Hi All After struggling with the problem below for a couple of days, I thought of asking for help- My big-M formulation is behaving in a way that i can't understand.
The problem is a stock hedging problem, with one of the component of a correct hedge being that the strike price of the option is >= the value of the stock. The enclosde model should have no solution, since I'm fixing the variable such that the price of the option is does not follow the constaint above. When my big-M = 9099999, I get the correct "No primal feasible" answer. But when I increase M to 9100000, a succesful solution is found, which is not correct. Are there any upper limits to the size of big-M that can be used? Thanks Yaron
/* RSU Hedger Yaron Kretchmer [email protected] */ /* 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" 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