# Implied Volatility calculation for European Option

### Description

The `EuropeanOptionImpliedVolatility`

function solves for the
(unobservable) implied volatility, given an option price as well as
the other required parameters to value an option.

### Usage

1 2 3 | ```
## Default S3 method:
EuropeanOptionImpliedVolatility(type, value,
underlying, strike, dividendYield, riskFreeRate, maturity, volatility)
``` |

### Arguments

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

`value` |
Value of the option (used only for ImpliedVolatility calculation) |

`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` |
Initial guess for the volatility of the underlying stock |

### Details

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

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

documentation for details on the `QuantLib`

implementation.

### Value

The `EuropeanOptionImpliedVolatility`

function returns an numeric
variable with volatility implied by the given market prices and given parameters.

### Note

The interface might change in future release as `QuantLib`

stabilises its own API.

### Author(s)

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

### References

http://quantlib.org for details on `QuantLib`

.

### See Also

`EuropeanOption`

,`AmericanOption`

,`BinaryOption`

### Examples

1 2 3 | ```
EuropeanOptionImpliedVolatility(type="call", value=11.10, underlying=100,
strike=100, dividendYield=0.01, riskFreeRate=0.03,
maturity=0.5, volatility=0.4)
``` |