RQuantLib (version 0.1.5)

AmericanOptionImpliedVolatility: 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

AmericanOptionImpliedVolatility.default(type, value, underlying, strike,
		dividendYield, riskFreeRate, maturity, volatility,
                timeSteps=150, gridPoints=151)
## S3 method for class 'ImpliedVolatility':
printundefined
## S3 method for class 'ImpliedVolatility':
summaryundefined

Arguments

type

A string with one of the values call, put or straddle

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

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

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.

References

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

See Also

EuropeanOption,AmericanOption,BinaryOption

Examples

AmericanOptionImpliedVolatility("call", value=11.10, strike=100, 100,
0.01, 0.03, 0.5, 0.4)