/* RSU Hedger Yaron Kretchmer address@hidden */ /* big M */ param M := 9100000 /*9099999*/ ; /* How many RSU grants */ set num_rsus := {1..4}; /* How many options */ set num_options := {1..998}; /* What's a put option? */ set put_option_params := {'cost' ,'strike_price', 'strike_date'}; /* What's an RSU? */ set rsu_params := {'value','quantity' ,'strike_date'}; /* Set of RSU's to protect */ param rsus {n in num_rsus,p in rsu_params} symbolic; param put_options {put in num_options,pop in put_option_params} symbolic ; var put_options_quantity {put in num_options} >=0 integer; var option_protects_rsu {rsu in num_rsus, option in num_options} binary ; var option_quantity_larger_than_rsu_quantity {rsu in num_rsus, option in num_options} binary ; var option_date_later_than_rsu_date {rsu in num_rsus, option in num_options} binary ; var option_covers_rsu_value {rsu in num_rsus, option in num_options} binary ; var cost_of_options ; /* Each option quantity and dates is larger than zero*/ /* Each RSU is protected by at least one option */ s.t. each_rsu_is_protected {rsu in num_rsus} : sum{option in num_options} option_protects_rsu[rsu,option] =1 ; /* Each option protects at most one RSU*/ s.t. each_option_protects_at_most_1 {option in num_options} : sum{rsu in num_rsus} option_protects_rsu[rsu,option] <=1 ; /* option_quantity_larger_than_rsu_quantity is true if the option quantity is larger than the RSU quantity */ s.t. define_option_quantity_larger_than_rsu_quantity {option in num_options,rsu in num_rsus} : -M <= put_options_quantity[option]-floor(rsus[rsu,'quantity'])-option_quantity_larger_than_rsu_quantity[rsu,option]*M<=0; /* option_date_later_than_rsu_date is true if the option date is later than the RSU date */ s.t. define_option_strike_price_greater_than_rsu_value {option in num_options,rsu in num_rsus} : (option_covers_rsu_value[rsu,option]-1)*M<= put_options[option,'strike_price']-rsus[rsu,'value']; s.t. define_option_strike_price_greater_than_rsu_value_2 {option in num_options,rsu in num_rsus} : put_options[option,'strike_price']-rsus[rsu,'value']<=option_covers_rsu_value[rsu,option]*M; s.t. define_option_date_later_than_rsu_date {option in num_options,rsu in num_rsus} : -M <= ceil((str2time(put_options[option,'strike_date'],"%m/%d/%y")-str2time(rsus[rsu,'strike_date'],"%m/%d/%y")) /86400 )-option_date_later_than_rsu_date[rsu,option]*M<=0; /* If an option protects an RSU, then its quantity is larger than the RSU quantity This constraint is of the "if-then variety", and is modeled as follows A <= B which means that if A is 1, B has to be 1, and if A is 0, B can be anything. A is "An option protects an RSU", and B is "the option quantity is larger than the RSU quantity" */ /* s.t. temp1 : option_protects_rsu[2,328] = 1; */ s.t. option_quantity_bigger_than_rsu {option in num_options,rsu in num_rsus} : option_protects_rsu[rsu,option] <= option_quantity_larger_than_rsu_quantity[rsu,option]; s.t. option_date_later_than_rsu {option in num_options,rsu in num_rsus} : option_protects_rsu[rsu,option] <= option_date_later_than_rsu_date[rsu,option]; s.t. option_strike_price_greater_than_rsu_value {option in num_options,rsu in num_rsus} : option_protects_rsu[rsu,option] <=option_covers_rsu_value[rsu,option] ; s.t. temp11 : option_protects_rsu[1,3]=1; s.t. temp12 : option_protects_rsu[2,403]=1; s.t. temp13 : option_protects_rsu[3,928]=1; s.t. temp14 : option_protects_rsu[4,929]=1; /* s.t. temp1 {option in num_options,rsu in num_rsus} : 3*option_protects_rsu[rsu,option] <= option_quantity_larger_than_rsu_quantity[rsu,option] + option_date_later_than_rsu_date[rsu,option] + option_covers_rsu_value[rsu,option] ; */ /* If an option protects an RSU, then its date is later than the RSU date. This is done using a similar formulation as above */ /* s.t. temp1 : option_protects_rsu[2,403]=1; */ s.t. cost_of_options_definition : cost_of_options =sum {option in num_options} put_options_quantity[option]*put_options[option,'cost']; minimize cost_of_options_min: cost_of_options; solve; for {option in num_options:put_options_quantity[option]>0} : printf "Option %d has quantity %d\n",option,put_options_quantity[option]; for {option in num_options, rsu in num_rsus : option_protects_rsu[rsu,option] } { printf "%d options(%d)=%f,%s protect %d rsus valued at %f and date %s. cost is %s\n",put_options_quantity[option],option,put_options[option,'strike_price'],put_options[option,'strike_date'],rsus[rsu,'quantity'],rsus[rsu,'value'],rsus[rsu,'strike_date'],put_options_quantity[option]*put_options[option,'cost']; } /* for {option in num_options} { printf 'Option Number %d = quantity %d, date %s,strike_price=%d\n' ,option,put_options_quantity[option],put_options[option,'strike_date'],put_options[option,'strike_price']; } */ for {rsu in num_rsus} { printf 'RSU Number %d = quantity %d, date %s,value=%d\n' ,rsu,rsus[rsu,'quantity'],rsus[rsu,'strike_date'],rsus[rsu,'value']; } printf "option protects RSU:\n"; for {option in num_options : sum {rsu in num_rsus} option_protects_rsu[rsu,option] > 0} { printf "option %d ", option; for {rsu in num_rsus} { printf '%d' ,option_protects_rsu[rsu,option]; } printf "\n"; } printf "option larger than RSU quantity:\n"; for {option in num_options : sum {rsu in num_rsus} option_quantity_larger_than_rsu_quantity[rsu,option] > 0} { printf "option %d ", option; for {rsu in num_rsus} { printf '%d' ,option_quantity_larger_than_rsu_quantity[rsu,option]; } printf "\n"; } printf "option_covers_rsu_value:\n"; for {option in num_options : sum {rsu in num_rsus} option_covers_rsu_value[rsu,option]*option_protects_rsu[rsu,option] > 0} { printf "option %d ", option; for {rsu in num_rsus} { printf '| %d,%f,%f,%f ' ,option_covers_rsu_value[rsu,option],-M ,put_options[option,'strike_price']-rsus[rsu,'value']-option_covers_rsu_value[rsu,option]*M,0; } printf "\n"; } printf "cost of option protection is %d\n" ,cost_of_options; data; param rsus : value quantity strike_date := 1 45.0 150 "07/15/11" 2 34.0 150 "06/17/11" 3 45.0 200 "07/15/12" 4 45.0 300 "1/1/13" ; param put_options : cost strike_price strike_date := 1 0.1 30 "4/15/11" 2 0.1 30 "4/15/11" 3 0.05 30 "4/15/11" 4 0.2 30 "4/15/11" 5 0.1 30 "4/15/11" 6 0.15 30 "4/15/11" 7 10 30 "4/15/11" 8 10 30 "4/15/11" 9 0.1 30 "4/15/11" 10 0.45 35 "4/15/11" 11 0.68 35 "4/15/11" 12 0.45 35 "4/15/11" 13 0.45 35 "4/15/11" 14 0.4 35 "4/15/11" 15 0.45 35 "4/15/11" 16 0.55 35 "4/15/11" 17 0.45 35 "4/15/11" 18 0.4 35 "4/15/11" 19 0.1 34 "4/15/11" 20 0.1 36 "4/15/11" 21 0.6 36 "4/15/11" 22 0.6 36 "4/15/11" 23 0.27 36 "4/15/11" 24 0.35 36 "4/15/11" 25 10 36 "4/15/11" 26 0.31 36 "4/15/11" 27 0.55 36 "4/15/11" 28 0.1 37 "4/15/11" 29 0.1 37 "4/15/11" 30 0.4 37 "4/15/11" 31 0.35 37 "4/15/11" 32 0.1 37 "4/15/11" 33 0.15 37 "4/15/11" 34 0.15 37 "4/15/11" 35 10 37 "4/15/11" 36 0.4 37 "4/15/11" 37 0.15 38 "4/15/11" 38 0.15 38 "4/15/11" 39 0.15 38 "4/15/11" 40 0.55 38 "4/15/11" 41 0.15 38 "4/15/11" 42 0.3 38 "4/15/11" 43 0.5 38 "4/15/11" 44 0.9 38 "4/15/11" 45 0.25 38 "4/15/11" 46 0.2 39 "4/15/11" 47 0.2 39 "4/15/11" 48 0.2 39 "4/15/11" 49 1.25 39 "4/15/11" 50 0.2 39 "4/15/11" 51 0.25 39 "4/15/11" 52 0.15 39 "4/15/11" 53 1.25 39 "4/15/11" 54 655.35 39 "4/15/11" 55 0.3 40 "4/15/11" 56 0.3 40 "4/15/11" 57 0.3 40 "4/15/11" 58 0.35 40 "4/15/11" 59 0.3 40 "4/15/11" 60 0.35 40 "4/15/11" 61 0.25 40 "4/15/11" 62 0.3 40 "4/15/11" 63 655.35 40 "4/15/11" 64 0.65 41 "4/15/11" 65 0.5 41 "4/15/11" 66 0.65 41 "4/15/11" 67 0.55 41 "4/15/11" 68 0.5 41 "4/15/11" 69 0.5 41 "4/15/11" 70 0.8 41 "4/15/11" 71 0.5 41 "4/15/11" 72 655.35 41 "4/15/11" 73 1 42 "4/15/11" 74 0.9 42 "4/15/11" 75 1.05 42 "4/15/11" 76 1 42 "4/15/11" 77 0.85 42 "4/15/11" 78 0.85 42 "4/15/11" 79 1 42 "4/15/11" 80 0.69 42 "4/15/11" 81 655.35 42 "4/15/11" 82 1.35 43 "4/15/11" 83 1.5 43 "4/15/11" 84 1.6 43 "4/15/11" 85 1.4 43 "4/15/11" 86 1.35 43 "4/15/11" 87 1.35 43 "4/15/11" 88 1.35 43 "4/15/11" 89 1.05 43 "4/15/11" 90 655.35 43 "4/15/11" 91 2 44 "4/15/11" 92 2 44 "4/15/11" 93 2 44 "4/15/11" 94 2 44 "4/15/11" 95 2 44 "4/15/11" 96 2 44 "4/15/11" 97 1.6 44 "4/15/11" 98 4.3 44 "4/15/11" 99 655.35 44 "4/15/11" 100 3 45 "4/15/11" 101 3 45 "4/15/11" 102 2.8 45 "4/15/11" 103 2.75 45 "4/15/11" 104 2.8 45 "4/15/11" 105 2.75 45 "4/15/11" 106 3 45 "4/15/11" 107 4.8 45 "4/15/11" 108 655.35 45 "4/15/11" 109 3.9 46 "4/15/11" 110 3.9 46 "4/15/11" 111 3.9 46 "4/15/11" 112 3.9 46 "4/15/11" 113 3.9 46 "4/15/11" 114 3.9 46 "4/15/11" 115 3.2 46 "4/15/11" 116 2.65 46 "4/15/11" 117 655.35 46 "4/15/11" 118 4.9 47 "4/15/11" 119 5.1 47 "4/15/11" 120 5 47 "4/15/11" 121 4.9 47 "4/15/11" 122 4.9 47 "4/15/11" 123 4.9 47 "4/15/11" 124 3.3 47 "4/15/11" 125 5 47 "4/15/11" 126 655.35 47 "4/15/11" 127 5.8 48 "4/15/11" 128 5.8 48 "4/15/11" 129 5.8 48 "4/15/11" 130 5.8 48 "4/15/11" 131 5.8 48 "4/15/11" 132 5.8 48 "4/15/11" 133 5.8 48 "4/15/11" 134 7.2 48 "4/15/11" 135 655.35 48 "4/15/11" 136 10 49 "4/15/11" 137 8 50 "4/15/11" 138 8 50 "4/15/11" 139 8 50 "4/15/11" 140 10 50 "4/15/11" 141 8 50 "4/15/11" 142 8.1 50 "4/15/11" 143 10 50 "4/15/11" 144 10 50 "4/15/11" 145 655.35 50 "4/15/11" 146 0.15 30 "5/20/11" 147 0.15 30 "5/20/11" 148 0.15 30 "5/20/11" 149 0.15 30 "5/20/11" 150 0.15 30 "5/20/11" 151 10 30 "5/20/11" 152 10 30 "5/20/11" 153 0.65 35 "5/20/11" 154 0.35 35 "5/20/11" 155 0.65 35 "5/20/11" 156 0.35 35 "5/20/11" 157 0.35 35 "5/20/11" 158 0.35 35 "5/20/11" 159 0.7 35 "5/20/11" 160 10 35 "5/20/11" 161 655.35 35 "5/20/11" 162 0.45 36 "5/20/11" 163 0.45 36 "5/20/11" 164 0.45 36 "5/20/11" 165 0.85 36 "5/20/11" 166 0.45 36 "5/20/11" 167 0.45 36 "5/20/11" 168 10 36 "5/20/11" 169 10 36 "5/20/11" 170 655.35 36 "5/20/11" 171 0.65 37 "5/20/11" 172 1.05 37 "5/20/11" 173 0.85 37 "5/20/11" 174 0.6 37 "5/20/11" 175 0.6 37 "5/20/11" 176 0.6 37 "5/20/11" 177 1.05 37 "5/20/11" 178 10 37 "5/20/11" 179 655.35 37 "5/20/11" 180 0.8 38 "5/20/11" 181 0.8 38 "5/20/11" 182 0.8 38 "5/20/11" 183 0.8 38 "5/20/11" 184 0.8 38 "5/20/11" 185 0.8 38 "5/20/11" 186 0.7 38 "5/20/11" 187 10 38 "5/20/11" 188 655.35 38 "5/20/11" 189 1 39 "5/20/11" 190 1 39 "5/20/11" 191 1.05 39 "5/20/11" 192 1.05 39 "5/20/11" 193 1 39 "5/20/11" 194 1 39 "5/20/11" 195 0.9 39 "5/20/11" 196 1.05 39 "5/20/11" 197 655.35 39 "5/20/11" 198 1.25 40 "5/20/11" 199 1.25 40 "5/20/11" 200 1.25 40 "5/20/11" 201 1.95 40 "5/20/11" 202 1.25 40 "5/20/11" 203 1.25 40 "5/20/11" 204 1.65 40 "5/20/11" 205 10 40 "5/20/11" 206 655.35 40 "5/20/11" 207 1.76 41 "5/20/11" 208 1.76 41 "5/20/11" 209 1.6 41 "5/20/11" 210 1.7 41 "5/20/11" 211 1.6 41 "5/20/11" 212 2.6 41 "5/20/11" 213 1.4 41 "5/20/11" 214 1.5 41 "5/20/11" 215 655.35 41 "5/20/11" 216 2 42 "5/20/11" 217 2 42 "5/20/11" 218 2 42 "5/20/11" 219 2 42 "5/20/11" 220 2.1 42 "5/20/11" 221 2 42 "5/20/11" 222 2 42 "5/20/11" 223 1.9 42 "5/20/11" 224 655.35 42 "5/20/11" 225 2.7 43 "5/20/11" 226 2.7 43 "5/20/11" 227 2.7 43 "5/20/11" 228 2.7 43 "5/20/11" 229 2.5 43 "5/20/11" 230 2.5 43 "5/20/11" 231 2.5 43 "5/20/11" 232 2.7 43 "5/20/11" 233 655.35 43 "5/20/11" 234 3.1 44 "5/20/11" 235 3.1 44 "5/20/11" 236 3.1 44 "5/20/11" 237 3.1 44 "5/20/11" 238 3.1 44 "5/20/11" 239 3.1 44 "5/20/11" 240 2.55 44 "5/20/11" 241 3.3 44 "5/20/11" 242 655.35 44 "5/20/11" 243 3.7 45 "5/20/11" 244 3.7 45 "5/20/11" 245 3.7 45 "5/20/11" 246 3.7 45 "5/20/11" 247 3.7 45 "5/20/11" 248 3.7 45 "5/20/11" 249 3.2 45 "5/20/11" 250 3.2 45 "5/20/11" 251 655.35 45 "5/20/11" 252 4.5 46 "5/20/11" 253 4.5 46 "5/20/11" 254 4.5 46 "5/20/11" 255 4.5 46 "5/20/11" 256 4.5 46 "5/20/11" 257 4.5 46 "5/20/11" 258 10 46 "5/20/11" 259 10 46 "5/20/11" 260 655.35 46 "5/20/11" 261 5.3 47 "5/20/11" 262 5.3 47 "5/20/11" 263 5.3 47 "5/20/11" 264 5.3 47 "5/20/11" 265 5.3 47 "5/20/11" 266 5.3 47 "5/20/11" 267 10 47 "5/20/11" 268 10 47 "5/20/11" 269 655.35 47 "5/20/11" 270 6.1 48 "5/20/11" 271 6.1 48 "5/20/11" 272 6.1 48 "5/20/11" 273 6.1 48 "5/20/11" 274 6.1 48 "5/20/11" 275 6.1 48 "5/20/11" 276 10 48 "5/20/11" 277 10 48 "5/20/11" 278 655.35 48 "5/20/11" 279 10 49 "5/20/11" 280 8 50 "5/20/11" 281 8 50 "5/20/11" 282 8 50 "5/20/11" 283 8 50 "5/20/11" 284 8 50 "5/20/11" 285 10 50 "5/20/11" 286 10 50 "5/20/11" 287 0.05 15 "6/17/11" 288 0.05 15 "6/17/11" 289 0.05 15 "6/17/11" 290 0.05 15 "6/17/11" 291 0.05 15 "6/17/11" 292 0.1 15 "6/17/11" 293 10 15 "6/17/11" 294 10 15 "6/17/11" 295 0.1 15 "6/17/11" 296 0.25 17.5 "6/17/11" 297 0.25 17.5 "6/17/11" 298 0.05 17.5 "6/17/11" 299 0.05 17.5 "6/17/11" 300 0.05 17.5 "6/17/11" 301 0.1 17.5 "6/17/11" 302 10 17.5 "6/17/11" 303 10 17.5 "6/17/11" 304 0.1 17.5 "6/17/11" 305 0.05 20 "6/17/11" 306 0.05 20 "6/17/11" 307 0.05 20 "6/17/11" 308 0.05 20 "6/17/11" 309 0.05 20 "6/17/11" 310 0.1 20 "6/17/11" 311 10 20 "6/17/11" 312 10 20 "6/17/11" 313 0.1 20 "6/17/11" 314 0.1 22.5 "6/17/11" 315 0.1 22.5 "6/17/11" 316 0.1 22.5 "6/17/11" 317 0.4 22.5 "6/17/11" 318 0.1 22.5 "6/17/11" 319 0.45 22.5 "6/17/11" 320 10 22.5 "6/17/11" 321 0.4 22.5 "6/17/11" 322 0.15 22.5 "6/17/11" 323 0.1 25 "6/17/11" 324 0.51 25 "6/17/11" 325 0.15 25 "6/17/11" 326 1.7 25 "6/17/11" 327 0.1 25 "6/17/11" 328 0.25 25 "6/17/11" 329 0.15 25 "6/17/11" 330 0.95 25 "6/17/11" 331 0.1 25 "6/17/11" 332 0.2 26 "6/17/11" 333 0.1 26 "6/17/11" 334 0.2 26 "6/17/11" 335 1.35 26 "6/17/11" 336 1.35 26 "6/17/11" 337 0.1 26 "6/17/11" 338 0.2 26 "6/17/11" 339 2.2 26 "6/17/11" 340 0.1 26 "6/17/11" 341 0.2 27 "6/17/11" 342 0.15 27 "6/17/11" 343 0.55 27 "6/17/11" 344 0.6 27 "6/17/11" 345 0.55 27 "6/17/11" 346 0.35 27 "6/17/11" 347 0.2 27 "6/17/11" 348 10 27 "6/17/11" 349 0.37 27 "6/17/11" 350 0.15 28 "6/17/11" 351 0.2 28 "6/17/11" 352 0.85 28 "6/17/11" 353 0.15 28 "6/17/11" 354 0.15 28 "6/17/11" 355 0.25 28 "6/17/11" 356 0.25 28 "6/17/11" 357 2.3 28 "6/17/11" 358 0.7 28 "6/17/11" 359 0.3 29 "6/17/11" 360 0.3 29 "6/17/11" 361 0.4 29 "6/17/11" 362 1 29 "6/17/11" 363 0.35 29 "6/17/11" 364 1.5 29 "6/17/11" 365 0.3 29 "6/17/11" 366 0.55 29 "6/17/11" 367 0.2 29 "6/17/11" 368 0.2 30 "6/17/11" 369 0.4 30 "6/17/11" 370 0.3 30 "6/17/11" 371 0.65 30 "6/17/11" 372 0.4 30 "6/17/11" 373 0.25 30 "6/17/11" 374 0.35 30 "6/17/11" 375 0.4 30 "6/17/11" 376 0.2 30 "6/17/11" 377 0.25 31 "6/17/11" 378 0.3 31 "6/17/11" 379 0.25 31 "6/17/11" 380 1.15 31 "6/17/11" 381 0.25 31 "6/17/11" 382 0.65 31 "6/17/11" 383 0.45 31 "6/17/11" 384 0.85 31 "6/17/11" 385 0.7 31 "6/17/11" 386 0.35 32 "6/17/11" 387 0.65 32 "6/17/11" 388 0.8 32 "6/17/11" 389 0.7 32 "6/17/11" 390 0.7 32 "6/17/11" 391 0.95 32 "6/17/11" 392 0.35 32 "6/17/11" 393 1.05 32 "6/17/11" 394 0.9 32 "6/17/11" 395 0.7 33 "6/17/11" 396 1.25 33 "6/17/11" 397 0.88 33 "6/17/11" 398 0.85 33 "6/17/11" 399 2.05 33 "6/17/11" 400 0.65 33 "6/17/11" 401 0.7 33 "6/17/11" 402 2.05 33 "6/17/11" 403 0.45 33 "6/17/11" 404 0.85 34 "6/17/11" 405 1.15 34 "6/17/11" 406 1.05 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