EuropeanOptionImpliedVolatility: 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

## S3 method for class 'default':
EuropeanOptionImpliedVolatility(type, value,
	underlying, strike, dividendYield, riskFreeRate, maturity, volatility)

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

Value

The EuropeanOptionImpliedVolatility 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 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.

References

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

Examples

Run this code

EuropeanOptionImpliedVolatility(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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