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

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

Value

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

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

Author

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

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

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

Examples

Run this code

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

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