En este ejercicio se eligio la accion Tesla, Inc. (TSLA), del indice S&P 500, por su alta liquidez en el mercado de opciones y su elevada volatilidad implicita, lo que permite observar con claridad el efecto de la convexidad en derivados financieros.
El objetivo es analizar una opcion call con vencimiento cercano a un ano, simular escenarios mensuales de precio, construir las tablas y figuras de convexidad, y calcular las principales griegas (delta, gamma, theta, vega y rho).
| Parametro | Valor |
|---|---|
| Subyacente | TSLA - Tesla, Inc. |
| Precio Spot (S0) | $400.62 |
| Strike (K) | $400 |
| Vencimiento (T) | 252 dias habiles |
| Tasa libre de riesgo (r) | 3.691% |
| Volatilidad implicita | 0.55 |
En este ejercicio se adopta el ano comercial de 252 dias habiles, estandar en finanzas de mercado. Una quincena comercial equivale a maximo 11 dias habiles y 30 dias calendario corresponden a aproximadamente 22 dias habiles. Esto asegura que el valor temporal de la opcion refleje unicamente los dias en que el mercado opera activamente.
La volatilidad implicita de referencia es 55% al vencimiento final. Se aplica un decremento lineal de 2% por mes hacia la fecha inicial, dando como resultado volatilidades que van del 33% (mayo 2026) al 55% (abril 2027).
La tasa libre de riesgo se toma de la curva CME Term SOFR publicada el 16/04/2026: SOFR 12M = 3.691%.
T = 21 dias | r = 3.691% | sigma = 33%
| S (USD) | Call BS | Lineal | Convexidad |
|---|---|---|---|
| $120 | 0.000 | 0.000 | 0.000 |
| $196 | 0.000 | 0.000 | 0.000 |
| $272 | 0.000 | 0.000 | 0.000 |
| $348 | 1.218 | 0.000 | 1.218 |
| $424 | 31.372 | 28.712 | 2.660 |
| $500 | 101.353 | 69.624 | 31.729 |
| $576 | 177.229 | 110.535 | 66.694 |
| $652 | 253.228 | 151.447 | 101.781 |
| $728 | 329.228 | 192.359 | 136.870 |
| $804 | 405.228 | 233.270 | 171.958 |
| $880 | 481.228 | 274.182 | 207.047 |
| $956 | 557.228 | 315.093 | 242.135 |
| $1032 | 633.228 | 356.005 | 277.224 |
T = 42 dias | r = 3.691% | sigma = 35%
| S (USD) | Call BS | Lineal | Convexidad |
|---|---|---|---|
| $120 | 0.000 | 0.000 | 0.000 |
| $196 | 0.000 | 0.000 | 0.000 |
| $272 | 0.057 | 0.000 | 0.057 |
| $348 | 5.028 | 0.000 | 5.028 |
| $424 | 38.956 | 37.155 | 1.800 |
| $500 | 103.915 | 78.946 | 24.969 |
| $576 | 178.555 | 120.736 | 57.819 |
| $652 | 254.458 | 162.526 | 91.932 |
| $728 | 330.453 | 204.316 | 126.137 |
| $804 | 406.453 | 246.106 | 160.347 |
| $880 | 482.453 | 287.897 | 194.557 |
| $956 | 558.453 | 329.687 | 228.766 |
| $1032 | 634.453 | 371.477 | 262.976 |
T = 63 dias | r = 3.691% | sigma = 37%
| S (USD) | Call BS | Lineal | Convexidad |
|---|---|---|---|
| $120 | 0.000 | 0.000 | 0.000 |
| $196 | 0.001 | 0.000 | 0.001 |
| $272 | 0.468 | 0.000 | 0.468 |
| $348 | 9.745 | 2.101 | 7.644 |
| $424 | 46.049 | 44.655 | 1.394 |
| $500 | 107.776 | 87.208 | 20.568 |
| $576 | 180.381 | 129.761 | 50.620 |
| $652 | 255.776 | 172.315 | 83.461 |
| $728 | 331.687 | 214.868 | 116.819 |
| $804 | 407.676 | 257.422 | 150.254 |
| $880 | 483.674 | 299.975 | 183.699 |
| $956 | 559.674 | 342.529 | 217.145 |
| $1032 | 635.674 | 385.082 | 250.592 |
T = 84 dias | r = 3.691% | sigma = 39%
| S (USD) | Call BS | Lineal | Convexidad |
|---|---|---|---|
| $120 | 0.000 | 0.000 | 0.000 |
| $196 | 0.016 | 0.000 | 0.016 |
| $272 | 1.487 | 0.000 | 1.487 |
| $348 | 14.879 | 8.541 | 6.339 |
| $424 | 52.938 | 51.793 | 1.145 |
| $500 | 112.498 | 95.045 | 17.453 |
| $576 | 182.973 | 138.297 | 44.676 |
| $652 | 257.409 | 181.549 | 75.860 |
| $728 | 333.013 | 224.801 | 108.211 |
| $804 | 408.919 | 268.054 | 140.865 |
| $880 | 484.897 | 311.306 | 173.592 |
| $956 | 560.893 | 354.558 | 206.335 |
| $1032 | 636.891 | 397.810 | 239.081 |
T = 105 dias | r = 3.691% | sigma = 41%
| S (USD) | Call BS | Lineal | Convexidad |
|---|---|---|---|
| $120 | 0.000 | 0.000 | 0.000 |
| $196 | 0.095 | 0.000 | 0.095 |
| $272 | 3.163 | 0.000 | 3.163 |
| $348 | 20.274 | 14.864 | 5.410 |
| $424 | 59.750 | 58.778 | 0.972 |
| $500 | 117.810 | 102.691 | 15.119 |
| $576 | 186.347 | 146.604 | 39.742 |
| $652 | 259.561 | 190.518 | 69.043 |
| $728 | 334.589 | 234.431 | 100.158 |
| $804 | 410.263 | 278.345 | 131.919 |
| $880 | 486.156 | 322.258 | 163.898 |
| $956 | 562.122 | 366.171 | 195.950 |
| $1032 | 638.110 | 410.085 | 228.025 |
T = 126 dias | r = 3.691% | sigma = 43%
| S (USD) | Call BS | Lineal | Convexidad |
|---|---|---|---|
| $120 | 0.001 | 0.000 | 0.001 |
| $196 | 0.319 | 0.000 | 0.319 |
| $272 | 5.445 | 0.000 | 5.445 |
| $348 | 25.862 | 21.153 | 4.709 |
| $424 | 66.549 | 65.705 | 0.844 |
| $500 | 123.554 | 110.258 | 13.296 |
| $576 | 190.422 | 154.810 | 35.612 |
| $652 | 262.332 | 199.362 | 62.970 |
| $728 | 336.575 | 243.915 | 92.661 |
| $804 | 411.838 | 288.467 | 123.372 |
| $880 | 487.532 | 333.019 | 154.513 |
| $956 | 563.406 | 377.571 | 185.834 |
| $1032 | 639.353 | 422.124 | 217.229 |
T = 147 dias | r = 3.691% | sigma = 45%
| S (USD) | Call BS | Lineal | Convexidad |
|---|---|---|---|
| $120 | 0.005 | 0.000 | 0.005 |
| $196 | 0.772 | 0.000 | 0.772 |
| $272 | 8.254 | 0.000 | 8.254 |
| $348 | 31.606 | 27.449 | 4.158 |
| $424 | 73.370 | 72.627 | 0.743 |
| $500 | 129.634 | 117.805 | 11.830 |
| $576 | 195.103 | 162.983 | 32.121 |
| $652 | 265.739 | 208.160 | 57.579 |
| $728 | 339.078 | 253.338 | 85.739 |
| $804 | 413.774 | 298.516 | 115.257 |
| $880 | 489.138 | 343.694 | 145.443 |
| $956 | 564.826 | 388.872 | 175.954 |
| $1032 | 640.674 | 434.050 | 206.623 |
T = 168 dias | r = 3.691% | sigma = 47%
| S (USD) | Call BS | Lineal | Convexidad |
|---|---|---|---|
| $120 | 0.024 | 0.000 | 0.024 |
| $196 | 1.514 | 0.000 | 1.514 |
| $272 | 11.512 | 0.000 | 11.512 |
| $348 | 37.485 | 33.773 | 3.711 |
| $424 | 80.232 | 79.570 | 0.663 |
| $500 | 135.987 | 125.366 | 10.621 |
| $576 | 200.301 | 171.162 | 29.139 |
| $652 | 269.756 | 216.958 | 52.798 |
| $728 | 342.147 | 262.754 | 79.393 |
| $804 | 416.169 | 308.550 | 107.618 |
| $880 | 491.084 | 354.347 | 136.737 |
| $956 | 566.486 | 400.143 | 166.344 |
| $1032 | 642.155 | 445.939 | 196.216 |
T = 189 dias | r = 3.691% | sigma = 49%
| S (USD) | Call BS | Lineal | Convexidad |
|---|---|---|---|
| $120 | 0.075 | 0.000 | 0.075 |
| $196 | 2.580 | 0.000 | 2.580 |
| $272 | 15.151 | 0.000 | 15.151 |
| $348 | 43.480 | 40.139 | 3.341 |
| $424 | 87.146 | 86.550 | 0.596 |
| $500 | 142.568 | 132.960 | 9.607 |
| $576 | 205.939 | 179.371 | 26.568 |
| $652 | 274.335 | 225.782 | 48.553 |
| $728 | 345.792 | 272.193 | 73.599 |
| $804 | 419.082 | 318.604 | 100.478 |
| $880 | 493.460 | 365.014 | 128.445 |
| $956 | 568.483 | 411.425 | 157.058 |
| $1032 | 643.891 | 457.836 | 186.056 |
T = 210 dias | r = 3.691% | sigma = 51%
| S (USD) | Call BS | Lineal | Convexidad |
|---|---|---|---|
| $120 | 0.185 | 0.000 | 0.185 |
| $196 | 3.984 | 0.000 | 3.984 |
| $272 | 19.114 | 0.000 | 19.114 |
| $348 | 49.581 | 46.551 | 3.030 |
| $424 | 94.116 | 93.575 | 0.541 |
| $500 | 149.344 | 140.600 | 8.744 |
| $576 | 211.956 | 187.624 | 24.332 |
| $652 | 279.420 | 234.648 | 44.772 |
| $728 | 349.994 | 281.673 | 68.322 |
| $804 | 422.537 | 328.697 | 93.840 |
| $880 | 496.324 | 375.721 | 120.603 |
| $956 | 570.898 | 422.746 | 148.152 |
| $1032 | 645.971 | 469.770 | 176.201 |
T = 231 dias | r = 3.691% | sigma = 53%
| S (USD) | Call BS | Lineal | Convexidad |
|---|---|---|---|
| $120 | 0.383 | 0.000 | 0.383 |
| $196 | 5.719 | 0.000 | 5.719 |
| $272 | 23.353 | 5.373 | 17.980 |
| $348 | 55.775 | 53.012 | 2.763 |
| $424 | 101.143 | 100.650 | 0.493 |
| $500 | 156.288 | 148.289 | 7.999 |
| $576 | 218.298 | 195.927 | 22.371 |
| $652 | 284.960 | 243.566 | 41.394 |
| $728 | 354.721 | 291.204 | 63.517 |
| $804 | 426.534 | 338.843 | 87.692 |
| $880 | 499.707 | 386.481 | 113.226 |
| $956 | 573.784 | 434.119 | 139.665 |
| $1032 | 648.466 | 481.758 | 166.708 |
T = 252 dias | r = 3.691% | sigma = 55%
| S (USD) | Call BS | Lineal | Convexidad |
|---|---|---|---|
| $120 | 0.699 | 0.000 | 0.699 |
| $196 | 7.773 | 0.000 | 7.773 |
| $272 | 27.828 | 11.267 | 16.562 |
| $348 | 62.053 | 59.521 | 2.532 |
| $424 | 108.227 | 107.775 | 0.452 |
| $500 | 163.379 | 156.029 | 7.349 |
| $576 | 224.922 | 204.284 | 20.638 |
| $652 | 290.902 | 252.538 | 38.364 |
| $728 | 359.932 | 300.792 | 59.140 |
| $804 | 431.054 | 349.047 | 82.008 |
| $880 | 503.616 | 397.301 | 106.315 |
| $956 | 577.174 | 445.555 | 131.619 |
| $1032 | 651.425 | 493.809 | 157.615 |
T = 21 dias | sigma = 33%
| S (USD) | Delta | Gamma | Theta | Vega | Rho |
|---|---|---|---|---|---|
| $120 | 0.0000 | 0.000000 | 0.0000 | 0.0000 | 0.0000 |
| $212 | 0.0000 | 0.000000 | 0.0000 | 0.0000 | 0.0000 |
| $304 | 0.0025 | 0.000273 | -0.0056 | 0.0069 | 0.0006 |
| $396 | 0.4898 | 0.010572 | -0.3846 | 0.4559 | 0.1502 |
| $488 | 0.9849 | 0.000820 | -0.0995 | 0.0537 | 0.3260 |
| $580 | 1.0000 | 0.000003 | -0.0586 | 0.0002 | 0.3323 |
| $672 | 1.0000 | 0.000000 | -0.0584 | 0.0000 | 0.3323 |
| $764 | 1.0000 | 0.000000 | -0.0584 | 0.0000 | 0.3323 |
| $856 | 1.0000 | 0.000000 | -0.0584 | 0.0000 | 0.3323 |
| $948 | 1.0000 | 0.000000 | -0.0584 | 0.0000 | 0.3323 |
| $1040 | 1.0000 | 0.000000 | -0.0584 | 0.0000 | 0.3323 |
T = 126 dias | sigma = 43%
| S (USD) | Delta | Gamma | Theta | Vega | Rho |
|---|---|---|---|---|---|
| $120 | 0.0001 | 0.000010 | -0.0001 | 0.0003 | 0.0001 |
| $212 | 0.0304 | 0.001067 | -0.0184 | 0.1031 | 0.0288 |
| $304 | 0.2451 | 0.003402 | -0.1246 | 0.6760 | 0.3144 |
| $396 | 0.5713 | 0.003260 | -0.2135 | 1.0992 | 0.8845 |
| $488 | 0.8070 | 0.001847 | -0.2024 | 0.9456 | 1.4003 |
| $580 | 0.9243 | 0.000808 | -0.1498 | 0.5846 | 1.7100 |
| $672 | 0.9725 | 0.000310 | -0.1058 | 0.3007 | 1.8590 |
| $764 | 0.9904 | 0.000111 | -0.0801 | 0.1392 | 1.9225 |
| $856 | 0.9967 | 0.000038 | -0.0674 | 0.0606 | 1.9478 |
| $948 | 0.9989 | 0.000013 | -0.0617 | 0.0255 | 1.9575 |
| $1040 | 0.9996 | 0.000005 | -0.0592 | 0.0105 | 1.9612 |
T = 252 dias | sigma = 55%
| S (USD) | Delta | Gamma | Theta | Vega | Rho |
|---|---|---|---|---|---|
| $120 | 0.0324 | 0.001098 | -0.0100 | 0.0870 | 0.0319 |
| $212 | 0.2083 | 0.002460 | -0.0713 | 0.6081 | 0.3337 |
| $304 | 0.4377 | 0.002357 | -0.1443 | 1.1980 | 0.9245 |
| $396 | 0.6270 | 0.001738 | -0.1868 | 1.4991 | 1.5826 |
| $488 | 0.7592 | 0.001160 | -0.1975 | 1.5199 | 2.1629 |
| $580 | 0.8456 | 0.000745 | -0.1888 | 1.3786 | 2.6214 |
| $672 | 0.9007 | 0.000473 | -0.1715 | 1.1736 | 2.9643 |
| $764 | 0.9356 | 0.000300 | -0.1521 | 0.9620 | 3.2137 |
| $856 | 0.9578 | 0.000191 | -0.1338 | 0.7708 | 3.3928 |
| $948 | 0.9720 | 0.000123 | -0.1180 | 0.6091 | 3.5206 |
| $1040 | 0.9812 | 0.000080 | -0.1050 | 0.4775 | 3.6119 |