Description Usage Arguments Details Value

Compute values of call and put options as well as the Greeks - the sensitivities of the option price to various input arguments using the Generalized Black Scholes model. "Generalized" means that the asset can have a continuous dividend yield.

1 |

`s` |
the spot price of the asset (the stock price for options on stocks) |

`X` |
the exercise or strike price of the option |

`r` |
the continuously compounded rate of interest in decimal (0.10 or 10e-2 for 10%)
(use |

`Sigma` |
the volatility of the asset price in decimal (0.20 or 20e-2 for 20%) |

`t` |
the maturity of the option in years |

`div_yield` |
the continuously compounded dividend yield (0.05 or 5e-2 for 5%)
(use |

The Generalized Black Scholes formula for call options is

*exp(-r * t) * (s * exp(g * t) * Nd1 - X * Nd2)*

where

*g = r - div\_yield*

*Nd1 = N(d1)* and *Nd2 = N(d2)*

*d1 = (log(s / X) + (g + Sigma^2/ 2) * t) / (Sigma * sqrt(t))*

*d2 = d1 - Sigma * sqrt(t)*

N denotes the normal CDF (`pnorm`

)

For put options, the formula is

*exp(-r * t) * (-s * exp(g * t) * Nminusd1 + X * Nminusd2)*

where

*Nminusd1 = N(-d1)* and *Nminusd2 = N(-d2)*

A list of the following elements

`call` |
the value of a call option |

`put` |
the value of a put option |

`Greeks` |
a list of the following elements |

`Greeks$callDelta` |
the delta of a call option - the sensitivity to the spot price of the asset |

`Greeks$putDelta` |
the delta of a put option - the sensitivity to the spot price of the asset |

`Greeks$callTheta` |
the theta of a call option - the time decay of the option value with passage of time. Note that time is measured in years. To find a daily theta divided by 365. |

`Greeks$putTheta` |
the theta of a put option |

`Greeks$Gamma` |
the gamma of a call or put option - the second derivative with respect to the spot price or the sensitivity of delta to the spot price |

`Greeks$Vega` |
the vega of a call or put option - the sensitivity to the volatility |

`Greeks$callRho` |
the rho of a call option - the sensitivity to the interest rate |

`Greeks$putRho` |
the rho of a put option - the sensitivity to the interest rate |

`extra` |
a list of the following elements |

`extra$d1` |
the d1 of the Generalized Black Scholes formula |

`extra$d2` |
the d2 of the Generalized Black Scholes formula |

`extra$Nd1` |
is |

`extra$Nd2` |
is |

`extra$Nminusd1` |
is |

`extra$Nminusd2` |
is |

`extra$callProb` |
the (risk neutral) probability that the call will be exercised = |

`extra$putProb` |
the (risk neutral) probability that the put will be exercised = |

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.