En este ejercicio se eligió la acción Tesla, Inc. (TSLA), integrante del índice S&P 500, por ser una de las empresas de mayor impacto en los sectores de movilidad eléctrica, energía renovable e inteligencia artificial aplicada a vehículos autónomos. Tesla presenta alta liquidez en el mercado de opciones y una volatilidad implícita significativa, lo que permite observar con claridad el efecto de la convexidad en derivados financieros.
El objetivo de este ejercicio es aplicar herramientas de ingeniería financiera para analizar una opción de compra (call) sobre TSLA con vencimiento cercano a un año, simulando escenarios de precios y volatilidad, construyendo tablas y figuras de convexidad para cada vencimiento mensual, y calculando las principales sensibilidades conocidas como griegas (delta, gamma, theta, vega y rho).
Con fecha de análisis del 17 de abril de 2026, TSLA cotizó en $400.62 USD por acción. Se seleccionó una opción call europea con vencimiento al 17 de abril de 2027, equivalente a un año comercial de 252 días hábiles bursátiles. El modelo de valoración utilizado es el de Black-Scholes-Merton (BSM), con la tasa libre de riesgo interpolada de la curva CME Term SOFR publicada el 16 de abril de 2026, y una volatilidad implícita de referencia del 55%, característica de opciones ATM a largo plazo en TSLA.
La convexidad de una opción refleja que su precio es una función no lineal (convexa) del precio del subyacente. Esta propiedad, conocida como gamma positiva, beneficia al tenedor de la opción: las ganancias crecen más de lo que indica la aproximación lineal (delta), y las pérdidas son menores. Esta asimetría es especialmente pronunciada en acciones de alta volatilidad como Tesla.
| Parametro | Valor |
|---|---|
| Subyacente | TSLA - Tesla, Inc. |
| Precio Spot (S0) | $400.62 |
| Strike (K) | $400.00 |
| Tipo de opcion | Call Europea |
| Vencimiento (T) | 252 dias habiles (~1 ano comercial) |
| Tasa libre de riesgo (r) | 3.691% (SOFR 12M interpolado) |
| Volatilidad implicita (s) | 55% (referencia implicita final) |
| Fecha de analisis | 17/04/2026 |
| Fecha de vencimiento | 17/04/2027 |
| Modelo de valoracion | Black-Scholes-Merton |
| Mes | Días.Hábiles | SOFR…. |
|---|---|---|
| May 2026 | 21 | 3.6610 |
| Jun 2026 | 42 | 3.6680 |
| Jul 2026 | 63 | 3.6750 |
| Ago 2026 | 84 | 3.6793 |
| Sep 2026 | 105 | 3.6837 |
| Oct 2026 | 126 | 3.6880 |
| Nov 2026 | 147 | 3.6885 |
| Dic 2026 | 168 | 3.6890 |
| Ene 2027 | 189 | 3.6895 |
| Feb 2027 | 210 | 3.6900 |
| Mar 2027 | 231 | 3.6905 |
| Abr 2027 | 252 | 3.6910 |
En este ejercicio se adopta el año comercial de 252 días hábiles, estándar en finanzas de mercado. Esta convención asegura que los cálculos reflejen únicamente los días en los que el mercado opera, evitando subestimar el paso efectivo del tiempo y el riesgo asociado. Por tanto:
La tasa libre de riesgo para cada vencimiento se obtiene por interpolación lineal entre los puntos de la curva CME Term SOFR publicada el 16 de abril de 2026: 1M = 3.661%, 3M = 3.675%, 6M = 3.688%, 12M = 3.691%.
La volatilidad implícita de referencia es 55% (punto final, abril 2027). Se aplica un decremento lineal de 2% por mes hacia la fecha inicial, reflejando la estructura temporal de la volatilidad de TSLA.
| Mes | Vencimiento.No. | Días.Hábiles | Volatilidad…. |
|---|---|---|---|
| May 2026 | 1 | 21 | 33 |
| Jun 2026 | 2 | 42 | 35 |
| Jul 2026 | 3 | 63 | 37 |
| Ago 2026 | 4 | 84 | 39 |
| Sep 2026 | 5 | 105 | 41 |
| Oct 2026 | 6 | 126 | 43 |
| Nov 2026 | 7 | 147 | 45 |
| Dic 2026 | 8 | 168 | 47 |
| Ene 2027 | 9 | 189 | 49 |
| Feb 2027 | 10 | 210 | 51 |
| Mar 2027 | 11 | 231 | 53 |
| Abr 2027 | 12 | 252 | 55 |
La simulación muestra tres posibles trayectorias del precio de TSLA desde el 17/04/2026 hasta el 17/04/2027:
El rango de precios simulados va de $122 a $1050, representando los percentiles 2.5% y 97.5% de la distribución log-normal de TSLA a 1 año. Se evalúa cada $2 con un total de 467 puntos.
T = 21 dias habiles (0.0833 anos) | r = 3.661% | sigma = 33%
| S (USD) | Call BS (USD) | Lineal (USD) | Convexidad (USD) |
|---|---|---|---|
| $120.00 | $0.0000 | $0.0000 | $0.0000 |
| $182.00 | $0.0000 | $0.0000 | $0.0000 |
| $244.00 | $0.0000 | $0.0000 | $0.0000 |
| $306.00 | $0.0271 | $0.0000 | $0.0271 |
| $368.00 | $4.0594 | $0.0000 | $4.0594 |
| $430.00 | $36.0312 | $31.9340 | $4.0972 |
| $492.00 | $93.4215 | $65.3028 | $28.1187 |
| $554.00 | $155.2216 | $98.6716 | $56.5501 |
| $616.00 | $217.2185 | $132.0404 | $85.1781 |
| $678.00 | $279.2185 | $165.4091 | $113.8094 |
| $740.00 | $341.2185 | $198.7779 | $142.4406 |
| $802.00 | $403.2185 | $232.1467 | $171.0718 |
| $864.00 | $465.2185 | $265.5154 | $199.7030 |
| $926.00 | $527.2185 | $298.8842 | $228.3343 |
| $988.00 | $589.2185 | $332.2530 | $256.9655 |
| $1050.00 | $651.2185 | $365.6217 | $285.5967 |
T = 42 dias habiles (0.1667 anos) | r = 3.668% | sigma = 35%
| S (USD) | Call BS (USD) | Lineal (USD) | Convexidad (USD) |
|---|---|---|---|
| $120.00 | $0.0000 | $0.0000 | $0.0000 |
| $182.00 | $0.0000 | $0.0000 | $0.0000 |
| $244.00 | $0.0036 | $0.0000 | $0.0036 |
| $306.00 | $0.6549 | $0.0000 | $0.6549 |
| $368.00 | $10.1253 | $6.3585 | $3.7667 |
| $430.00 | $43.2418 | $40.4439 | $2.7979 |
| $492.00 | $96.3223 | $74.5294 | $21.7929 |
| $554.00 | $156.6674 | $108.6148 | $48.0526 |
| $616.00 | $218.4593 | $142.7002 | $75.7591 |
| $678.00 | $280.4395 | $176.7856 | $103.6539 |
| $740.00 | $342.4380 | $210.8710 | $131.5669 |
| $802.00 | $404.4379 | $244.9565 | $159.4814 |
| $864.00 | $466.4379 | $279.0419 | $187.3960 |
| $926.00 | $528.4379 | $313.1273 | $215.3106 |
| $988.00 | $590.4379 | $347.2127 | $243.2252 |
| $1050.00 | $652.4379 | $381.2981 | $271.1397 |
T = 63 dias habiles (0.25 anos) | r = 3.675% | sigma = 37%
| S (USD) | Call BS (USD) | Lineal (USD) | Convexidad (USD) |
|---|---|---|---|
| $120.00 | $0.0000 | $0.0000 | $0.0000 |
| $182.00 | $0.0001 | $0.0000 | $0.0001 |
| $244.00 | $0.0782 | $0.0000 | $0.0782 |
| $306.00 | $2.3639 | $0.0000 | $2.3639 |
| $368.00 | $16.2223 | $13.2945 | $2.9278 |
| $430.00 | $50.1777 | $48.0039 | $2.1738 |
| $492.00 | $100.5300 | $82.7132 | $17.8167 |
| $554.00 | $158.8603 | $117.4226 | $41.4377 |
| $616.00 | $219.9185 | $152.1319 | $67.7865 |
| $678.00 | $281.7096 | $186.8413 | $94.8683 |
| $740.00 | $343.6677 | $221.5507 | $122.1170 |
| $802.00 | $405.6599 | $256.2600 | $149.3998 |
| $864.00 | $467.6585 | $290.9694 | $176.6891 |
| $926.00 | $529.6582 | $325.6787 | $203.9795 |
| $988.00 | $591.6582 | $360.3881 | $231.2701 |
| $1050.00 | $653.6582 | $395.0975 | $258.5607 |
T = 84 dias habiles (0.3333 anos) | r = 3.679% | sigma = 39%
| S (USD) | Call BS (USD) | Lineal (USD) | Convexidad (USD) |
|---|---|---|---|
| $120.00 | $0.0000 | $0.0000 | $0.0000 |
| $182.00 | $0.0044 | $0.0000 | $0.0044 |
| $244.00 | $0.4017 | $0.0000 | $0.4017 |
| $306.00 | $4.9879 | $0.0000 | $4.9879 |
| $368.00 | $22.3247 | $19.9175 | $2.4072 |
| $430.00 | $56.9859 | $55.1980 | $1.7879 |
| $492.00 | $105.5328 | $90.4785 | $15.0543 |
| $554.00 | $161.9424 | $125.7589 | $36.1835 |
| $616.00 | $221.8869 | $161.0394 | $60.8475 |
| $678.00 | $283.1931 | $196.3199 | $86.8733 |
| $740.00 | $344.9722 | $231.6003 | $113.3719 |
| $802.00 | $406.9045 | $266.8808 | $140.0237 |
| $864.00 | $468.8843 | $302.1613 | $166.7230 |
| $926.00 | $530.8783 | $337.4417 | $193.4366 |
| $988.00 | $592.8765 | $372.7222 | $220.1544 |
| $1050.00 | $654.8760 | $408.0027 | $246.8734 |
T = 105 dias habiles (0.4167 anos) | r = 3.684% | sigma = 41%
| S (USD) | Call BS (USD) | Lineal (USD) | Convexidad (USD) |
|---|---|---|---|
| $120.00 | $0.0000 | $0.0000 | $0.0000 |
| $182.00 | $0.0359 | $0.0000 | $0.0359 |
| $244.00 | $1.1353 | $0.0000 | $1.1353 |
| $306.00 | $8.3012 | $0.0000 | $8.3012 |
| $368.00 | $28.4605 | $26.4160 | $2.0444 |
| $430.00 | $63.7568 | $62.2373 | $1.5194 |
| $492.00 | $111.0642 | $98.0586 | $13.0055 |
| $554.00 | $165.8237 | $133.8800 | $31.9437 |
| $616.00 | $224.5224 | $169.7013 | $54.8211 |
| $678.00 | $285.0951 | $205.5226 | $79.5725 |
| $740.00 | $346.4994 | $241.3439 | $105.1555 |
| $802.00 | $408.2562 | $277.1652 | $131.0910 |
| $864.00 | $470.1581 | $312.9865 | $157.1716 |
| $926.00 | $532.1189 | $348.8078 | $183.3111 |
| $988.00 | $594.1032 | $384.6291 | $209.4740 |
| $1050.00 | $656.0969 | $420.4504 | $235.6464 |
T = 126 dias habiles (0.5 anos) | r = 3.688% | sigma = 43%
| S (USD) | Call BS (USD) | Lineal (USD) | Convexidad (USD) |
|---|---|---|---|
| $120.00 | $0.0007 | $0.0000 | $0.0007 |
| $182.00 | $0.1473 | $0.0000 | $0.1473 |
| $244.00 | $2.3544 | $0.0000 | $2.3544 |
| $306.00 | $12.1375 | $0.0000 | $12.1375 |
| $368.00 | $34.6492 | $32.8752 | $1.7740 |
| $430.00 | $70.5386 | $69.2193 | $1.3193 |
| $492.00 | $116.9799 | $105.5634 | $11.4165 |
| $554.00 | $170.3735 | $141.9075 | $28.4660 |
| $616.00 | $227.8494 | $178.2516 | $49.5977 |
| $678.00 | $287.5502 | $214.5957 | $72.9545 |
| $740.00 | $348.4065 | $250.9398 | $97.4667 |
| $802.00 | $409.8448 | $287.2839 | $122.5608 |
| $864.00 | $471.5706 | $323.6280 | $147.9425 |
| $926.00 | $533.4370 | $359.9722 | $173.4648 |
| $988.00 | $595.3718 | $396.3163 | $199.0556 |
| $1050.00 | $657.3399 | $432.6604 | $224.6795 |
T = 147 dias habiles (0.5833 anos) | r = 3.689% | sigma = 45%
| S (USD) | Call BS (USD) | Lineal (USD) | Convexidad (USD) |
|---|---|---|---|
| $120.00 | $0.0054 | $0.0000 | $0.0054 |
| $182.00 | $0.4083 | $0.0000 | $0.4083 |
| $244.00 | $4.0668 | $0.0000 | $4.0668 |
| $306.00 | $16.3796 | $2.4809 | $13.8987 |
| $368.00 | $40.8987 | $39.3356 | $1.5631 |
| $430.00 | $77.3535 | $76.1903 | $1.1632 |
| $492.00 | $123.1888 | $113.0449 | $10.1439 |
| $554.00 | $175.4694 | $149.8996 | $25.5699 |
| $616.00 | $231.8197 | $186.7543 | $45.0655 |
| $678.00 | $290.6053 | $223.6089 | $66.9964 |
| $740.00 | $350.7997 | $260.4636 | $90.3360 |
| $802.00 | $411.7919 | $297.3183 | $114.4737 |
| $864.00 | $473.2308 | $334.1729 | $139.0578 |
| $926.00 | $534.9180 | $371.0276 | $163.8904 |
| $988.00 | $596.7432 | $407.8823 | $188.8609 |
| $1050.00 | $658.6450 | $444.7369 | $213.9080 |
T = 168 dias habiles (0.6667 anos) | r = 3.689% | sigma = 47%
| S (USD) | Call BS (USD) | Lineal (USD) | Convexidad (USD) |
|---|---|---|---|
| $120.00 | $0.0241 | $0.0000 | $0.0241 |
| $182.00 | $0.8841 | $0.0000 | $0.8841 |
| $244.00 | $6.2453 | $0.0000 | $6.2453 |
| $306.00 | $20.9470 | $8.4639 | $12.4831 |
| $368.00 | $47.2164 | $45.8231 | $1.3933 |
| $430.00 | $84.2198 | $83.1823 | $1.0375 |
| $492.00 | $129.6405 | $120.5415 | $9.0990 |
| $554.00 | $181.0244 | $157.9007 | $23.1237 |
| $616.00 | $236.3762 | $195.2599 | $41.1163 |
| $678.00 | $294.2674 | $232.6191 | $61.6483 |
| $740.00 | $353.7456 | $269.9783 | $83.7673 |
| $802.00 | $414.2019 | $307.3375 | $106.8644 |
| $864.00 | $475.2564 | $344.6967 | $130.5597 |
| $926.00 | $536.6758 | $382.0559 | $154.6199 |
| $988.00 | $598.3178 | $419.4151 | $178.9027 |
| $1050.00 | $660.0960 | $456.7743 | $203.3217 |
T = 189 dias habiles (0.75 anos) | r = 3.689% | sigma = 49%
| S (USD) | Call BS (USD) | Lineal (USD) | Convexidad (USD) |
|---|---|---|---|
| $120.00 | $0.0752 | $0.0000 | $0.0752 |
| $182.00 | $1.6231 | $0.0000 | $1.6231 |
| $244.00 | $8.8476 | $0.0000 | $8.8476 |
| $306.00 | $25.7804 | $14.4899 | $11.2905 |
| $368.00 | $53.6039 | $52.3507 | $1.2532 |
| $430.00 | $91.1452 | $90.2115 | $0.9337 |
| $492.00 | $136.2967 | $128.0723 | $8.2245 |
| $554.00 | $186.9654 | $165.9331 | $21.0323 |
| $616.00 | $241.4517 | $203.7938 | $37.6579 |
| $678.00 | $298.5068 | $241.6546 | $56.8521 |
| $740.00 | $357.2619 | $279.5154 | $77.7465 |
| $802.00 | $417.1325 | $317.3762 | $99.7563 |
| $864.00 | $477.7318 | $355.2370 | $122.4948 |
| $926.00 | $538.8071 | $393.0978 | $145.7093 |
| $988.00 | $600.1938 | $430.9586 | $169.2352 |
| $1050.00 | $661.7848 | $468.8194 | $192.9654 |
T = 210 dias habiles (0.8333 anos) | r = 3.69% | sigma = 51%
| S (USD) | Call BS (USD) | Lineal (USD) | Convexidad (USD) |
|---|---|---|---|
| $120.00 | $0.1850 | $0.0000 | $0.1850 |
| $182.00 | $2.6537 | $0.0000 | $2.6537 |
| $244.00 | $11.8273 | $0.0000 | $11.8273 |
| $306.00 | $30.8355 | $20.5632 | $10.2723 |
| $368.00 | $60.0602 | $58.9247 | $1.1355 |
| $430.00 | $98.1327 | $97.2862 | $0.8464 |
| $492.00 | $143.1287 | $135.6478 | $7.4809 |
| $554.00 | $193.2342 | $174.0093 | $19.2249 |
| $616.00 | $246.9833 | $212.3708 | $34.6125 |
| $678.00 | $303.2795 | $250.7323 | $52.5472 |
| $740.00 | $361.3372 | $289.0938 | $72.2434 |
| $802.00 | $420.6070 | $327.4553 | $93.1517 |
| $864.00 | $480.7096 | $365.8168 | $114.8927 |
| $926.00 | $541.3851 | $404.1783 | $137.2067 |
| $988.00 | $602.4559 | $442.5399 | $159.9160 |
| $1050.00 | $663.8004 | $480.9014 | $182.8991 |
T = 231 dias habiles (0.9167 anos) | r = 3.691% | sigma = 53%
| S (USD) | Call BS (USD) | Lineal (USD) | Convexidad (USD) |
|---|---|---|---|
| $120.00 | $0.3831 | $0.0000 | $0.3831 |
| $182.00 | $3.9870 | $0.0000 | $3.9870 |
| $244.00 | $15.1398 | $0.0000 | $15.1398 |
| $306.00 | $36.0778 | $26.6850 | $9.3928 |
| $368.00 | $66.5827 | $65.5477 | $1.0350 |
| $430.00 | $105.1823 | $104.4104 | $0.7719 |
| $492.00 | $150.1136 | $143.2732 | $6.8404 |
| $554.00 | $199.7840 | $182.1359 | $17.6481 |
| $616.00 | $252.9143 | $220.9986 | $31.9156 |
| $678.00 | $308.5369 | $259.8614 | $48.6755 |
| $740.00 | $365.9432 | $298.7241 | $67.2191 |
| $802.00 | $424.6232 | $337.5868 | $87.0364 |
| $864.00 | $484.2134 | $376.4496 | $107.7639 |
| $926.00 | $544.4557 | $415.3123 | $129.1435 |
| $988.00 | $605.1670 | $454.1750 | $150.9920 |
| $1050.00 | $666.2169 | $493.0377 | $173.1791 |
T = 252 dias habiles (1 anos) | r = 3.691% | sigma = 55%
| S (USD) | Call BS (USD) | Lineal (USD) | Convexidad (USD) |
|---|---|---|---|
| $120.00 | $0.6986 | $0.0000 | $0.6986 |
| $182.00 | $5.6209 | $0.0000 | $5.6209 |
| $244.00 | $18.7440 | $0.0000 | $18.7440 |
| $306.00 | $41.4796 | $32.8540 | $8.6256 |
| $368.00 | $73.1675 | $72.2194 | $0.9481 |
| $430.00 | $112.2921 | $111.5847 | $0.7074 |
| $492.00 | $157.2327 | $150.9500 | $6.2827 |
| $554.00 | $206.5761 | $190.3154 | $16.2607 |
| $616.00 | $259.1950 | $229.6807 | $29.5143 |
| $678.00 | $314.2302 | $269.0460 | $45.1842 |
| $740.00 | $371.0425 | $308.4113 | $62.6312 |
| $802.00 | $429.1619 | $347.7767 | $81.3852 |
| $864.00 | $488.2449 | $387.1420 | $101.1029 |
| $926.00 | $548.0408 | $426.5073 | $121.5335 |
| $988.00 | $608.3665 | $465.8727 | $142.4938 |
| $1050.00 | $669.0877 | $505.2380 | $163.8497 |
Las griegas cuantifican la sensibilidad del precio de la opción ante cambios en los factores de mercado. Se calculan para el primer (mayo 2026), sexto (octubre 2026) y último (abril 2027) vencimiento, evaluadas en el rango de precios [2.5%, 97.5%].
| Griega | Definición | Interpretación |
|---|---|---|
| Delta (Δ) | ∂C/∂S | Cambio en el precio del call por $1 de cambio en S |
| Gamma (Γ) | ∂²C/∂S² | Tasa de cambio de Delta; mide la curvatura (convexidad) |
| Theta (Θ) | ∂C/∂t | Pérdida de valor temporal por día hábil |
| Vega (ν) | ∂C/∂σ | Sensibilidad ante un cambio del 1% en volatilidad implícita |
| Rho (ρ) | ∂C/∂r | Sensibilidad ante un cambio del 1% en la tasa libre de riesgo |
T = 21 dias habiles (0.0833 anos) | r = 3.661% | sigma = 33%
| S (USD) | Delta | Gamma | Theta | Vega | Rho |
|---|---|---|---|---|---|
| $120 | 0.0000 | 0.000000 | 0.0000 | 0.0000 | 0.0000 |
| $196 | 0.0000 | 0.000000 | 0.0000 | 0.0000 | 0.0000 |
| $272 | 0.0000 | 0.000006 | -0.0001 | 0.0001 | 0.0000 |
| $348 | 0.0835 | 0.004630 | -0.1252 | 0.1542 | 0.0232 |
| $424 | 0.7553 | 0.007778 | -0.3441 | 0.3845 | 0.2407 |
| $500 | 0.9923 | 0.000446 | -0.0814 | 0.0306 | 0.3290 |
| $576 | 1.0000 | 0.000004 | -0.0582 | 0.0003 | 0.3323 |
| $652 | 1.0000 | 0.000000 | -0.0579 | 0.0000 | 0.3323 |
| $728 | 1.0000 | 0.000000 | -0.0579 | 0.0000 | 0.3323 |
| $804 | 1.0000 | 0.000000 | -0.0579 | 0.0000 | 0.3323 |
| $880 | 1.0000 | 0.000000 | -0.0579 | 0.0000 | 0.3323 |
| $956 | 1.0000 | 0.000000 | -0.0579 | 0.0000 | 0.3323 |
| $1032 | 1.0000 | 0.000000 | -0.0579 | 0.0000 | 0.3323 |
T = 126 dias habiles (0.5 anos) | r = 3.688% | sigma = 43%
| S (USD) | Delta | Gamma | Theta | Vega | Rho |
|---|---|---|---|---|---|
| $120 | 0.0001 | 0.000010 | -0.0001 | 0.0003 | 0.0001 |
| $196 | 0.0164 | 0.000688 | -0.0101 | 0.0568 | 0.0145 |
| $272 | 0.1455 | 0.002763 | -0.0800 | 0.4395 | 0.1707 |
| $348 | 0.4031 | 0.003659 | -0.1793 | 0.9526 | 0.5721 |
| $424 | 0.6570 | 0.002852 | -0.2191 | 1.1022 | 1.0601 |
| $500 | 0.8281 | 0.001677 | -0.1963 | 0.9012 | 1.4524 |
| $576 | 0.9210 | 0.000841 | -0.1521 | 0.5997 | 1.7004 |
| $652 | 0.9656 | 0.000384 | -0.1137 | 0.3513 | 1.8362 |
| $728 | 0.9855 | 0.000167 | -0.0881 | 0.1899 | 1.9042 |
| $804 | 0.9939 | 0.000070 | -0.0733 | 0.0975 | 1.9365 |
| $880 | 0.9975 | 0.000029 | -0.0654 | 0.0485 | 1.9513 |
| $956 | 0.9990 | 0.000012 | -0.0613 | 0.0236 | 1.9580 |
| $1032 | 0.9996 | 0.000005 | -0.0593 | 0.0114 | 1.9610 |
T = 252 dias habiles (1 anos) | r = 3.691% | sigma = 55%
| S (USD) | Delta | Gamma | Theta | Vega | Rho |
|---|---|---|---|---|---|
| $120 | 0.0324 | 0.001098 | -0.0100 | 0.0870 | 0.0319 |
| $196 | 0.1698 | 0.002346 | -0.0578 | 0.4956 | 0.2551 |
| $272 | 0.3598 | 0.002500 | -0.1213 | 1.0174 | 0.7003 |
| $348 | 0.5354 | 0.002076 | -0.1691 | 1.3828 | 1.2427 |
| $424 | 0.6729 | 0.001547 | -0.1929 | 1.5300 | 1.7710 |
| $500 | 0.7727 | 0.001097 | -0.1972 | 1.5081 | 2.2298 |
| $576 | 0.8426 | 0.000760 | -0.1895 | 1.3866 | 2.6040 |
| $652 | 0.8907 | 0.000522 | -0.1756 | 1.2201 | 2.8986 |
| $728 | 0.9238 | 0.000358 | -0.1596 | 1.0434 | 3.1257 |
| $804 | 0.9465 | 0.000246 | -0.1439 | 0.8756 | 3.2990 |
| $880 | 0.9621 | 0.000170 | -0.1294 | 0.7257 | 3.4304 |
| $956 | 0.9730 | 0.000119 | -0.1168 | 0.5965 | 3.5298 |
| $1032 | 0.9806 | 0.000083 | -0.1060 | 0.4879 | 3.6051 |
La convexidad de una opción call se manifiesta en la curvatura positiva de su precio respecto al precio del subyacente, que siempre excede al precio estimado por la aproximación lineal (delta). Esta propiedad es especialmente relevante en TSLA por su alta volatilidad implícita (55%).
A medida que se aproxima el vencimiento (T → 0):
La diferencia entre el precio BSM y el precio lineal en la tabla de cada vencimiento cuantifica el beneficio de la convexidad para el tenedor del call.
Delta aumenta de 0 a 1 a medida que S pasa de OTM a ITM; para el vencimiento a largo plazo (T=252 días), la curva es más gradual; para el primer vencimiento (T=22 días), es un escalón más pronunciado.
Gamma presenta su máximo siempre alrededor del strike. A corto plazo (T=22 días), el gamma es muy alto y concentrado (alta curvatura); a largo plazo (T=252 días) es bajo y disperso.
Theta es negativo para calls largas (el tiempo deteriora el valor temporal). Es más negativo (mayor pérdida por día) en opciones ATM, y su magnitud aumenta conforme se acerca el vencimiento.
Vega indica que TSLA es muy sensible a cambios en volatilidad implícita. Una caída del 1% en σ reduce significativamente el precio del call, especialmente para vencimientos lejanos.
Rho es positivo para calls europeas: una tasa más alta reduce el valor presente del strike, beneficiando al call. Su impacto es mayor para vencimientos largos.
Tesla, Inc. cerró el 17 de abril de 2026 en $400.62 en el NASDAQ, rompiendo una racha de ocho semanas de pérdidas. La compañía tiene previsto publicar sus resultados trimestrales el 22 de abril de 2026, lo que añade una prima de riesgo adicional a la volatilidad implícita observada del 55% para opciones ATM a 1 año.
El elevado nivel de volatilidad implícita de TSLA amplifica el efecto de la convexidad y hace que las griegas —especialmente gamma y vega— sean clave para gestionar el riesgo en posiciones con opciones de Tesla.
Ejercicio realizado con datos de mercado al 17/04/2026. Tasa libre de riesgo: CME Term SOFR publicada el 16/04/2026 (12M = 3.691%). Precio spot TSLA: $400.62 (NASDAQ). Volatilidad implícita de referencia: 55% (opciones ATM ~1 año). Modelo: Black-Scholes-Merton con año comercial de 252 días hábiles.