157587 3.5218704 3.5026735 3.5575289

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

87 88 89 90 91 92 93 94

13 12 11 10 9 8 7 6

-13 -12 -11 -10 -9 -8 -7 -6

100 100 100 100 100 100 100 100

13 12 11 10 9 8 7 6

3 2 1 0 0 0 0 0

87 88 89 90 91 92 93 94

-4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417

4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417

-8.155583 -7.155583 -6.155583 -5.155583 -4.155583 -3.155583 -2.155583 -1.155583

9.8773973 8.8773973 7.8773973 6.8773973 5.8773973 4.8773973 3.8773973 2.8773973

-9.877397 -8.877397 -7.877397 -6.877397 -5.877397 -4.877397 -3.877397 -2.877397

-3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603

5.0329803 4.0329803 3.0329803 2.0329803 1.0329803 0.0329803 -0.96702 -1.96702

-2.337664 -3.337664 -4.337664 -5.337664 -5.337664 -5.337664 -5.337664 -5.337664


110/148


111/148


112/148

95 96 97 98 99 100 101 102

2.4203981 2.8243152 3.268755 3.7538507 4.2793058 4.844417 5.4481069 6.0889666


113/148

-2.420398 -2.824315 -3.268755 -3.753851 -4.279306 -4.844417 -5.448107 -6.088967

92.579602 93.175685 93.731245 94.246149 94.720694 95.155583 95.551893 95.911033

5.6612241 5.0726131 4.5245249 4.0170925 3.5500196 3.1226027 2.7337646 2.3820962

-5.661224 -5.072613 -4.524525 -4.017092 -3.55002 -3.122603 -2.733765 -2.382096

100.66122 101.07261 101.52452 102.01709 102.55002 103.1226 103.73376 104.3821

8.0816221 7.8969283 7.79328 7.7709432 7.8293254 7.9670197 8.1818716 8.4710629

95 96 97 98 99 100 101 102

1.2648047 1.0595986 0.8826342 0.731078 0.602165 0.4932466 0.4018279 0.3255936

3.6852028 3.8839138 4.1513893 4.4849287 4.8814708 5.3376636 5.8499348 6.4145603

0 0 0 0 0 0 1 2

0 0 0 0 0 0 -1 -2

95 96 97 98 99 100 100 100

5 4 3 2 1 0 0 0

-5 -4 -3 -2 -1 0 0 0

100 100 100 100 100 100 101 102

5 4 3 2 1 0 1 2

0 0 0 0 0 0 1 2

95 96 97 98 99 100 101 102

-4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -4.844417 -3.844417 -2.844417

4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 3.844417 2.844417

-0.155583 0.844417 1.844417 2.844417 3.844417 4.844417 4.844417 4.844417

1.8773973 0.8773973 -0.122603 -1.122603 -2.122603 -3.122603 -3.122603 -3.122603

-1.877397 -0.877397 0.1226027 1.1226027 2.1226027 3.1226027 3.1226027 3.1226027

-3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -2.122603 -1.122603

-2.96702 -3.96702 -4.96702 -5.96702 -6.96702 -7.96702 -6.96702 -5.96702

-5.337664 -5.337664 -5.337664 -5.337664 -5.337664 -5.337664 -4.337664 -3.337664


114/148


115/148


116/148

103 104 105 106 107 108 109 110

6.7653044 7.4751986 8.216553 8.9871501 9.7847035 10.606906 11.45147 12.316167


117/148

-6.765304 -7.475199 -8.216553 -8.98715 -9.784704 -10.60691 -11.45147 -12.316167

96.234696 96.524801 96.783447 97.01285 97.215296 97.393094 97.54853 97.683833

2.0659059 1.7832721 1.5320984 1.3101675 1.1151929 0.9448668 0.7969028 0.6690722

-2.065906 -1.783272 -1.532098 -1.310167 -1.115193 -0.944867 -0.7969028 -0.6690722

105.06591 105.78327 106.5321 107.31017 108.11519 108.94487 109.7969 110.66907

8.8312103 9.2584708 9.7486514 10.297318 10.899896 11.551772 12.248372 12.985239

103 104 105 106 107 108 109 110

0.2624255 0.21041 0.1678395 0.1332072 0.1051976 0.0826739 0.064663 0.0503394

7.0277299 7.6856087 8.3843925 9.1203573 9.8899012 10.689579 11.516133 12.366506

3 4 5 6 7 8 9 10

-3 -4 -5 -6 -7 -8 -9 -10

100 100 100 100 100 100 100 100

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

103 104 105 106 107 108 109 110

3 4 5 6 7 8 9 10

3 4 5 6 7 8 9 10

103 104 105 106 107 108 109 110

-1.844417 -0.844417 0.155583 1.155583 2.155583 3.155583 4.155583 5.155583

1.844417 0.844417 -0.155583 -1.155583 -2.155583 -3.155583 -4.155583 -5.155583

4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417

-3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.122603 -3.1226027 -3.1226027

3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027

-0.122603 0.8773973 1.8773973 2.8773973 3.8773973 4.8773973 5.8773973 6.8773973

-4.96702 -3.96702 -2.96702 -1.96702 -0.96702 0.0329803 1.0329803 2.0329803

-2.337664 -1.337664 -0.337664 0.6623364 1.6623364 2.6623364 3.6623364 4.6623364


118/148


119/148


120/148

111 112 113 114 115 116 117 118

13.198857 14.097513 15.010234 15.935265 16.870996 17.815971 18.76888 19.728557


121/148

-13.198857 -14.097513 -15.010234 -15.935265 -16.870996 -17.815971 -18.76888 -19.728557

97.801143 97.902487 97.989766 98.064735 98.129004 98.184029 98.23112 98.271443

0.5592346 0.4653617 0.385555 0.3180577 0.2612614 0.2137081 0.1740887 0.1412382

-0.5592346 -0.4653617 -0.385555 -0.3180577 -0.2612614 -0.2137081 -0.1740887 -0.1412382

111.55923 112.46536 113.38555 114.31806 115.26126 116.21371 117.17409 118.14124

13.758092 14.562874 15.395789 16.253322 17.132258 18.029679 18.942969 19.869796

111 112 113 114 115 116 117 118

0.0390091 0.0300934 0.0231133 0.0176759 0.0134607 0.0102085 0.0077109 0.0058014

13.237867 14.127606 15.033347 15.952941 16.884457 17.82618 18.776591 19.734359

11 12 13 14 15 16 17 18

-11 -12 -13 -14 -15 -16 -17 -18

100 100 100 100 100 100 100 100

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

111 112 113 114 115 116 117 118

11 12 13 14 15 16 17 18

11 12 13 14 15 16 17 18

111 112 113 114 115 116 117 118

6.155583 7.155583 8.155583 9.155583 10.155583 11.155583 12.155583 13.155583

-6.155583 -7.155583 -8.155583 -9.155583 -10.155583 -11.155583 -12.155583 -13.155583

4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417

-3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027

3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027

7.8773973 8.8773973 9.8773973 10.877397 11.877397 12.877397 13.877397 14.877397

3.0329803 4.0329803 5.0329803 6.0329803 7.0329803 8.0329803 9.0329803 10.03298

5.6623364 6.6623364 7.6623364 8.6623364 9.6623364 10.662336 11.662336 12.662336


122/148


123/148


124/148

119 120 121 122 123 124 125 126

20.693976 21.664235 22.638554 23.616258 24.596771 25.579602 26.564335 27.550624


125/148

-20.693976 -21.664235 -22.638554 -23.616258 -24.596771 -25.579602 -26.564335 -27.550624

98.306024 98.335765 98.361446 98.383742 98.403229 98.420398 98.435665 98.449376

0.1141286 0.0918599 0.0736507 0.0588269 0.0468116 0.037114 0.0293198 0.0230807

-0.1141286 -0.0918599 -0.0736507 -0.0588269 -0.0468116 -0.037114 -0.0293198 -0.0230807

119.11413 120.09186 121.07365 122.05883 123.04681 124.03711 125.02932 126.02308

20.808104 21.756095 22.712205 23.675085 24.643583 25.616716 26.593655 27.573705

119 120 121 122 123 124 125 126

0.004348 0.0032465 0.0024151 0.0017902 0.0013223 0.0009734 0.0007141 0.0005222

20.698324 21.667482 22.640969 23.618049 24.598093 25.580575 26.56505 27.551147

19 20 21 22 23 24 25 26

-19 -20 -21 -22 -23 -24 -25 -26

100 100 100 100 100 100 100 100

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

119 120 121 122 123 124 125 126

19 20 21 22 23 24 25 26

19 20 21 22 23 24 25 26

119 120 121 122 123 124 125 126

14.155583 15.155583 16.155583 17.155583 18.155583 19.155583 20.155583 21.155583

-14.155583 -15.155583 -16.155583 -17.155583 -18.155583 -19.155583 -20.155583 -21.155583

4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417

-3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027

3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027

15.877397 16.877397 17.877397 18.877397 19.877397 20.877397 21.877397 22.877397

11.03298 12.03298 13.03298 14.03298 15.03298 16.03298 17.03298 18.03298

13.662336 14.662336 15.662336 16.662336 17.662336 18.662336 19.662336 20.662336


126/148


127/148


128/148

127 128 129 130 131 132 133 134

28.538178 29.526756 30.516159 31.506224 32.496817 33.487832 34.479179 35.47079


129/148

-28.538178 -29.526756 -30.516159 -31.506224 -32.496817 -33.487832 -34.479179 -35.47079

98.461822 98.473244 98.483841 98.493776 98.503183 98.512168 98.520821 98.52921

0.0181065 0.0141562 0.011031 0.0085677 0.0066333 0.0051195 0.0039391 0.0030218

-0.0181065 -0.0141562 -0.011031 -0.0085677 -0.0066333 -0.0051195 -0.0039391 -0.0030218

127.01811 128.01416 129.01103 130.00857 131.00663 132.00512 133.00394 134.00302

28.556285 29.540912 30.52719 31.514791 32.50345 33.492951 34.483118 35.473812

127 128 129 130 131 132 133 134

0.0003807 0.0002766 0.0002004 0.0001448 0.0001043 7.488E-05 5.364E-05 3.832E-05

28.538559 29.527033 30.516359 31.506368 32.496921 33.487906 34.479233 35.470828

27 28 29 30 31 32 33 34

-27 -28 -29 -30 -31 -32 -33 -34

100 100 100 100 100 100 100 100

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

127 128 129 130 131 132 133 134

27 28 29 30 31 32 33 34

27 28 29 30 31 32 33 34

127 128 129 130 131 132 133 134

22.155583 23.155583 24.155583 25.155583 26.155583 27.155583 28.155583 29.155583

-22.155583 -23.155583 -24.155583 -25.155583 -26.155583 -27.155583 -28.155583 -29.155583

4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417

-3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027

3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027

23.877397 24.877397 25.877397 26.877397 27.877397 28.877397 29.877397 30.877397

19.03298 20.03298 21.03298 22.03298 23.03298 24.03298 25.03298 26.03298

21.662336 22.662336 23.662336 24.662336 25.662336 26.662336 27.662336 28.662336


130/148


131/148


132/148

135 136 137 138 139 140 141 142

36.462608 37.454587 38.446693 39.438897 40.431178 41.423517 42.415901 43.40832


133/148

-36.462608 -37.454587 -38.446693 -39.438897 -40.431178 -41.423517 -42.415901 -43.40832

98.537392 98.545413 98.553307 98.561103 98.568822 98.576483 98.584099 98.59168

0.0023113 0.0017628 0.0013407 0.0010168 0.0007691 0.0005802 0.0004366 0.0003277

-0.0023113 -0.0017628 -0.0013407 -0.0010168 -0.0007691 -0.0005802 -0.0004366 -0.0003277

135.00231 136.00176 137.00134 138.00102 139.00077 140.00058 141.00044 142.00033

36.464919 37.45635 38.448034 39.439914 40.431947 41.424097 42.416338 43.408648

135 136 137 138 139 140 141 142

2.73E-05 1.94E-05 1.375E-05 9.726E-06 6.862E-06 4.83E-06 3.393E-06 2.378E-06

36.462635 37.454606 38.446707 39.438907 40.431184 41.423522 42.415905 43.408323

35 36 37 38 39 40 41 42

-35 -36 -37 -38 -39 -40 -41 -42

100 100 100 100 100 100 100 100

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

135 136 137 138 139 140 141 142

35 36 37 38 39 40 41 42

35 36 37 38 39 40 41 42

135 136 137 138 139 140 141 142

30.155583 31.155583 32.155583 33.155583 34.155583 35.155583 36.155583 37.155583

-30.155583 -31.155583 -32.155583 -33.155583 -34.155583 -35.155583 -36.155583 -37.155583

4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417

-3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027

3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027

31.877397 32.877397 33.877397 34.877397 35.877397 36.877397 37.877397 38.877397

27.03298 28.03298 29.03298 30.03298 31.03298 32.03298 33.03298 34.03298

29.662336 30.662336 31.662336 32.662336 33.662336 34.662336 35.662336 36.662336


134/148


135/148


136/148

143 144 145 146 147 148 149 150

44.400766 45.393232 46.385713 47.378206 48.370708 49.363217 50.35573 51.348247


137/148

-44.400766 -45.393232 -46.385713 -47.378206 -48.370708 -49.363217 -50.35573 -51.348247

98.599234 98.606768 98.614287 98.621794 98.629292 98.636783 98.64427 98.651753

0.0002454 0.0001833 0.0001366 0.0001015 7.53E-05 5.573E-05 4.116E-05 3.033E-05

-0.0002454 -0.0001833 -0.0001366 -0.0001015 -7.53E-05 -5.573E-05 -4.116E-05 -3.033E-05

143.00025 144.00018 145.00014 146.0001 147.00008 148.00006 149.00004 150.00003

44.401011 45.393415 46.38585 47.378308 48.370783 49.363272 50.355771 51.348278

143 144 145 146 147 148 149 150

1.663E-06 1.16E-06 8.081E-07 5.617E-07 3.897E-07 2.699E-07 1.865E-07 1.287E-07

44.400768 45.393233 46.385714 47.378207 48.370709 49.363217 50.35573 51.348247

43 44 45 46 47 48 49 50

-43 -44 -45 -46 -47 -48 -49 -50

100 100 100 100 100 100 100 100

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

143 144 145 146 147 148 149 150

43 44 45 46 47 48 49 50

43 44 45 46 47 48 49 50

143 144 145 146 147 148 149 150

38.155583 39.155583 40.155583 41.155583 42.155583 43.155583 44.155583 45.155583

-38.155583 -39.155583 -40.155583 -41.155583 -42.155583 -43.155583 -44.155583 -45.155583

4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417 4.844417

-3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027 -3.1226027

3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027 3.1226027

39.877397 40.877397 41.877397 42.877397 43.877397 44.877397 45.877397 46.877397

35.03298 36.03298 37.03298 38.03298 39.03298 40.03298 41.03298 42.03298

37.662336 38.662336 39.662336 40.662336 41.662336 42.662336 43.662336 44.662336


138/148

Black-Scholes Option Pricing Model copyright THC 2003. All rights reserved by Thom

reference number 9 classification 40401


publication date Jul-03 1. The risk source of both the call and


affiliation Hanyang University input option terms and conditio

email address [email protected] output option price and the sensilast revised date Jan-04

references Black, F. and M. Scholes, 1973, The Pricing of Options and Corporate Liabiliti

Ch. 4 of "The Oxford Guide to Financial Modeling" by Thomas S.Y. Ho and S

Descriptions








key words the law of one price, no abitrage condition, dynamic hedging, hedge ratio, gre

Links

data N/A

financial models

Inputs

Stock Price (S) 100






Outputs

Dividend yields () 0 0.02

Call value 4.8444 5.2954 4.9920

Interim Calcuations

d1 0.2250

d2 0.1250

Call PutPrice 4.8444 3.1226

1( )

C S S

N dS C C

P

21

ln 2S K r T d

T

2 1d d T

1 2( ) ( )T rT

C S e N d K e N d


139/148

as Ho Company, New York, NY. USA www. thomasho.com [email protected]


s

tivities

ies, Journal of Political Economy , Vol.81, 637-654.

ang Bin Lee, 2004, Oxford University Press

eks

1( )

S S

N dC C

1 2( ) ( )T rT

P S e N d K e N d

1 2( ) ( )T rT

e N d K e N d


140/148


141/148

Black-Scholes Option Pricing Model copyright THC 2003. All rights reserve

reference number 9 classification 40401


publication date Jul-03 1. The risk source of both t

author Hanyang Financial Engineering Lab. 2. Enter the option descripti

affiliation Hanyang University input option terms

email address [email protected] output option price

last revised date Jan-04

references Black, F. and M. Scholes, 1973, The Pricing of Options and Corpo

Ch. 4 of "The Oxford Guide to Financial Modeling" by Thomas S.Y

Descriptions








key words the law of one price, no abitrage condition, dynamic hedging, hedg

Links

data N/A

financial models

Inputs

Stock Price (S) 100





Dividend yields () 0

Outputs

stock price 100 100.1

call value 9.9250537 9.9250537 9.9869401

S +( S2)/2 0.0618865

C 0.0618864

Interim Calcuations

d1 0.3000

d2 0.1000

Call

21

ln 2S K r T d

T

2 1d d T


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Price 9.9251

(Delta) 0.6179

(Gamma) 0.0191

v (Vega) 38.1388

(Theta) -5.8885

(Rho) 51.8661

(Omega) 6.2258sensitivity to dividend yield (f/) -61.7911

1 2( ) ( )



143/148

d by Thomas Ho Company, New York, NY. USA www. thomasho.com [email protected]

e call and put options and the underlying asset is the same.

ons

and conditions

nd the sensitivities

ate Liabilities, Journal of Political Economy , Vol.81, 637-654.

. Ho and Sang Bin Lee, 2004, Oxford University Press

ratio, greeks


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1 2( ) ( )

T rTP S e N d K e N d


145/148


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email address [email protected] output option price and the sen

last revised date Jan-04



Descriptions









Links

data N/A

financial models

Inputs

Stock Price (S) 100






Outputs

4.8444 0.25 10

0.04 4.0782 21.2461

0.05 4.2005 24.2314

0.0300 0.1405

Interim Calcuations

d1 0.2250

d2 0.1250

Call Put

Price 4.8444 3.1226P

21

ln 2S K r T d

T

2 1d d T

1 2( ) ( )



147/148

as Ho Company, New York, NY. USA www. thomasho.com [email protected]


ns

itivities


Sang Bin Lee, 2004, Oxford University Press

reeks

1 2( ) ( )

T rTP S e N d K e N d

1 2( ) ( )

T rTe N d K e N d

Documents

23Black-Scholes Model V3