AmericanOptionImpliedVolatility {RQuantLib} | R Documentation

## Implied Volatility calculation for American Option

### Description

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

### Usage

    ## Default S3 method:
    AmericanOptionImpliedVolatility(type, value,
                    underlying, strike,
                    dividendYield, riskFreeRate, maturity, volatility,
                    timeSteps=150, gridPoints=151)

    ## S3 method for class 'ImpliedVolatility':
    print
    ## S3 method for class 'ImpliedVolatility':
    summary

### Arguments

`type` | A string with one of the values `call` or `put`
`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
`timeSteps` | Time steps for the Finite Differences method, default value is 150
`gridPoints` | Grid points for the Finite Differences method, default value is 151

### Details

The Finite Differences method is used to value the American Option. 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 `AmericanOptionImpliedVolatility` function returns an object of class `ImpliedVolatility`. It contains a list with the following elements:

`impliedVol` | The volatility implied by the given market prices
`parameters` | List with the option parameters used

### 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

    AmericanOptionImpliedVolatility(type="call", value=11.10, underlying=100,
            strike=100, dividendYield=0.01, riskFreeRate=0.03,
            maturity=0.5, volatility=0.4)

[Package RQuantLib version 0.2.7 Index]