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| Black–Scholes | | | | | |

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| | The Black–Scholes model or Black–Scholes–Merton is a mathematical model of a financial market containing certain derivative investment instruments. From the model, one can deduce the Black–Scholes forsigmala, which gives the price of European-style options. | | |

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| Inputs | | | | | |

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| | Stock Price | | | | | S, the price of the stock | | |

| | Strike Price | | | | | K, the strike of the option | | |

| | Time To Expiry | | | | | T, current time until expiration | | |

| | Volatility | | | | | σ, the volatility of the stock's returns; this is the square root of the quadratic variation of the stock's log price process | | |

| | Risk Free Rate | | | | | r, the annualized risk-free interest rate, continuously compounded (the force of interest) | | |

| | Dividend Yield | | | | | d, how sigmach a company pays out in dividends each year relative to its share price | | |

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| Outputs | | | | | |

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| | d1 | -0.4135 | | | | | | |

| | N(d1) | 0.3396 | | | | standard normal cusigmalative distribution of d1, a measure how far in the money the option is expected to be if it does expire in the money | | |

| | N'(d1) | 0.3663 | | | | standard normal probability density of d1 | | |

| | d2 | -0.6635 | | | | | | |

| | N(d2) | 0.2535 | | | | the probability of exercise (paying the strike price) | | |

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| | | Calls | Puts | | | | | | |

| | Value | 2.4301 | 9.4926 | | | | C, call option value; P, put option value | | |

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| Partial Derivatives | | | | | |

| | | Calls | Puts | | | | | | |

| | Delta | 0.3396 | -0.6604 | | | | Δ, measures the rate of change of option value with respect to changes in the underlying asset's price | | |

| | Gamma | 0.0293 | | | | Γ, measures the rate of change in the delta with respect to changes in the underlying price | | |

| | Vega | 0.1831 | | | | V, measures sensitivity to volatility | | |

| | Theta | -0.0036 | -0.0140 | | | | θ, measures the sensitivity of the value of the derivative to the passage of time | | |

| | Rho | 0.1421 | -0.4186 | | | | ρ, measures sensitivity to the interest rate | | |

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