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 class 'default':
AmericanOptionImpliedVolatility(type, value,
underlying, strike,dividendYield, riskFreeRate, maturity, volatility,
timeSteps=150, gridPoints=151)
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
Value
The AmericanOptionImpliedVolatility function returns an object
of class ImpliedVolatility. It contains a list with the
following elements:
impliedVolThe volatility implied by the given market prices
parametersList 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.