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\name{AmericanOption}
\alias{AmericanOption}
\alias{AmericanOption.default}
\title{American Option evaluation using Finite Differences}
\description{
This function evaluations an American-style option on a common stock
using finite differences. The option value as well as the common first
derivatives ("Greeks") are returned.}
\usage{
\method{AmericanOption}{default}(type, underlying, strike,
dividendYield, riskFreeRate, maturity, volatility,
timeSteps=150, gridPoints=149, engine="BaroneAdesiWhaley",
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{timeSteps}{Time steps for the \dQuote{CrankNicolson} finite
differences method engine, default value is 150}
\item{gridPoints}{Grid points for the \dQuote{CrankNicolson} finite differences method,
default value is 149}
\item{engine}{String selecting pricing engine, currently supported are
\dQuote{BaroneAdesiWhaley} and \dQuote{CrankNicolson}}
\item{discreteDividends}{Vector of discrete dividends (optional)}
\item{discreteDividendsTimeUntil}{Vector of times to discrete dividends
(in fractional years, optional)}
}
\value{
An object of class \code{AmericanOption} (which inherits from class
\code{\link{Option}}) is returned. 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}
Note that under the new pricing framework used in QuantLib,
pricers do not provide analytics for all 'Greeks'. When
\dQuote{CrankNicolson} is selected, then at least delta, gamma and
vega are available. With the default pricing engine of
\dQuote{BaroneAdesiWhaley}, no greeks are returned.
The \dQuote{CrankNicolson} engine needs to be used when setting
discrete dividends.
}
\details{
The Finite Differences method is used to value the American Option.
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{EuropeanOption}}}
\examples{
# simple call with unnamed parameters
AmericanOption("call", 100, 100, 0.02, 0.03, 0.5, 0.4)
# simple call with some explicit parameters
AmericanOption("put", strike=100, volatility=0.4, 100, 0.02, 0.03, 0.5)
# simple call with unnamed parameters, using Crank-Nicolons
AmericanOption("put", strike=100, volatility=0.4, 100, 0.02, 0.03, 0.5, engine="CrankNicolson")
}
\keyword{misc}
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