https://github.com/cran/fOptions
Tip revision: a5963c756ac49275517b88d15ac61c699c5089a2 authored by Diethelm Wuertz on 08 August 1977, 00:00:00 UTC
version 240.10067
version 240.10067
Tip revision: a5963c7
2F-AsianOptions.Rd
\name{AsianOptions}
\alias{AsianOptions}
\alias{GeometricAverageRateOption}
\alias{TurnbullWakemanAsianApproxOption}
\alias{LevyAsianApproxOption}
\title{Valuation of Asian Options}
\description{
This is a collection of functions to valuate Asian
options. Asian options are path-dependent options,
with payoffs that depend on the average price of the
underlying asset or the average exercise price.
There are two categories or types of Asian options:
average rate options (also known as average price
options) and average strike options. The payoffs
depend on the average price of the underlying asset
over a predetermined time period. An average is less
volatile than the underlying asset, therefore making
Asian options less expensive than standard European
options. Asian options are commonly used in currency
and commodity markets. Asian options are of interest
in markets with thinly traded assets. Due to the
little effect it will have on the option's value,
options based on an average, such as Asian options,
have a reduced incentive to manipulate the underlying
price at expiration.
\cr
The functions are:
\tabular{ll}{
\code{GeometricAverageRateOption} \tab Geometric Average Rate Option, \cr
\code{TurnbullWakemanAsianApproxOption} \tab Turnbull and Wakeman's Approximation, \cr
\code{LevyAsianApproxOption} \tab Levy's Approximation. }
}
\usage{
GeometricAverageRateOption(TypeFlag, S, X, Time, r, b, sigma,
title = NULL, description = NULL)
TurnbullWakemanAsianApproxOption(TypeFlag, S, SA, X, Time, time,
tau, r, b, sigma, title = NULL, description = NULL)
LevyAsianApproxOption(TypeFlag, S, SA, X, Time, 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{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, SA}{
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{tau}{
[TurnWakeAsianApprox*] - \cr
is the time to the beginning of the average period.
}
\item{time, Time}{
the 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 \code{"c"} for a call option or
a \code{"p"} for a put option.
}
\item{X}{
the exercise price, a numeric value.
}
}
\details{
The Geometric average is the nth root of the product of the n sample
points. The Arithmetic average is the sum of the stock values divided
by the number of sampling points. Although Geometric Asian options are
not commonly used in practice, they are often used as a good initial
guess for the price of arithmetic Asian options. This technique is
used to improve the convergence rate of the Monte Carlo model when
pricing arithmetic Asian options.
\cr
Two cases are considered, the geometric and the arithmetic average-rate
option. For the latter one can choose between three different kinds of
approximations: Turnbull and Wakeman's approximations, Levy's approximation
and Curran's approximation.
\cr
[Haug's Book, Chapter 2.12]
}
\note{
The functions implement the algorithms to valuate plain vanilla
options as described in Chapter 2.12 of Haug's Book (1997).
}
\value{
The option price, a numeric value.
}
\references{
Haug E.G. (1997);
\emph{The complete Guide to Option Pricing Formulas},
Chapter 2.12, McGraw-Hill, New York.
}
\author{
Diethelm Wuertz for the Rmetrics \R-port.
}
\examples{
## SOURCE("fOptions.082F-AsianOptions")
## Examples from Chapter 2.12 in E.G. Haug's Option Guide (1997)
## Geometric Average Rate Option:
xmpOptions("\nStart: Geometric Average Rate Option > ")
GeometricAverageRateOption(TypeFlag = "p", S = 80, X = 85,
Time = 0.25, r = 0.05, b = 0.08, sigma = 0.20)
## Turnbull Wakeman Approximation:
xmpOptions("\nNext: Turnbull Wakeman Option > ")
TurnbullWakemanAsianApproxOption(TypeFlag = "p", S = 90, SA = 88,
X = 95, Time = 0.50, time = 0.25, tau = 0.0, r = 0.07,
b = 0.02, sigma = 0.25)
## Levy Asian Approximation:
xmpOptions("\nNext: Levy Asian Option > ")
LevyAsianApproxOption(TypeFlag = "c", S = 100, SA = 100, X = 105,
Time = 0.75, time = 0.50, r = 0.10, b = 0.05, sigma = 0.15)
}
\keyword{math}