Input interpretation
![vanilla option](../image_source/b28a9ea462c5bb0035a1ce65afcd7867.png)
vanilla option
Input values
![option name | European option type | call strike price | $50 (US dollars) time to expiration | 3 months underlying price | $49 (US dollars) volatility | 20% dividend yield | 1% risk-free interest rate | 0.12%](../image_source/a6090e598114dfd263f8f1e28c565b35.png)
option name | European option type | call strike price | $50 (US dollars) time to expiration | 3 months underlying price | $49 (US dollars) volatility | 20% dividend yield | 1% risk-free interest rate | 0.12%
Payout profile at expiration
![Payout profile at expiration](../image_source/7ab4f6f943c13a8f24a2b299ee0cdc65.png)
Payout profile at expiration
Computed option value and greeks
![value | delta | gamma | vega | theta | rho $1.46 | 0.430 | 0.080 | 9.590 | -3.659 | 4.885](../image_source/07a4650f7a5036bf7eef6b611199e8e3.png)
value | delta | gamma | vega | theta | rho $1.46 | 0.430 | 0.080 | 9.590 | -3.659 | 4.885
Option ladder
![strike price | call rho | put rho $40 | 9.721 | -0.249 $45 | 8.777 | -2.439 $50 | 4.885 | -7.577 $55 | 1.503 | -12.206 $60 | 0.267 | -14.687](../image_source/c7ae1f17c801428f972a9e8c2f98c326.png)
strike price | call rho | put rho $40 | 9.721 | -0.249 $45 | 8.777 | -2.439 $50 | 4.885 | -7.577 $55 | 1.503 | -12.206 $60 | 0.267 | -14.687
Plots as a function of risk-free interest rate
![Plots as a function of risk-free interest rate](../image_source/ecccbd47342b34117e65b012958acef0.png)
Plots as a function of risk-free interest rate
Time evolution of rho
![Time evolution of rho](../image_source/73b7a8c519fffc767c085e6afde1b2c8.png)
Time evolution of rho
Delta hedging
![new price | δ shares short | δ tracking error | δ-γ shares short | δ-γ tracking error $43.12 | 42.9725 | -81.73% | 19.4234 | +12.83% $44.10 | 42.9725 | -59.00% | 23.3483 | +6.67% $45.08 | 42.9725 | -39.06% | 27.2731 | +2.97% $46.06 | 42.9725 | -22.60% | 31.198 | +1.05% $47.04 | 42.9725 | -10.26% | 35.1228 | +0.24% $48.02 | 42.9725 | -2.61% | 39.0477 | +0.02% $49.98 | 42.9725 | -2.63% | 46.8974 | -0.00% $50.96 | 42.9725 | -10.47% | 50.8222 | +0.03% $51.94 | 42.9725 | -23.31% | 54.7471 | +0.33% $52.92 | 42.9725 | -40.77% | 58.6719 | +1.26% $53.90 | 42.9725 | -62.35% | 62.5968 | +3.32% $54.88 | 42.9725 | -87.52% | 66.5216 | +7.05%](../image_source/8006a2c2efc5114052917952251a3c9b.png)
new price | δ shares short | δ tracking error | δ-γ shares short | δ-γ tracking error $43.12 | 42.9725 | -81.73% | 19.4234 | +12.83% $44.10 | 42.9725 | -59.00% | 23.3483 | +6.67% $45.08 | 42.9725 | -39.06% | 27.2731 | +2.97% $46.06 | 42.9725 | -22.60% | 31.198 | +1.05% $47.04 | 42.9725 | -10.26% | 35.1228 | +0.24% $48.02 | 42.9725 | -2.61% | 39.0477 | +0.02% $49.98 | 42.9725 | -2.63% | 46.8974 | -0.00% $50.96 | 42.9725 | -10.47% | 50.8222 | +0.03% $51.94 | 42.9725 | -23.31% | 54.7471 | +0.33% $52.92 | 42.9725 | -40.77% | 58.6719 | +1.26% $53.90 | 42.9725 | -62.35% | 62.5968 | +3.32% $54.88 | 42.9725 | -87.52% | 66.5216 | +7.05%