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\name{BasicAmericanOptions}
\alias{BasicAmericanOptions}
\alias{RollGeskeWhaleyOption}
\alias{BAWAmericanApproxOption}
\alias{BSAmericanApproxOption}
\title{Valuation of Basic American Options}
\description{
A collection and description of functions to valuate
basic American options. Approximative formulas for
American calls are given for the Roll, Geske and
Whaley Approximation, for the Barone-Adesi and Whaley
Approximation, and for the Bjerksund and Stensland
Approximation.
\cr
The functions are:
\tabular{ll}{
\code{RollGeskeWhaleyOption} \tab Roll, Geske and Whaley Approximation, \cr
\code{BAWAmericanApproxOption} \tab Barone-Adesi and Whaley Approximation, \cr
\code{BSAmericanApproxOption} \tab Bjerksund and Stensland Approximation. }
}
\usage{
RollGeskeWhaleyOption(S, X, time1, Time2, r, D, sigma,
title = NULL, description = NULL)
BAWAmericanApproxOption(TypeFlag, S, X, Time, r, b, sigma,
title = NULL, description = NULL)
BSAmericanApproxOption(TypeFlag, S, X, Time, r, b, sigma,
title = NULL, description = NULL)
}
\arguments{
\item{b}{
the annualized cost-of-carry rate, a numeric value;
e.g. 0.1 means 10\% pa.
}
\item{D}{
a single dividend with time to dividend payout \code{t1}.
}
\item{description}{
a character string which allows for a brief description.
}
\item{r}{
the annualized rate of interest, a numeric value;
e.g. 0.25 means 25\% pa.
}
\item{S}{
the asset price, a numeric value.
}
\item{sigma}{
the annualized volatility of the underlying security,
a numeric value; e.g. 0.3 means 30\% volatility pa.
}
\item{Time}{
the time to maturity measured in years, a numeric value.
}
\item{time1, Time2}{
[RollGeskeWhaley*] -
the first value measures time to dividend payout in years,
e.g. 0.25 denotes a quarter, and the second value measures
time to maturity measured in years, a numeric value; e.g.
0.5 means 6 months.
}
\item{title}{
a character string which allows for a project title.
}
\item{TypeFlag}{
a character string either "c" for a call option or a "p"
for a put option.
}
\item{X}{
the exercise price, a numeric value.
}
}
\value{
\code{RollGeskeWhaleyOption} \cr
\code{BAWAmericanApproxOption}
\cr
return the option price, a numeric value.
\cr
\code{BSAmericanApproxOption}
\cr
returns a list with the following two elements: \code{Premium} the
option price, and \code{TriggerPrice} the trigger price.
\cr
}
\details{
\bold{Roll-Geske-Whaley Option:}
\cr\cr
The function \code{RollGeskeWhaleyOption} valuates American calls
on a stock paying a single dividend with specified time to dividend
payout according to the pricing formula derived by Roll, Geske and
Whaley (1977).
\cr
\code{Approximations for American Options:}
\cr\cr
The function \code{BSAmericanApproxOption} valuates American calls
or puts on an underlying asset for a given cost-of-carry rate
according to the quadratic approximation method due to Barone-Adesi
and Whaley (1987). The function \code{BSAmericanApproxOption} valuates
American calls or puts on stocks, futures, and currencies due to
the approximation method of Bjerksund and Stensland (1993).
}
\note{
The functions implement the algorithms to valuate basic American
options as described in Chapter 1.4 of Haug's Option Guide (1997).
}
\references{
Barone-Adesi G., Whaley R.E. (1987);
\emph{Efficient Analytic Approximation of American Option Values},
Journal of Finance 42, 301--320.
Bjerksund P., Stensland G. (1993);
\emph{Closed Form Approximation of American Options},
Scandinavian Journal of Management 9, 87--99.
Geske R. (1979);
\emph{A Note on an Analytical Formula for Unprotected
American Call Options on Stocks with known Dividends},
Journal of Financial Economics 7, 63--81.
Haug E.G. (1997);
\emph{The Complete Guide to Option Pricing Formulas},
Chapter 1, McGraw-Hill, New York.
Roll R. (1977);
\emph{An Analytic Valuation Formula for Unprotected
American Call Options on Stocks with known Dividends},
Journal of Financial Economics 5, 251--258.
}
\author{
Diethelm Wuertz for the Rmetrics \R-port.
}
\examples{
## All the examples are from Haug's Option Guide (1997)
## CHAPTER 1.4: ANALYTICAL MODELS FOR AMERICAN OPTIONS
## Roll-Geske-Whaley American Calls on Dividend Paying
# Stocks [Haug 1.4.1]
RollGeskeWhaleyOption(S = 80, X = 82, time1 = 1/4,
Time2 = 1/3, r = 0.06, D = 4, sigma = 0.30)
## Barone-Adesi and Whaley Approximation for American
# Options [Haug 1.4.2] vs. Black76 Option on Futures:
BAWAmericanApproxOption(TypeFlag = "p", S = 100,
X = 100, Time = 0.5, r = 0.10, b = 0, sigma = 0.25)
Black76Option(TypeFlag = "c", FT = 100, X = 100,
Time = 0.5, r = 0.10, sigma = 0.25)
## Bjerksund and Stensland Approximation for American Options:
BSAmericanApproxOption(TypeFlag = "c", S = 42, X = 40,
Time = 0.75, r = 0.04, b = 0.04-0.08, sigma = 0.35)
}
\keyword{math}
|
