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Black-Scholes Option Pricing Model

Time to Expiration 0.082192 Time to Expiration 0.082192 Time to ExExercise Price $40.00 Exercise Price $40.00 Exercise P

Current Stock Price $42.50 Current Stock Price $42.50 Current StoVolatility 50.00% Volatility 50.00% VolatilityRisk-Free Rate 3.00% Risk-Free Rate 3.00% Risk-Free

d1 0.511801 d1 0.511801 d1d2 0.368455 d2 0.368455 d2N(d1) 0.695605 N(d1) 0.695605 N(d1)N(d2) 0.643733 N(d2) 0.643733 N(d2)Call Option Value $3.88 Call Option Value $3.88 Call Option

Intrinsic Value $2.50 Intrinsic Value $2.50 Intrinsic

Speculative Prem. $1.38 Speculative Prem. $1.38 SpeculatiPut Option Value $1.28 Put Option Value $1.28 Put Option

Intrinsic Value $0.00 Intrinsic Value $0.00 IntrinsicSpeculative Prem. $1.28 Speculative Prem. $1.28 Speculati

Call Call

Delta 0.6956 Delta 0.6956Gamma 0.0574 Gamma 0.0574Theta -13.7407 Theta -13.7407Vega 4.2642 Vega 4.2642Rho 2.111171 Rho 2.111171

Put Put

Delta -0.3044 Delta -0.3044Gamma 0.0574 Gamma 0.0574Theta -12.5437 Theta -12.5437

Vega 4.2642 Vega 4.2642Rho -1.1684 Rho -1.1684

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iration 0.082192ice $40.00

ck Price $42.5050.00%

ate 3.00%

0.5118010.3684550.6956050.643733

Value $3.88alue $2.50

e Prem. $1.38Value $1.28alue $0.00e Prem. $1.28

Call

Delta 0.6956Gamma 0.0574Theta -13.7407Vega 4.2642Rho 2.111171

Put

Delta -0.3044Gamma 0.0574Theta -12.5437

Vega 4.2642Rho -1.1684

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Stock Price, Volatility and Option Prices (Simulation)

This is a simplified simulation to illustrate the impact of standard deviation (volatility) of the underlying asset

on option value. The spreadsheet randomly generates 300 possible stock prices based on a mean return ofa standard deviation equal to the selected volatility measure. The spreadsheet calculates the option value AEXPIRATION. At the bottom you will find the average value for the stock, the call, and the put based on you

Run this simulation using a 15% annual volatility, a 25% annual volatility and a 35% annual volatility. Whathappens to the average values as you change the volatility?

Step 1: Go to the Data tab and to the far right (in the Analysis box) you will see an icon for Data Analysis. FIf you do not see a heading for Data Analysis, you will have to go to the Add-ins to add this. Go to thFrom there, select the Add-In heading and Manage Excel Add-ins. On the next screen check the ta

Step 2: Fill in the dialog box according to the following informationNumber of Variables 1

Number of Random Numbers 300Distribution NormalMean 0.08Standard Deviation 0.15

Random Seed Pick a number between 1 and 20,000Output Range B33..B332

Step 3: Repeat the above using .25 and .35 for standard deviation and H33..H332 and N33..N332 for outputuse a different random seed

Step 4: Save your spreadsheet

Current Stock Price $50.00Exercise Price $50.00

Stock Price Call Put

Average 50 0 0 Average

RandomReturn Stock Price

Option Value(Call)

Option Value(Put)

Trial 1 50 $0.00 $0.00 Trial 1

Trial 2 50 $0.00 $0.00 Trial 2Trial 3 50 $0.00 $0.00 Trial 3Trial 4 50 $0.00 $0.00 Trial 4Trial 5 50 $0.00 $0.00 Trial 5Trial 6 50 $0.00 $0.00 Trial 6Trial 7 50 $0.00 $0.00 Trial 7Trial 8 50 $0.00 $0.00 Trial 8Trial 9 50 $0.00 $0.00 Trial 9Trial 10 50 $0.00 $0.00 Trial 10

Trial 11 50 $0.00 $0.00 Trial 11Trial 12 50 $0.00 $0.00 Trial 12Trial 13 50 $0.00 $0.00 Trial 13Trial 14 50 $0.00 $0.00 Trial 14Trial 15 50 $0.00 $0.00 Trial 15Trial 16 50 $0.00 $0.00 Trial 16Trial 17 50 $0.00 $0.00 Trial 17Trial 18 50 $0.00 $0.00 Trial 18

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Trial 19 50 $0.00 $0.00 Trial 19Trial 20 50 $0.00 $0.00 Trial 20Trial 21 50 $0.00 $0.00 Trial 21Trial 22 50 $0.00 $0.00 Trial 22Trial 23 50 $0.00 $0.00 Trial 23Trial 24 50 $0.00 $0.00 Trial 24

Trial 25 50 $0.00 $0.00 Trial 25Trial 26 50 $0.00 $0.00 Trial 26Trial 27 50 $0.00 $0.00 Trial 27Trial 28 50 $0.00 $0.00 Trial 28Trial 29 50 $0.00 $0.00 Trial 29Trial 30 50 $0.00 $0.00 Trial 30Trial 31 50 $0.00 $0.00 Trial 31Trial 32 50 $0.00 $0.00 Trial 32Trial 33 50 $0.00 $0.00 Trial 33

Trial 34 50 $0.00 $0.00 Trial 34Trial 35 50 $0.00 $0.00 Trial 35Trial 36 50 $0.00 $0.00 Trial 36

Trial 37 50 $0.00 $0.00 Trial 37Trial 38 50 $0.00 $0.00 Trial 38Trial 39 50 $0.00 $0.00 Trial 39Trial 40 50 $0.00 $0.00 Trial 40Trial 41 50 $0.00 $0.00 Trial 41Trial 42 50 $0.00 $0.00 Trial 42Trial 43 50 $0.00 $0.00 Trial 43Trial 44 50 $0.00 $0.00 Trial 44Trial 45 50 $0.00 $0.00 Trial 45

Trial 46 50 $0.00 $0.00 Trial 46Trial 47 50 $0.00 $0.00 Trial 47Trial 48 50 $0.00 $0.00 Trial 48Trial 49 50 $0.00 $0.00 Trial 49

Trial 50 50 $0.00 $0.00 Trial 50Trial 51 50 $0.00 $0.00 Trial 51Trial 52 50 $0.00 $0.00 Trial 52Trial 53 50 $0.00 $0.00 Trial 53Trial 54 50 $0.00 $0.00 Trial 54Trial 55 50 $0.00 $0.00 Trial 55

Trial 56 50 $0.00 $0.00 Trial 56Trial 57 50 $0.00 $0.00 Trial 57Trial 58 50 $0.00 $0.00 Trial 58Trial 59 50 $0.00 $0.00 Trial 59Trial 60 50 $0.00 $0.00 Trial 60Trial 61 50 $0.00 $0.00 Trial 61

Trial 62 50 $0.00 $0.00 Trial 62Trial 63 50 $0.00 $0.00 Trial 63Trial 64 50 $0.00 $0.00 Trial 64

Trial 65 50 $0.00 $0.00 Trial 65Trial 66 50 $0.00 $0.00 Trial 66Trial 67 50 $0.00 $0.00 Trial 67Trial 68 50 $0.00 $0.00 Trial 68Trial 69 50 $0.00 $0.00 Trial 69

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Trial 70 50 $0.00 $0.00 Trial 70Trial 71 50 $0.00 $0.00 Trial 71Trial 72 50 $0.00 $0.00 Trial 72Trial 73 50 $0.00 $0.00 Trial 73Trial 74 50 $0.00 $0.00 Trial 74Trial 75 50 $0.00 $0.00 Trial 75

Trial 76 50 $0.00 $0.00 Trial 76Trial 77 50 $0.00 $0.00 Trial 77Trial 78 50 $0.00 $0.00 Trial 78Trial 79 50 $0.00 $0.00 Trial 79Trial 80 50 $0.00 $0.00 Trial 80Trial 81 50 $0.00 $0.00 Trial 81Trial 82 50 $0.00 $0.00 Trial 82Trial 83 50 $0.00 $0.00 Trial 83Trial 84 50 $0.00 $0.00 Trial 84

Trial 85 50 $0.00 $0.00 Trial 85Trial 86 50 $0.00 $0.00 Trial 86Trial 87 50 $0.00 $0.00 Trial 87

Trial 88 50 $0.00 $0.00 Trial 88Trial 89 50 $0.00 $0.00 Trial 89Trial 90 50 $0.00 $0.00 Trial 90Trial 91 50 $0.00 $0.00 Trial 91Trial 92 50 $0.00 $0.00 Trial 92Trial 93 50 $0.00 $0.00 Trial 93Trial 94 50 $0.00 $0.00 Trial 94Trial 95 50 $0.00 $0.00 Trial 95Trial 96 50 $0.00 $0.00 Trial 96

Trial 97 50 $0.00 $0.00 Trial 97Trial 98 50 $0.00 $0.00 Trial 98Trial 99 50 $0.00 $0.00 Trial 99Trial 100 50 $0.00 $0.00 Trial 100

Trial 101 50 $0.00 $0.00 Trial 101Trial 102 50 $0.00 $0.00 Trial 102Trial 103 50 $0.00 $0.00 Trial 103Trial 104 50 $0.00 $0.00 Trial 104Trial 105 50 $0.00 $0.00 Trial 105Trial 106 50 $0.00 $0.00 Trial 106

Trial 107 50 $0.00 $0.00 Trial 107Trial 108 50 $0.00 $0.00 Trial 108Trial 109 50 $0.00 $0.00 Trial 109Trial 110 50 $0.00 $0.00 Trial 110Trial 111 50 $0.00 $0.00 Trial 111Trial 112 50 $0.00 $0.00 Trial 112

Trial 113 50 $0.00 $0.00 Trial 113Trial 114 50 $0.00 $0.00 Trial 114Trial 115 50 $0.00 $0.00 Trial 115

Trial 116 50 $0.00 $0.00 Trial 116Trial 117 50 $0.00 $0.00 Trial 117Trial 118 50 $0.00 $0.00 Trial 118Trial 119 50 $0.00 $0.00 Trial 119Trial 120 50 $0.00 $0.00 Trial 120

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Trial 121 50 $0.00 $0.00 Trial 121Trial 122 50 $0.00 $0.00 Trial 122Trial 123 50 $0.00 $0.00 Trial 123Trial 124 50 $0.00 $0.00 Trial 124Trial 125 50 $0.00 $0.00 Trial 125Trial 126 50 $0.00 $0.00 Trial 126

Trial 127 50 $0.00 $0.00 Trial 127Trial 128 50 $0.00 $0.00 Trial 128Trial 129 50 $0.00 $0.00 Trial 129Trial 130 50 $0.00 $0.00 Trial 130Trial 131 50 $0.00 $0.00 Trial 131Trial 132 50 $0.00 $0.00 Trial 132Trial 133 50 $0.00 $0.00 Trial 133Trial 134 50 $0.00 $0.00 Trial 134Trial 135 50 $0.00 $0.00 Trial 135

Trial 136 50 $0.00 $0.00 Trial 136Trial 137 50 $0.00 $0.00 Trial 137Trial 138 50 $0.00 $0.00 Trial 138

Trial 139 50 $0.00 $0.00 Trial 139Trial 140 50 $0.00 $0.00 Trial 140Trial 141 50 $0.00 $0.00 Trial 141Trial 142 50 $0.00 $0.00 Trial 142Trial 143 50 $0.00 $0.00 Trial 143Trial 144 50 $0.00 $0.00 Trial 144Trial 145 50 $0.00 $0.00 Trial 145Trial 146 50 $0.00 $0.00 Trial 146Trial 147 50 $0.00 $0.00 Trial 147

Trial 148 50 $0.00 $0.00 Trial 148Trial 149 50 $0.00 $0.00 Trial 149Trial 150 50 $0.00 $0.00 Trial 150Trial 151 50 $0.00 $0.00 Trial 151

Trial 152 50 $0.00 $0.00 Trial 152Trial 153 50 $0.00 $0.00 Trial 153Trial 154 50 $0.00 $0.00 Trial 154Trial 155 50 $0.00 $0.00 Trial 155Trial 156 50 $0.00 $0.00 Trial 156Trial 157 50 $0.00 $0.00 Trial 157

Trial 158 50 $0.00 $0.00 Trial 158Trial 159 50 $0.00 $0.00 Trial 159Trial 160 50 $0.00 $0.00 Trial 160Trial 161 50 $0.00 $0.00 Trial 161Trial 162 50 $0.00 $0.00 Trial 162Trial 163 50 $0.00 $0.00 Trial 163

Trial 164 50 $0.00 $0.00 Trial 164Trial 165 50 $0.00 $0.00 Trial 165Trial 166 50 $0.00 $0.00 Trial 166

Trial 167 50 $0.00 $0.00 Trial 167Trial 168 50 $0.00 $0.00 Trial 168Trial 169 50 $0.00 $0.00 Trial 169Trial 170 50 $0.00 $0.00 Trial 170Trial 171 50 $0.00 $0.00 Trial 171

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Trial 172 50 $0.00 $0.00 Trial 172Trial 173 50 $0.00 $0.00 Trial 173Trial 174 50 $0.00 $0.00 Trial 174Trial 175 50 $0.00 $0.00 Trial 175Trial 176 50 $0.00 $0.00 Trial 176Trial 177 50 $0.00 $0.00 Trial 177

Trial 178 50 $0.00 $0.00 Trial 178Trial 179 50 $0.00 $0.00 Trial 179Trial 180 50 $0.00 $0.00 Trial 180Trial 181 50 $0.00 $0.00 Trial 181Trial 182 50 $0.00 $0.00 Trial 182Trial 183 50 $0.00 $0.00 Trial 183Trial 184 50 $0.00 $0.00 Trial 184Trial 185 50 $0.00 $0.00 Trial 185Trial 186 50 $0.00 $0.00 Trial 186

Trial 187 50 $0.00 $0.00 Trial 187Trial 188 50 $0.00 $0.00 Trial 188Trial 189 50 $0.00 $0.00 Trial 189

Trial 190 50 $0.00 $0.00 Trial 190Trial 191 50 $0.00 $0.00 Trial 191Trial 192 50 $0.00 $0.00 Trial 192Trial 193 50 $0.00 $0.00 Trial 193Trial 194 50 $0.00 $0.00 Trial 194Trial 195 50 $0.00 $0.00 Trial 195Trial 196 50 $0.00 $0.00 Trial 196Trial 197 50 $0.00 $0.00 Trial 197Trial 198 50 $0.00 $0.00 Trial 198

Trial 199 50 $0.00 $0.00 Trial 199Trial 200 50 $0.00 $0.00 Trial 200Trial 201 50 $0.00 $0.00 Trial 201Trial 202 50 $0.00 $0.00 Trial 202

Trial 203 50 $0.00 $0.00 Trial 203Trial 204 50 $0.00 $0.00 Trial 204Trial 205 50 $0.00 $0.00 Trial 205Trial 206 50 $0.00 $0.00 Trial 206Trial 207 50 $0.00 $0.00 Trial 207Trial 208 50 $0.00 $0.00 Trial 208

Trial 209 50 $0.00 $0.00 Trial 209Trial 210 50 $0.00 $0.00 Trial 210Trial 211 50 $0.00 $0.00 Trial 211Trial 212 50 $0.00 $0.00 Trial 212Trial 213 50 $0.00 $0.00 Trial 213Trial 214 50 $0.00 $0.00 Trial 214

Trial 215 50 $0.00 $0.00 Trial 215Trial 216 50 $0.00 $0.00 Trial 216Trial 217 50 $0.00 $0.00 Trial 217

Trial 218 50 $0.00 $0.00 Trial 218Trial 219 50 $0.00 $0.00 Trial 219Trial 220 50 $0.00 $0.00 Trial 220Trial 221 50 $0.00 $0.00 Trial 221Trial 222 50 $0.00 $0.00 Trial 222

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Trial 223 50 $0.00 $0.00 Trial 223Trial 224 50 $0.00 $0.00 Trial 224Trial 225 50 $0.00 $0.00 Trial 225Trial 226 50 $0.00 $0.00 Trial 226Trial 227 50 $0.00 $0.00 Trial 227Trial 228 50 $0.00 $0.00 Trial 228

Trial 229 50 $0.00 $0.00 Trial 229Trial 230 50 $0.00 $0.00 Trial 230Trial 231 50 $0.00 $0.00 Trial 231Trial 232 50 $0.00 $0.00 Trial 232Trial 233 50 $0.00 $0.00 Trial 233Trial 234 50 $0.00 $0.00 Trial 234Trial 235 50 $0.00 $0.00 Trial 235Trial 236 50 $0.00 $0.00 Trial 236Trial 237 50 $0.00 $0.00 Trial 237

Trial 238 50 $0.00 $0.00 Trial 238Trial 239 50 $0.00 $0.00 Trial 239Trial 240 50 $0.00 $0.00 Trial 240

Trial 241 50 $0.00 $0.00 Trial 241Trial 242 50 $0.00 $0.00 Trial 242Trial 243 50 $0.00 $0.00 Trial 243Trial 244 50 $0.00 $0.00 Trial 244Trial 245 50 $0.00 $0.00 Trial 245Trial 246 50 $0.00 $0.00 Trial 246Trial 247 50 $0.00 $0.00 Trial 247Trial 248 50 $0.00 $0.00 Trial 248Trial 249 50 $0.00 $0.00 Trial 249

Trial 250 50 $0.00 $0.00 Trial 250Trial 251 50 $0.00 $0.00 Trial 251Trial 252 50 $0.00 $0.00 Trial 252Trial 253 50 $0.00 $0.00 Trial 253

Trial 254 50 $0.00 $0.00 Trial 254Trial 255 50 $0.00 $0.00 Trial 255Trial 256 50 $0.00 $0.00 Trial 256Trial 257 50 $0.00 $0.00 Trial 257Trial 258 50 $0.00 $0.00 Trial 258Trial 259 50 $0.00 $0.00 Trial 259

Trial 260 50 $0.00 $0.00 Trial 260Trial 261 50 $0.00 $0.00 Trial 261Trial 262 50 $0.00 $0.00 Trial 262Trial 263 50 $0.00 $0.00 Trial 263Trial 264 50 $0.00 $0.00 Trial 264Trial 265 50 $0.00 $0.00 Trial 265

Trial 266 50 $0.00 $0.00 Trial 266Trial 267 50 $0.00 $0.00 Trial 267Trial 268 50 $0.00 $0.00 Trial 268

Trial 269 50 $0.00 $0.00 Trial 269Trial 270 50 $0.00 $0.00 Trial 270Trial 271 50 $0.00 $0.00 Trial 271Trial 272 50 $0.00 $0.00 Trial 272Trial 273 50 $0.00 $0.00 Trial 273

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Trial 274 50 $0.00 $0.00 Trial 274Trial 275 50 $0.00 $0.00 Trial 275Trial 276 50 $0.00 $0.00 Trial 276Trial 277 50 $0.00 $0.00 Trial 277Trial 278 50 $0.00 $0.00 Trial 278Trial 279 50 $0.00 $0.00 Trial 279

Trial 280 50 $0.00 $0.00 Trial 280Trial 281 50 $0.00 $0.00 Trial 281Trial 282 50 $0.00 $0.00 Trial 282Trial 283 50 $0.00 $0.00 Trial 283Trial 284 50 $0.00 $0.00 Trial 284Trial 285 50 $0.00 $0.00 Trial 285Trial 286 50 $0.00 $0.00 Trial 286Trial 287 50 $0.00 $0.00 Trial 287Trial 288 50 $0.00 $0.00 Trial 288

Trial 289 50 $0.00 $0.00 Trial 289Trial 290 50 $0.00 $0.00 Trial 290Trial 291 50 $0.00 $0.00 Trial 291

Trial 292 50 $0.00 $0.00 Trial 292Trial 293 50 $0.00 $0.00 Trial 293Trial 294 50 $0.00 $0.00 Trial 294Trial 295 50 $0.00 $0.00 Trial 295Trial 296 50 $0.00 $0.00 Trial 296Trial 297 50 $0.00 $0.00 Trial 297Trial 298 50 $0.00 $0.00 Trial 298Trial 299 50 $0.00 $0.00 Trial 299Trial 300 50 $0.00 $0.00 Trial 300

Average Return #DIV/0!Standard Deviation #DIV/0!

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8% andTr sample.

om there, select Random Number Generation.e Office Button and select Excel Optionsfor Analysis Toolpak and Solver

range. Also

Stock Price Call Put Stock Price

50 0 0 Average 50

RandomReturn Stock Price

Option Value(Call)

Option Value(Put)

RandomReturn Stock Price

50 $0.00 $0.00 Trial 1 50

50 $0.00 $0.00 Trial 2 5050 $0.00 $0.00 Trial 3 5050 $0.00 $0.00 Trial 4 5050 $0.00 $0.00 Trial 5 5050 $0.00 $0.00 Trial 6 5050 $0.00 $0.00 Trial 7 5050 $0.00 $0.00 Trial 8 5050 $0.00 $0.00 Trial 9 5050 $0.00 $0.00 Trial 10 50

50 $0.00 $0.00 Trial 11 5050 $0.00 $0.00 Trial 12 5050 $0.00 $0.00 Trial 13 5050 $0.00 $0.00 Trial 14 5050 $0.00 $0.00 Trial 15 5050 $0.00 $0.00 Trial 16 5050 $0.00 $0.00 Trial 17 5050 $0.00 $0.00 Trial 18 50

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50 $0.00 $0.00 Trial 19 5050 $0.00 $0.00 Trial 20 5050 $0.00 $0.00 Trial 21 5050 $0.00 $0.00 Trial 22 5050 $0.00 $0.00 Trial 23 5050 $0.00 $0.00 Trial 24 50

50 $0.00 $0.00 Trial 25 5050 $0.00 $0.00 Trial 26 5050 $0.00 $0.00 Trial 27 5050 $0.00 $0.00 Trial 28 5050 $0.00 $0.00 Trial 29 5050 $0.00 $0.00 Trial 30 5050 $0.00 $0.00 Trial 31 5050 $0.00 $0.00 Trial 32 5050 $0.00 $0.00 Trial 33 50

50 $0.00 $0.00 Trial 34 5050 $0.00 $0.00 Trial 35 5050 $0.00 $0.00 Trial 36 50

50 $0.00 $0.00 Trial 37 5050 $0.00 $0.00 Trial 38 5050 $0.00 $0.00 Trial 39 5050 $0.00 $0.00 Trial 40 5050 $0.00 $0.00 Trial 41 5050 $0.00 $0.00 Trial 42 5050 $0.00 $0.00 Trial 43 5050 $0.00 $0.00 Trial 44 5050 $0.00 $0.00 Trial 45 50

50 $0.00 $0.00 Trial 46 5050 $0.00 $0.00 Trial 47 5050 $0.00 $0.00 Trial 48 5050 $0.00 $0.00 Trial 49 50

50 $0.00 $0.00 Trial 50 5050 $0.00 $0.00 Trial 51 5050 $0.00 $0.00 Trial 52 5050 $0.00 $0.00 Trial 53 5050 $0.00 $0.00 Trial 54 5050 $0.00 $0.00 Trial 55 50

50 $0.00 $0.00 Trial 56 5050 $0.00 $0.00 Trial 57 5050 $0.00 $0.00 Trial 58 5050 $0.00 $0.00 Trial 59 5050 $0.00 $0.00 Trial 60 5050 $0.00 $0.00 Trial 61 50

50 $0.00 $0.00 Trial 62 5050 $0.00 $0.00 Trial 63 5050 $0.00 $0.00 Trial 64 50

50 $0.00 $0.00 Trial 65 5050 $0.00 $0.00 Trial 66 5050 $0.00 $0.00 Trial 67 5050 $0.00 $0.00 Trial 68 5050 $0.00 $0.00 Trial 69 50

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50 $0.00 $0.00 Trial 70 5050 $0.00 $0.00 Trial 71 5050 $0.00 $0.00 Trial 72 5050 $0.00 $0.00 Trial 73 5050 $0.00 $0.00 Trial 74 5050 $0.00 $0.00 Trial 75 50

50 $0.00 $0.00 Trial 76 5050 $0.00 $0.00 Trial 77 5050 $0.00 $0.00 Trial 78 5050 $0.00 $0.00 Trial 79 5050 $0.00 $0.00 Trial 80 5050 $0.00 $0.00 Trial 81 5050 $0.00 $0.00 Trial 82 5050 $0.00 $0.00 Trial 83 5050 $0.00 $0.00 Trial 84 50

50 $0.00 $0.00 Trial 85 5050 $0.00 $0.00 Trial 86 5050 $0.00 $0.00 Trial 87 50

50 $0.00 $0.00 Trial 88 5050 $0.00 $0.00 Trial 89 5050 $0.00 $0.00 Trial 90 5050 $0.00 $0.00 Trial 91 5050 $0.00 $0.00 Trial 92 5050 $0.00 $0.00 Trial 93 5050 $0.00 $0.00 Trial 94 5050 $0.00 $0.00 Trial 95 5050 $0.00 $0.00 Trial 96 50

50 $0.00 $0.00 Trial 97 5050 $0.00 $0.00 Trial 98 5050 $0.00 $0.00 Trial 99 5050 $0.00 $0.00 Trial 100 50

50 $0.00 $0.00 Trial 101 5050 $0.00 $0.00 Trial 102 5050 $0.00 $0.00 Trial 103 5050 $0.00 $0.00 Trial 104 5050 $0.00 $0.00 Trial 105 5050 $0.00 $0.00 Trial 106 50

50 $0.00 $0.00 Trial 107 5050 $0.00 $0.00 Trial 108 5050 $0.00 $0.00 Trial 109 5050 $0.00 $0.00 Trial 110 5050 $0.00 $0.00 Trial 111 5050 $0.00 $0.00 Trial 112 50

50 $0.00 $0.00 Trial 113 5050 $0.00 $0.00 Trial 114 5050 $0.00 $0.00 Trial 115 50

50 $0.00 $0.00 Trial 116 5050 $0.00 $0.00 Trial 117 5050 $0.00 $0.00 Trial 118 5050 $0.00 $0.00 Trial 119 5050 $0.00 $0.00 Trial 120 50

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50 $0.00 $0.00 Trial 121 5050 $0.00 $0.00 Trial 122 5050 $0.00 $0.00 Trial 123 5050 $0.00 $0.00 Trial 124 5050 $0.00 $0.00 Trial 125 5050 $0.00 $0.00 Trial 126 50

50 $0.00 $0.00 Trial 127 5050 $0.00 $0.00 Trial 128 5050 $0.00 $0.00 Trial 129 5050 $0.00 $0.00 Trial 130 5050 $0.00 $0.00 Trial 131 5050 $0.00 $0.00 Trial 132 5050 $0.00 $0.00 Trial 133 5050 $0.00 $0.00 Trial 134 5050 $0.00 $0.00 Trial 135 50

50 $0.00 $0.00 Trial 136 5050 $0.00 $0.00 Trial 137 5050 $0.00 $0.00 Trial 138 50

50 $0.00 $0.00 Trial 139 5050 $0.00 $0.00 Trial 140 5050 $0.00 $0.00 Trial 141 5050 $0.00 $0.00 Trial 142 5050 $0.00 $0.00 Trial 143 5050 $0.00 $0.00 Trial 144 5050 $0.00 $0.00 Trial 145 5050 $0.00 $0.00 Trial 146 5050 $0.00 $0.00 Trial 147 50

50 $0.00 $0.00 Trial 148 5050 $0.00 $0.00 Trial 149 5050 $0.00 $0.00 Trial 150 5050 $0.00 $0.00 Trial 151 50

50 $0.00 $0.00 Trial 152 5050 $0.00 $0.00 Trial 153 5050 $0.00 $0.00 Trial 154 5050 $0.00 $0.00 Trial 155 5050 $0.00 $0.00 Trial 156 5050 $0.00 $0.00 Trial 157 50

50 $0.00 $0.00 Trial 158 5050 $0.00 $0.00 Trial 159 5050 $0.00 $0.00 Trial 160 5050 $0.00 $0.00 Trial 161 5050 $0.00 $0.00 Trial 162 5050 $0.00 $0.00 Trial 163 50

50 $0.00 $0.00 Trial 164 5050 $0.00 $0.00 Trial 165 5050 $0.00 $0.00 Trial 166 50

50 $0.00 $0.00 Trial 167 5050 $0.00 $0.00 Trial 168 5050 $0.00 $0.00 Trial 169 5050 $0.00 $0.00 Trial 170 5050 $0.00 $0.00 Trial 171 50

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50 $0.00 $0.00 Trial 172 5050 $0.00 $0.00 Trial 173 5050 $0.00 $0.00 Trial 174 5050 $0.00 $0.00 Trial 175 5050 $0.00 $0.00 Trial 176 5050 $0.00 $0.00 Trial 177 50

50 $0.00 $0.00 Trial 178 5050 $0.00 $0.00 Trial 179 5050 $0.00 $0.00 Trial 180 5050 $0.00 $0.00 Trial 181 5050 $0.00 $0.00 Trial 182 5050 $0.00 $0.00 Trial 183 5050 $0.00 $0.00 Trial 184 5050 $0.00 $0.00 Trial 185 5050 $0.00 $0.00 Trial 186 50

50 $0.00 $0.00 Trial 187 5050 $0.00 $0.00 Trial 188 5050 $0.00 $0.00 Trial 189 50

50 $0.00 $0.00 Trial 190 5050 $0.00 $0.00 Trial 191 5050 $0.00 $0.00 Trial 192 5050 $0.00 $0.00 Trial 193 5050 $0.00 $0.00 Trial 194 5050 $0.00 $0.00 Trial 195 5050 $0.00 $0.00 Trial 196 5050 $0.00 $0.00 Trial 197 5050 $0.00 $0.00 Trial 198 50

50 $0.00 $0.00 Trial 199 5050 $0.00 $0.00 Trial 200 5050 $0.00 $0.00 Trial 201 5050 $0.00 $0.00 Trial 202 50

50 $0.00 $0.00 Trial 203 5050 $0.00 $0.00 Trial 204 5050 $0.00 $0.00 Trial 205 5050 $0.00 $0.00 Trial 206 5050 $0.00 $0.00 Trial 207 5050 $0.00 $0.00 Trial 208 50

50 $0.00 $0.00 Trial 209 5050 $0.00 $0.00 Trial 210 5050 $0.00 $0.00 Trial 211 5050 $0.00 $0.00 Trial 212 5050 $0.00 $0.00 Trial 213 5050 $0.00 $0.00 Trial 214 50

50 $0.00 $0.00 Trial 215 5050 $0.00 $0.00 Trial 216 5050 $0.00 $0.00 Trial 217 50

50 $0.00 $0.00 Trial 218 5050 $0.00 $0.00 Trial 219 5050 $0.00 $0.00 Trial 220 5050 $0.00 $0.00 Trial 221 5050 $0.00 $0.00 Trial 222 50

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15/23

50 $0.00 $0.00 Trial 223 5050 $0.00 $0.00 Trial 224 5050 $0.00 $0.00 Trial 225 5050 $0.00 $0.00 Trial 226 5050 $0.00 $0.00 Trial 227 5050 $0.00 $0.00 Trial 228 50

50 $0.00 $0.00 Trial 229 5050 $0.00 $0.00 Trial 230 5050 $0.00 $0.00 Trial 231 5050 $0.00 $0.00 Trial 232 5050 $0.00 $0.00 Trial 233 5050 $0.00 $0.00 Trial 234 5050 $0.00 $0.00 Trial 235 5050 $0.00 $0.00 Trial 236 5050 $0.00 $0.00 Trial 237 50

50 $0.00 $0.00 Trial 238 5050 $0.00 $0.00 Trial 239 5050 $0.00 $0.00 Trial 240 50

50 $0.00 $0.00 Trial 241 5050 $0.00 $0.00 Trial 242 5050 $0.00 $0.00 Trial 243 5050 $0.00 $0.00 Trial 244 5050 $0.00 $0.00 Trial 245 5050 $0.00 $0.00 Trial 246 5050 $0.00 $0.00 Trial 247 5050 $0.00 $0.00 Trial 248 5050 $0.00 $0.00 Trial 249 50

50 $0.00 $0.00 Trial 250 5050 $0.00 $0.00 Trial 251 5050 $0.00 $0.00 Trial 252 5050 $0.00 $0.00 Trial 253 50

50 $0.00 $0.00 Trial 254 5050 $0.00 $0.00 Trial 255 5050 $0.00 $0.00 Trial 256 5050 $0.00 $0.00 Trial 257 5050 $0.00 $0.00 Trial 258 5050 $0.00 $0.00 Trial 259 50

50 $0.00 $0.00 Trial 260 5050 $0.00 $0.00 Trial 261 5050 $0.00 $0.00 Trial 262 5050 $0.00 $0.00 Trial 263 5050 $0.00 $0.00 Trial 264 5050 $0.00 $0.00 Trial 265 50

50 $0.00 $0.00 Trial 266 5050 $0.00 $0.00 Trial 267 5050 $0.00 $0.00 Trial 268 50

50 $0.00 $0.00 Trial 269 5050 $0.00 $0.00 Trial 270 5050 $0.00 $0.00 Trial 271 5050 $0.00 $0.00 Trial 272 5050 $0.00 $0.00 Trial 273 50

8/2/2019 BS Option Pricing Model

16/23

50 $0.00 $0.00 Trial 274 5050 $0.00 $0.00 Trial 275 5050 $0.00 $0.00 Trial 276 5050 $0.00 $0.00 Trial 277 5050 $0.00 $0.00 Trial 278 5050 $0.00 $0.00 Trial 279 50

50 $0.00 $0.00 Trial 280 5050 $0.00 $0.00 Trial 281 5050 $0.00 $0.00 Trial 282 5050 $0.00 $0.00 Trial 283 5050 $0.00 $0.00 Trial 284 5050 $0.00 $0.00 Trial 285 5050 $0.00 $0.00 Trial 286 5050 $0.00 $0.00 Trial 287 5050 $0.00 $0.00 Trial 288 50

50 $0.00 $0.00 Trial 289 5050 $0.00 $0.00 Trial 290 5050 $0.00 $0.00 Trial 291 50

50 $0.00 $0.00 Trial 292 5050 $0.00 $0.00 Trial 293 5050 $0.00 $0.00 Trial 294 5050 $0.00 $0.00 Trial 295 5050 $0.00 $0.00 Trial 296 5050 $0.00 $0.00 Trial 297 5050 $0.00 $0.00 Trial 298 5050 $0.00 $0.00 Trial 299 5050 $0.00 $0.00 Trial 300 50

#DIV/0! #DIV/0!#DIV/0! #DIV/0!

8/2/2019 BS Option Pricing Model

17/23

Call Put

0 0

Option Value(Call)

Option Value(Put)

$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

8/2/2019 BS Option Pricing Model

18/23

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

8/2/2019 BS Option Pricing Model

19/23

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

8/2/2019 BS Option Pricing Model

20/23

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

8/2/2019 BS Option Pricing Model

21/23

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

8/2/2019 BS Option Pricing Model

22/23

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

8/2/2019 BS Option Pricing Model

23/23

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00

$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00$0.00 $0.00