RQuantLib (version 0.4.24)

EuropeanOption: European Option evaluation using Closed-Form solution

Description

The EuropeanOption function evaluations an European-style option on a common stock using the Black-Scholes-Merton solution. The option value, the common first derivatives ("Greeks") as well as the calling parameters are returned.

Usage

# S3 method for default
EuropeanOption(type, underlying, strike,
	dividendYield, riskFreeRate, maturity, volatility, 
	discreteDividends, discreteDividendsTimeUntil)

Value

The EuropeanOption function returns an object of class

EuropeanOption (which inherits from class

Option). It contains a list with the following components:

value

Value of option

delta

Sensitivity of the option value for a change in the underlying

gamma

Sensitivity of the option delta for a change in the underlying

vega

Sensitivity of the option value for a change in the underlying's volatility

theta

Sensitivity of the option value for a change in t, the remaining time to maturity

rho

Sensitivity of the option value for a change in the risk-free interest rate

dividendRho

Sensitivity of the option value for a change in the dividend yield

Arguments

type

A string with one of the values call or put

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

Volatility of the underlying stock

discreteDividends

Vector of discrete dividends (optional)

discreteDividendsTimeUntil

Vector of times to discrete dividends (in fractional years, optional)

Author

Dirk Eddelbuettel for the R interface; the QuantLib Group for QuantLib

Details

The well-known closed-form solution derived by Black, Scholes and Merton is used for valuation. Implied volatilities are 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.

See Also

EuropeanOptionImpliedVolatility, EuropeanOptionArrays, AmericanOption,BinaryOption

Examples

## simple call with unnamed parameters
EuropeanOption("call", 100, 100, 0.01, 0.03, 0.5, 0.4)
## simple call with some explicit parameters, and slightly increased vol:
EuropeanOption(type="call", underlying=100, strike=100, dividendYield=0.01, 
riskFreeRate=0.03, maturity=0.5, volatility=0.5)
## simple call with slightly shorter maturity: QuantLib 1.7 compiled with 
## intra-day time calculation support with create slightly changed values
EuropeanOption(type="call", underlying=100, strike=100, dividendYield=0.01, 
riskFreeRate=0.03, maturity=0.499, volatility=0.5)