EuropeanOption: European Option evaluation using Closed-Form solution

In RQuantLib: R Interface to the 'QuantLib' Library

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 [e-mail] for the R interface; the QuantLib Group for QuantLib

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)

RQuantLib documentation built on Nov. 27, 2023, 1:07 a.m.