https://github.com/cran/fOptions
Tip revision: 429a9b1805024ce58873e3229048371980a535a2 authored by Diethelm Wuertz on 08 August 1977, 00:00:00 UTC
version 221.10065
version 221.10065
Tip revision: 429a9b1
083E-EBMAsianOptions.Rd
\name{EBMAsianOptions}
\alias{EBMAsianOptions}
\alias{MomentMatchedAsianOption}
\alias{MomentMatchedAsianDensity}
\alias{GramCharlierAsianOption}
\alias{AsianOptionMoments}
\alias{DufresneAsianOptionMoments}
\alias{AbrahamsonAsianOptionMoments}
\alias{TurnbullWakemanAsianOptionMoments}
\alias{TolmatzAsianOptionMoments}
%\alias{Schroeder1AsianDensity}
%\alias{Schroeder2AsianDensity}
%\alias{Yor1AsianDensity}
%\alias{Yor2AsianDensity}
%\alias{TolmatzAsianDensity}
%\alias{TolmatzAsianProbability}
\alias{ZhangAsianOption}
\alias{VecerAsianOption}
\alias{ZhangApproximateAsianOption}
\alias{gGemanYor}
\alias{GemanYorAsianOption}
\alias{gLinetzky}
\alias{LinetzkyAsianOption}
\alias{BoundsOnAsianOption}
\alias{CurranThompsonAsianOption}
\alias{RogerShiThompsonAsianOption}
\alias{ThompsonAsianOption}
\alias{TolmatzAsianOption}
\alias{CallPutParityAsianOption}
\alias{WithDividendsAsianOption}
\alias{FuMadanWangTable}
\alias{FusaiTaglianiTable}
\alias{GemanTable}
\alias{LinetzkyTable}
\alias{ZhangTable}
\alias{ZhangLongTable}
\alias{ZhangShortTable}
\title{Exponential Brownian Motion Distributions}
\description{
A collection and description of functions
used in the theory of exponential Brownian
Motion and in the valuation of Asian options.
\cr
The functions for Moment matching and Series Expansions are:
\tabular{ll}{
\code{MomentMatchedAsianOption} \tab Valuate moment matched option prices, \cr
\code{... method="LN"} \tab Log-Normal Approximation of Levy, Turnbull and Wakeman, \cr
\code{... method="RG"} \tab Reciprocal-Gamma Approximation of Milevski and Posner, \cr
\code{... method="JI"} \tab Johnson Type I Approximation of Posner and Milevsky, \cr
\code{MomentMatchedAsianDensity} \tab Valuate moment matched option densities, \cr
\code{... method="LN"} \tab Log-Normal Approximation, \cr
\code{... method="RG"} \tab Reciprocal-Gamma Approximation, \cr
\code{... method="JI"} \tab Johnson Type I Approximation, \cr
\code{GramCharlierAsianOption} \tab Calculate Gram-Charlier option prices. }
\tabular{ll}{
\code{AsianOptionMoments} \tab Methods to calculate Asian Moments, \cr
\code{... method="A"} \tab Moments from Abrahamson's Formula, \cr
\code{... method="D"} \tab Moments from Dufresne's Formula, \cr
\code{... method="TW"} \tab First 2 Moments from Turnbull-Wakeman, \cr
\code{... method="T"} \tab Asymptotic Behavior after Tolmatz. }
%\tabular{ll}{
%\code{Schroeder1AsianDensity} \tab
%\code{Schroeder2AsianDensity} \tab
%\code{Yor1AsianDensity} \tab
%\code{Yor2AsianDensity} \tab
%\code{TolmatzAsianDensity} \tab
%\code{TolmatzAsianProbability} \tab
\tabular{ll}{
\code{ZhangAsianOption} \tab Asian option price by Zhang's 1D PDE, \cr
\code{VecerAsianOption} \tab Asian option price by Vecer's 1D PDE. }
\tabular{ll}{
\code{gGemanYor} \tab Function to be Laplace inverted, \cr
\code{GemanYorAsianOption} \tab Asian option price by Laplace Inversion, \cr
\code{gLinetzky} \tab Function to be integrated, \cr
\code{LinetzkyAsianOption} \tab Asian option price by Spectral Expansion. }
\tabular{ll}{
\code{BoundsOnAsianOption} \tab Lower and upper bonds on Asian calls, \cr
\code{CurranThompsonAsianOption} \tab From Thompson's continuous limit, \cr
\code{RogerShiThompsonAsianOption} \tab From Thompson's single integral formula, \cr
\code{ThompsonAsianOption} \tab Thompson's upper bound, \cr
\code{TolmatzAsianOption} \tab Lower Bound from Tolmatz' symptotics. }
\tabular{ll}{
\code{CallPutParityAsianOption} \tab Call-Put parity Relation, \cr
\code{WithDividendsAsianOption} \tab Adds dividends to Asian option formula. }
\tabular{ll}{
\code{FuMadanWangTable} \tab Table from Fu, Madan and Wang's paper, \cr
\code{FusaiTaglianiTable} \tab Table from Fusai und tagliani's paper, \cr
\code{GemanTable} \tab Table from Geman's paper, \cr
\code{LinetzkyTable} \tab Table from Linetzky's paper, \cr
\code{ZhangTable} \tab Table from Zhang's paper, \cr
\code{ZhangLongTable} \tab Long Table from Zhang's paper, \cr
\code{ZhangShortTable} \tab Short Table from Zhang's paper. }
Sorry - The Documentation is still Uncomplete.
}
\usage{
MomentMatchedAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1,
r = 0.09, sigma = 0.30, table = NA, method = c("LN", "RG", "JI"))
MomentMatchedAsianDensity(x, Time = 1, r = 0.09, sigma = 0.30,
method = c("LN", "RG", "JI"))
GramCharlierAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1,
r = 0.09, sigma = 0.30, table = NA, method = c("LN", "RG", "JI"))
AsianOptionMoments(M = 4, Time = 1, r = 0.045, sigma = 0.30, log = FALSE,
method = c("A", "D", "TW", "T"))
%Schroeder1AsianDensity()
%Schroeder2AsianDensity()
%Yor1AsianDensity()
%Yor2AsianDensity()
%TolmatzAsianDensity()
%TolmatzAsianProbability()
ZhangAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1,
r = 0.09, sigma = 0.30, table = NA, correction = TRUE, nint = 800,
eps = 1.0e-8, dt = 1.0e-10)
VecerAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1,
r = 0.09, sigma = 0.30, table = NA, nint = 800, eps = 1.0e-8,
dt = 1.0e-10)
gGemanYor(lambda, S = 100, X = 100, Time = 1, r = 0.05, sigma = 0.30,
log = FALSE, doplot = FALSE)
GemanYorAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1,
r = 0.09, sigma = 0.30, doprint = FALSE)
gLinetzky(x, y, tau, nu, ip = 0)
LinetzkyAsianOption(TypeFlag = c("c", "p"), S = 2, X = 2, Time = 1,
r = 0.02, sigma = 0.1, table = NA, lower = 0, upper = 100,
method = "adaptive", subdivisions = 100, ip = 0, doprint = TRUE,
doplot = TRUE, \dots)
BoundsOnAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1,
r = 0.09, sigma = 0.30, table = NA, method = c("CT", "RST", "T"))
CurranThompsonAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100,
Time = 1, r = 0.09, sigma = 0.30)
RogerShiThompsonAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100,
Time = 1, r = 0.09, sigma = 0.30)
ThompsonAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1,
r = 0.09, sigma = 0.30)
TolmatzAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1,
r = 0.09, sigma = 0.30)
CallPutParityAsianOption(TypeFlag = "p", Price = 8.828759, S = 100,
X = 100, Time = 1, r = 0.09, sigma = 0.3, table = NA)
WithDividendsAsianOption(TypeFlag = "c", Dividends = 0.45, S = 100,
X = 100, Time = 1, r = 0.09, sigma = 0.3,
calculator = MomentMatchedAsianOption, method = "LN")
FuMadanWangTable()
FusaiTaglianiTable()
GemanTable()
LinetzkyTable()
ZhangTable()
ZhangLongTable()
ZhangShortTable()
}
\arguments{
\item{calculator}{
[*] - \cr
xxx.
}
\item{correction}{
[*] - \cr
xxx.
}
\item{Dividends}{
[*] - \cr
xxx.
}
\item{doplot}{
[*] - \cr
xxx.
}
\item{doprint}{
[*] - \cr
xxx.
}
\item{dt}{
[*] - \cr
xxx.
}
\item{eps}{
[*] - \cr
xxx.
}
\item{ip}{
[*] - \cr
xxx.
}
\item{lambda}{
[*] - \cr
xxx.
}
\item{log}{
[*] - \cr
xxx.
}
\item{lower}{
[*] - \cr
xxx.
}
\item{M}{
[*] - \cr
xxx.
}
\item{method}{
[*] - \cr
xxx.
}
\item{nint}{
[*] - \cr
xxx.
}
\item{nu}{
[*] - \cr
xxx.
}
\item{Price}{
[*] - \cr
xxx.
}
\item{r}{
[*] - \cr
xxx.
}
\item{S}{
[*] - \cr
xxx.
}
\item{sigma}{
[*] - \cr
xxx.
}
\item{subdivisions}{
[*] - \cr
xxx.
}
\item{table}{
[*] - \cr
xxx.
}
\item{tau}{
[*] - \cr
xxx.
}
\item{Time}{
[*] - \cr
xxx.
}
\item{TypeFlag}{
[*] - \cr
xxx.
}
\item{upper}{
[*] - \cr
xxx.
}
\item{x}{
[*] - \cr
xxx.
}
\item{X}{
[*] - \cr
xxx.
}
\item{y}{
[*] - \cr
xxx.
}
\item{\dots}{
[*] - \cr
xxx.
}
}
%\details{
%
% ...
%
%}
%\value{
%
% The functions ...
%
%}
\author{
Diethelm Wuertz for the Rmetrics \R-port.
}
\examples{
## SOURCE("fOptions.E4-EBMAsianOptions")
## Examples:
# none ...
}
\keyword{math}