EuropeanOption | R Documentation |

The `EuropeanOption`

function evaluations an European-style
option on a common stock using the Black-Scholes-Merton solution. The
option value, the common first derivatives ("Greeks") as well as the
calling parameters are returned.

```
## Default S3 method:
EuropeanOption(type, underlying, strike,
dividendYield, riskFreeRate, maturity, volatility,
discreteDividends, discreteDividendsTimeUntil)
```

`type` |
A string with one of the values |

`underlying` |
Current price of the underlying stock |

`strike` |
Strike price of the option |

`dividendYield` |
Continuous dividend yield (as a fraction) of the stock |

`riskFreeRate` |
Risk-free rate |

`maturity` |
Time to maturity (in fractional years) |

`volatility` |
Volatility of the underlying stock |

`discreteDividends` |
Vector of discrete dividends (optional) |

`discreteDividendsTimeUntil` |
Vector of times to discrete dividends (in fractional years, optional) |

The well-known closed-form solution derived by Black, Scholes and Merton is used for valuation. Implied volatilities are calculated numerically.

Please see any decent Finance textbook for background reading, and the
`QuantLib`

documentation for details on the `QuantLib`

implementation.

The `EuropeanOption`

function returns an object of class
`EuropeanOption`

(which inherits from class
`Option`

). It contains a list with the following
components:

`value` |
Value of option |

`delta` |
Sensitivity of the option value for a change in the underlying |

`gamma` |
Sensitivity of the option delta for a change in the underlying |

`vega` |
Sensitivity of the option value for a change in the underlying's volatility |

`theta` |
Sensitivity of the option value for a change in t, the remaining time to maturity |

`rho` |
Sensitivity of the option value for a change in the risk-free interest rate |

`dividendRho` |
Sensitivity of the option value for a change in the dividend yield |

The interface might change in future release as `QuantLib`

stabilises its own API.

Dirk Eddelbuettel edd@debian.org for the **R** interface;
the QuantLib Group for `QuantLib`

https://www.quantlib.org/ for details on `QuantLib`

.

`EuropeanOptionImpliedVolatility`

,
`EuropeanOptionArrays`

,
`AmericanOption`

,`BinaryOption`

```
## simple call with unnamed parameters
EuropeanOption("call", 100, 100, 0.01, 0.03, 0.5, 0.4)
## simple call with some explicit parameters, and slightly increased vol:
EuropeanOption(type="call", underlying=100, strike=100, dividendYield=0.01,
riskFreeRate=0.03, maturity=0.5, volatility=0.5)
## simple call with slightly shorter maturity: QuantLib 1.7 compiled with
## intra-day time calculation support with create slightly changed values
EuropeanOption(type="call", underlying=100, strike=100, dividendYield=0.01,
riskFreeRate=0.03, maturity=0.499, volatility=0.5)
```

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