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\name{EuropeanOption}
\alias{EuropeanOption}
\alias{EuropeanOption.default}
\title{European Option evaluation using Closed-Form solution}
\description{
The \code{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{
\method{EuropeanOption}{default}(type, underlying, strike,
dividendYield, riskFreeRate, maturity, volatility,
discreteDividends, discreteDividendsTimeUntil)
}
\arguments{
\item{type}{A string with one of the values \code{call} or \code{put}}
\item{underlying}{Current price of the underlying stock}
\item{strike}{Strike price of the option}
\item{dividendYield}{Continuous dividend yield (as a fraction) of the stock}
\item{riskFreeRate}{Risk-free rate}
\item{maturity}{Time to maturity (in fractional years)}
\item{volatility}{Volatility of the underlying stock}
\item{discreteDividends}{Vector of discrete dividends (optional)}
\item{discreteDividendsTimeUntil}{Vector of times to discrete dividends
(in fractional years, optional)}
}
\value{
The \code{EuropeanOption} function returns an object of class
\code{EuropeanOption} (which inherits from class
\code{\link{Option}}). It contains a list with the following
components:
\item{value}{Value of option}
\item{delta}{Sensitivity of the option value for a change in the underlying}
\item{gamma}{Sensitivity of the option delta for a change in the underlying}
\item{vega}{Sensitivity of the option value for a change in the
underlying's volatility}
\item{theta}{Sensitivity of the option value for a change in t, the
remaining time to maturity}
\item{rho}{Sensitivity of the option value for a change in the
risk-free interest rate}
\item{dividendRho}{Sensitivity of the option value for a change in the
dividend yield}
}
\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
\code{QuantLib} documentation for details on the \code{QuantLib}
implementation.
}
\references{\url{https://www.quantlib.org/} for details on \code{QuantLib}.}
\author{Dirk Eddelbuettel \email{edd@debian.org} for the \R interface;
the QuantLib Group for \code{QuantLib}}
\note{The interface might change in future release as \code{QuantLib}
stabilises its own API.}
\seealso{\code{\link{EuropeanOptionImpliedVolatility}},
\code{\link{EuropeanOptionArrays}},
\code{\link{AmericanOption}},\code{\link{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)
}
\keyword{misc}
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