EuropeanOption: European Option evaluation using Closed-Form solution
In RQuantLib: R Interface to the 'QuantLib' Library

EuropeanOption

R Documentation

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

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

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)

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.

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

Note

The interface might change in future release as QuantLib stabilises its own API.

Author(s)

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

References

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

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)

RQuantLib documentation built on April 3, 2025, 8:52 p.m.