[Returnanalytics-commits] r3676 - in pkg/Dowd: . R man
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Tue Jun 16 16:22:15 CEST 2015
Author: dacharya
Date: 2015-06-16 16:22:14 +0200 (Tue, 16 Jun 2015)
New Revision: 3676
Added:
pkg/Dowd/R/GParetoMultipleMEFPlot.R
pkg/Dowd/R/GParetoVaR.R
pkg/Dowd/R/GumbelES.R
pkg/Dowd/R/GumbelESPlot2DCl.R
pkg/Dowd/R/GumbelVaR.R
pkg/Dowd/R/GumbelVaRPlot2DCl.R
pkg/Dowd/man/GParetoMultipleMEFPlot.Rd
pkg/Dowd/man/GParetoVaR.Rd
pkg/Dowd/man/GumbelES.Rd
pkg/Dowd/man/GumbelESPlot2DCl.Rd
pkg/Dowd/man/GumbelVaR.Rd
pkg/Dowd/man/GumbelVaRPlot2DCl.Rd
Modified:
pkg/Dowd/NAMESPACE
pkg/Dowd/R/FrechetES.R
pkg/Dowd/R/GParetoMEFPlot.R
pkg/Dowd/man/FrechetES.Rd
pkg/Dowd/man/GParetoMEFPlot.Rd
Log:
Gumbel Functions and remaining Gpareto functions: source and documentation.
Modified: pkg/Dowd/NAMESPACE
===================================================================
--- pkg/Dowd/NAMESPACE 2015-06-15 19:18:04 UTC (rev 3675)
+++ pkg/Dowd/NAMESPACE 2015-06-16 14:22:14 UTC (rev 3676)
@@ -24,8 +24,14 @@
export(FrechetVaRPlot2DCl)
export(GParetoES)
export(GParetoMEFPlot)
+export(GParetoMultipleMEFPlot)
+export(GParetoVaR)
export(GaussianCopulaVaR)
export(GumbelCopulaVaR)
+export(GumbelES)
+export(GumbelESPlot2DCl)
+export(GumbelVaR)
+export(GumbelVaRPlot2DCl)
export(HSES)
export(HSVaR)
export(HillEstimator)
Modified: pkg/Dowd/R/FrechetES.R
===================================================================
--- pkg/Dowd/R/FrechetES.R 2015-06-15 19:18:04 UTC (rev 3675)
+++ pkg/Dowd/R/FrechetES.R 2015-06-16 14:22:14 UTC (rev 3676)
@@ -13,7 +13,7 @@
#' @param n Block size from which maxima are drawn
#' @param cl Confidence level
#' @param hp Holding period
-#' @return Value at Risk. If cl and hp are scalars, it returns scalar VaR. If cl
+#' @return Estimated ES. If cl and hp are scalars, it returns scalar VaR. If cl
#' is vector and hp is a scalar, or viceversa, returns vector of VaRs. If both
#' cl and hp are vectors, returns a matrix of VaRs.
#'
Modified: pkg/Dowd/R/GParetoMEFPlot.R
===================================================================
--- pkg/Dowd/R/GParetoMEFPlot.R 2015-06-15 19:18:04 UTC (rev 3675)
+++ pkg/Dowd/R/GParetoMEFPlot.R 2015-06-16 14:22:14 UTC (rev 3676)
@@ -13,8 +13,8 @@
#' @examples
#'
#' # Computes ES assuming generalised Pareto for following parameters
-#' Ra <- 5 * randn(100)
-#' mu <- 1
+#' Ra <- 5 * rnorm(100)
+#' mu <- 0
#' beta <- 1.2
#' zeta <- 1.6
#' GParetoMEFPlot(Ra, mu, beta, zeta)
Added: pkg/Dowd/R/GParetoMultipleMEFPlot.R
===================================================================
--- pkg/Dowd/R/GParetoMultipleMEFPlot.R (rev 0)
+++ pkg/Dowd/R/GParetoMultipleMEFPlot.R 2015-06-16 14:22:14 UTC (rev 3676)
@@ -0,0 +1,56 @@
+#' @title Plot of Emperical and 2 Generalised Pareto mean excess functions
+#'
+#' @description Plots of emperical mean excess function and two generalized pareto mean excess functions which differ in their tail-index value.
+#'
+#' @param Ra Vector of daily Profit/Loss data
+#' @param mu Location parameter
+#' @param beta Scale parameter
+#' @param zeta1 Assumed tail index for first mean excess function
+#' @param zeta2 Assumed tail index for second mean excess function
+#'
+#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
+#'
+#' @author Dinesh Acharya
+#' @examples
+#'
+#' # Computes ES assuming generalised Pareto for following parameters
+#' Ra <- 5 * rnorm(100)
+#' mu <- 1
+#' beta <- 1.2
+#' zeta1 <- 1.6
+#' zeta2 <- 2.2
+#' GParetoMultipleMEFPlot(Ra, mu, beta, zeta1, zeta2)
+#'
+#' @export
+GParetoMultipleMEFPlot <- function(Ra, mu, beta, zeta1, zeta2) {
+ x <- as.vector(Ra)
+ x <- sort(x)
+ u <- x
+ n <- length(u)
+ mef <- double(n - 1)
+
+ for (i in 1:(n - 1)) {
+ x <- x[which(x > u[i])]
+ mef[i] <- mean(x) - u[i]
+ }
+
+ u <- t(u)
+ u <- u[u!=max(u)]
+ gpmef1 <- (1 + zeta1 * (u - mu) / beta)/(1 - zeta1);
+ gpmef2 <- (1 + zeta2 * (u - mu) / beta)/(1 - zeta2);
+ # Plot
+ # Limits of axis
+ xlims <- c(min(u),max(u))
+ ylims <- c(min(mef, gpmef1, gpmef2), max(mef, gpmef1, gpmef2))
+ plot(u , mef, xlims, ylims, type = "l", xlab = "Threshold (u)",
+ col = 5, ylab = "e(u)")
+ par(new = TRUE)
+ plot(u , gpmef1, xlims, ylims, type = "l", xlab = "Threshold (u)",
+ col = 4, ylab = "e(u)")
+ par(new = TRUE)
+ plot(u , gpmef2, xlims, ylims, type = "l", xlab = "Threshold (u)",
+ col = 3, ylab = "e(u)")
+ title("Emperical and Two Generalised Pareto MEFs")
+ legend("topright", legend = c("Emperical MEF", "Generalized Pareto MEF1", "Generalized Pareto MEF1"), text.col = c(5,4,3))
+
+}
\ No newline at end of file
Added: pkg/Dowd/R/GParetoVaR.R
===================================================================
--- pkg/Dowd/R/GParetoVaR.R (rev 0)
+++ pkg/Dowd/R/GParetoVaR.R 2015-06-16 14:22:14 UTC (rev 3676)
@@ -0,0 +1,48 @@
+#' @title VaR for Generalized Pareto
+#'
+#' @description Estimates the Value at Risk of a portfolio assuming losses are
+#' distributed as a generalised Pareto.
+#'
+#' @param Ra Vector of daily Profit/Loss data
+#' @param beta Assumed scale parameter
+#' @param zeta Assumed tail index
+#' @param threshold.prob Threshold probability corresponding to threshold u and
+#' x
+#' @param cl VaR confidence level
+#'
+#' @return Expected Shortfall
+#'
+#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
+#'
+#' McNeil, A., Extreme value theory for risk managers. Mimeo, ETHZ, 1999.
+#'
+#' @author Dinesh Acharya
+#' @examples
+#'
+#' # Computes ES assuming generalised Pareto for following parameters
+#' Ra <- 5 * randn(100)
+#' beta <- 1.2
+#' zeta <- 1.6
+#' threshold.prob <- .85
+#' cl <- .99
+#' GParetoVaR(Ra, beta, zeta, threshold.prob, cl)
+#'
+#' @export
+GParetoVaR <- function(Ra, beta, zeta, threshold.prob, cl){
+
+ if ( max(cl) >= 1){
+ stop("Confidence level(s) must be less than 1")
+ }
+ if ( min(cl) <= 0){
+ stop("Confidence level(s) must be greater than 0")
+ }
+
+ x <- as.vector(Ra)
+ n <- length(x)
+ x <- sort(x)
+ Nu <- threshold.prob * n
+ Nu <- ((Nu >= 0) * floor(Nu) + (Nu < 0) * ceiling(Nu))
+ u <- x[n - Nu]
+ y <- u+(beta/zeta)*((((1/threshold.prob)*(1-cl))^(-zeta))-1)
+
+}
\ No newline at end of file
Added: pkg/Dowd/R/GumbelES.R
===================================================================
--- pkg/Dowd/R/GumbelES.R (rev 0)
+++ pkg/Dowd/R/GumbelES.R 2015-06-16 14:22:14 UTC (rev 3676)
@@ -0,0 +1,77 @@
+#' @title Gumbel ES
+#'
+#' @description Estimates the ES of a portfolio assuming extreme losses are
+#' Gumbel distributed, for specified confidence level and holding period.
+#' Note that the long-right-hand tail is fitted to losses, not profits.
+#'
+#' @param mu Location parameter for daily L/P
+#' @param sigma Assumed scale parameter for daily L/P
+#' @param n Assumed block size from which the maxima are drawn
+#' @param cl VaR confidence level
+#' @param hp VaR holding period
+#' @return Estimated ES. If cl and hp are scalars, it returns scalar VaR. If cl
+#' is vector and hp is a scalar, or viceversa, returns vector of VaRs. If both
+#' cl and hp are vectors, returns a matrix of VaRs.
+#'
+#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
+#'
+#' National Institute of Standards and Technology, Dataplot Reference Manual. Volume 1: Commands. NIST: Washington, DC, 1997, p. 8-67.
+#'
+#' @author Dinesh Acharya
+#' @examples
+#'
+#' # Gumber ES Plot
+#' GumbelES(0, 1.2, 100, c(.9,.88, .85, .8), 280)
+#'
+#' @export
+GumbelES<- function(mu, sigma, n, cl, hp){
+
+ # Check that inputs have correct dimensions
+ if (!length(mu) == 1) {
+ stop("Mean must be a scalar")
+ }
+ if (!length(sigma) == 1) {
+ stop("Standard Deviation must be a scalar")
+ }
+ if (!is.vector(cl)) {
+ stop("cl must be a vector")
+ }
+ if (!length(hp) == 1) {
+ stop("hp must be a scalar")
+ }
+
+ # To check that cl is read as a scalar or row vector and hp is read as a scalar of column vector as required
+ cl <- t(as.matrix(cl))
+ hp <- as.matrix(hp)
+
+ # Check that inputs obey sign and value restrictions
+ if (sigma < 0) {
+ stop("Standard deviation must be non-negative")
+ }
+ if (max(cl) >= 1) {
+ stop("Confidence levels must be less than 1")
+ }
+ if (min(cl) <= 0) {
+ stop("Confidence levels must be less than 1")
+ }
+ if (min(hp) <= 0) {
+ stop("Holding period must be greated than 0")
+ }
+
+ # VaR Estimation
+ VaR <- mu * matrix(1, dim(cl)[1], dim(cl)[2]) - sigma * log(- n * log(cl)); # Gumberl VaR
+
+ # ES Estimation
+ number.slices <- 1000 # Number of slices into which tail is divided
+ cl0 <- cl # Initial confidence level
+ term <- VaR
+
+ delta.cl <- (1 - cl)/number.slices # Increment to confidence level as each slice is taken
+ for (i in 1:(number.slices - 1)) {
+ cl <- cl0 + i * delta.cl # Revised cl
+ term <- term + mu * matrix(1, dim(cl)[1], dim(cl)[2]) - sigma * log(-n * log(cl)) # NB Gumber term
+ }
+ y <- term / (number.slices - 1)
+
+ return(y)
+}
\ No newline at end of file
Added: pkg/Dowd/R/GumbelESPlot2DCl.R
===================================================================
--- pkg/Dowd/R/GumbelESPlot2DCl.R (rev 0)
+++ pkg/Dowd/R/GumbelESPlot2DCl.R 2015-06-16 14:22:14 UTC (rev 3676)
@@ -0,0 +1,87 @@
+#' @title Gumbel VaR
+#'
+#' @description Estimates the EV VaR of a portfolio assuming extreme losses are Gumbel distributed, for specified confidence level and holding period.
+#'
+#' @param mu Location parameter for daily L/P
+#' @param sigma Assumed scale parameter for daily L/P
+#' @param n size from which the maxima are drawn
+#' @param cl VaR confidence level
+#' @param hp VaR holding period
+#'
+#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
+#'
+#'
+#' @author Dinesh Acharya
+#' @examples
+#'
+#' # Plots ES against Cl
+#' GumbelESPlot2DCl(0, 1.2, 100, c(.9,.88, .85, .8), 280)
+#'
+#' @export
+GumbelESPlot2DCl<- function(mu, sigma, n, cl, hp){
+
+ # Check that inputs have correct dimensions
+ if (!length(mu) == 1) {
+ stop("Mean must be a scalar")
+ }
+ if (!length(sigma) == 1) {
+ stop("Standard Deviation must be a scalar")
+ }
+ if (!is.vector(cl)) {
+ stop("cl must be a vector")
+ }
+ if (!length(hp) == 1) {
+ stop("hp must be a scalar")
+ }
+
+ # To check that cl is read as a row vector as required
+ cl <- t(as.matrix(cl))
+
+ # Check that inputs obey sign and value restrictions
+ if (sigma < 0) {
+ stop("Standard deviation must be non-negative")
+ }
+ if (max(cl) >= 1) {
+ stop("Confidence levels must be less than 1")
+ }
+ if (min(cl) <= 0) {
+ stop("Confidence levels must be less than 1")
+ }
+ if (min(hp) <= 0) {
+ stop("Holding period must be greated than 0")
+ }
+
+ # VaR Estimation
+ VaR <- mu * matrix(1, dim(cl)[1], dim(cl)[2]) - sigma * log(- n * log(cl));
+
+ # ES Estimation
+ number.slices <- 1000 # Number of slices into which tail is divided
+ cl0 <- cl # Initial confidence level
+ term <- VaR
+
+ delta.cl <- (1 - cl)/number.slices # Increment to confidence level as each slice is taken
+ for (i in 1:(number.slices - 1)) {
+ cl <- cl0 + i * delta.cl # Revised cl
+ term <- term + mu * matrix(1, dim(cl)[1], dim(cl)[2]) - sigma * log(-n * log(cl)) # NB Gumber term
+ }
+ v <- term / (number.slices - 1)
+
+ # Plotting
+ plot(cl0, v, xlab = "Confidence Level", ylab = "ES", type = "l")
+
+ text(mean(cl0),
+ max(v) - .1*(max(v) - min(v)),
+ 'Input parameters')
+ text(mean(cl0),
+ max(v)-.2*(max(v)-min(v)),
+ paste('Location parameter for daily L/P = ', mu))
+ text(mean(cl0),
+ max(v) - .3 * (max(v) - min(v)),
+ paste('Scale parameter for daily L/P = ', sigma))
+ text(mean(cl0),
+ max(v) - .4 * (max(v) - min(v)),
+ paste('Holding period = ', hp, ' days'))
+
+ title("Gumbel ES against confidence level")
+
+}
\ No newline at end of file
Added: pkg/Dowd/R/GumbelVaR.R
===================================================================
--- pkg/Dowd/R/GumbelVaR.R (rev 0)
+++ pkg/Dowd/R/GumbelVaR.R 2015-06-16 14:22:14 UTC (rev 3676)
@@ -0,0 +1,59 @@
+#' @title Gumbel VaR
+#'
+#' @description Estimates the EV VaR of a portfolio assuming extreme losses are Gumbel distributed, for specified confidence level and holding period.
+#'
+#' @param mu Location parameter for daily L/P
+#' @param sigma Assumed scale parameter for daily L/P
+#' @param n Size from which the maxima are drawn
+#' @param cl VaR confidence level
+#' @param hp VaR holding period
+#' @return Estimated VaR
+#'
+#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
+#'
+#'
+#' @author Dinesh Acharya
+#' @examples
+#'
+#' # Gumbel VaR
+#' GumbelVaR(0, 1.2, 100, c(.9,.88, .85, .8), 280)
+#'
+#' @export
+GumbelVaR<- function(mu, sigma, n, cl, hp){
+
+ # Check that inputs have correct dimensions
+ if (!length(mu) == 1) {
+ stop("Mean must be a scalar")
+ }
+ if (!length(sigma) == 1) {
+ stop("Standard Deviation must be a scalar")
+ }
+ if (!is.vector(cl)) {
+ stop("cl must be a vector")
+ }
+ if (!length(hp) == 1) {
+ stop("hp must be a scalar")
+ }
+
+ # To check that cl is read as a row vector as required
+ cl <- t(as.matrix(cl))
+
+ # Check that inputs obey sign and value restrictions
+ if (sigma < 0) {
+ stop("Standard deviation must be non-negative")
+ }
+ if (max(cl) >= 1) {
+ stop("Confidence levels must be less than 1")
+ }
+ if (min(cl) <= 0) {
+ stop("Confidence levels must be less than 1")
+ }
+ if (min(hp) <= 0) {
+ stop("Holding period must be greated than 0")
+ }
+
+ # VaR Estimation
+ y <- mu * matrix(1, dim(cl)[1], dim(cl)[2]) - sigma * log(- n * log(cl));
+
+ return(y)
+}
\ No newline at end of file
Added: pkg/Dowd/R/GumbelVaRPlot2DCl.R
===================================================================
--- pkg/Dowd/R/GumbelVaRPlot2DCl.R (rev 0)
+++ pkg/Dowd/R/GumbelVaRPlot2DCl.R 2015-06-16 14:22:14 UTC (rev 3676)
@@ -0,0 +1,74 @@
+#' @title Gumbel VaR
+#'
+#' @description Estimates the EV VaR of a portfolio assuming extreme losses are Gumbel distributed, for specified confidence level and holding period.
+#'
+#' @param mu Location parameter for daily L/P
+#' @param sigma Assumed scale parameter for daily L/P
+#' @param n size from which the maxima are drawn
+#' @param cl VaR confidence level
+#' @param hp VaR holding period
+#'
+#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
+#'
+#'
+#' @author Dinesh Acharya
+#' @examples
+#'
+#' # Plots VaR against Cl
+#' GumbelVaRPlot2DCl(0, 1.2, 100, c(.9,.88, .85, .8), 280)
+#'
+#' @export
+GumbelVaRPlot2DCl<- function(mu, sigma, n, cl, hp){
+
+ # Check that inputs have correct dimensions
+ if (!length(mu) == 1) {
+ stop("Mean must be a scalar")
+ }
+ if (!length(sigma) == 1) {
+ stop("Standard Deviation must be a scalar")
+ }
+ if (!is.vector(cl)) {
+ stop("cl must be a vector")
+ }
+ if (!length(hp) == 1) {
+ stop("hp must be a scalar")
+ }
+
+ # To check that cl is read as a row vector as required
+ cl <- t(as.matrix(cl))
+
+ # Check that inputs obey sign and value restrictions
+ if (sigma < 0) {
+ stop("Standard deviation must be non-negative")
+ }
+ if (max(cl) >= 1) {
+ stop("Confidence levels must be less than 1")
+ }
+ if (min(cl) <= 0) {
+ stop("Confidence levels must be less than 1")
+ }
+ if (min(hp) <= 0) {
+ stop("Holding period must be greated than 0")
+ }
+
+ # VaR Estimation
+ VaR <- mu * matrix(1, dim(cl)[1], dim(cl)[2]) - sigma * log(- n * log(cl));
+
+ # Plotting
+ plot(cl, VaR, xlab = "Confidence Level", ylab = "VaR", type = "l")
+ text(mean(cl),
+ max(VaR) - .1*(max(VaR) - min(VaR)),
+ 'Input parameters')
+ text(mean(cl),
+ max(VaR)-.2*(max(VaR)-min(VaR)),
+ paste('Location parameter for daily L/P = ', mu))
+ text(mean(cl),
+ max(VaR) - .3 * (max(VaR) - min(VaR)),
+ paste('Scale parameter for daily L/P = ', sigma))
+ text(mean(cl),
+ max(VaR) - .4 * (max(VaR) - min(VaR)),
+ paste('Holding period = ', hp, ' days'))
+
+ title("Gumbel VaR against confidence level")
+
+}
\ No newline at end of file
Modified: pkg/Dowd/man/FrechetES.Rd
===================================================================
--- pkg/Dowd/man/FrechetES.Rd 2015-06-15 19:18:04 UTC (rev 3675)
+++ pkg/Dowd/man/FrechetES.Rd 2015-06-16 14:22:14 UTC (rev 3676)
@@ -20,7 +20,7 @@
\item{hp}{Holding period}
}
\value{
-Value at Risk. If cl and hp are scalars, it returns scalar VaR. If cl
+Estimated ES. If cl and hp are scalars, it returns scalar VaR. If cl
is vector and hp is a scalar, or viceversa, returns vector of VaRs. If both
cl and hp are vectors, returns a matrix of VaRs.
}
Modified: pkg/Dowd/man/GParetoMEFPlot.Rd
===================================================================
--- pkg/Dowd/man/GParetoMEFPlot.Rd 2015-06-15 19:18:04 UTC (rev 3675)
+++ pkg/Dowd/man/GParetoMEFPlot.Rd 2015-06-16 14:22:14 UTC (rev 3676)
@@ -20,8 +20,8 @@
}
\examples{
# Computes ES assuming generalised Pareto for following parameters
- Ra <- 5 * randn(100)
- mu <- 1
+ Ra <- 5 * rnorm(100)
+ mu <- 0
beta <- 1.2
zeta <- 1.6
GParetoMEFPlot(Ra, mu, beta, zeta)
Added: pkg/Dowd/man/GParetoMultipleMEFPlot.Rd
===================================================================
--- pkg/Dowd/man/GParetoMultipleMEFPlot.Rd (rev 0)
+++ pkg/Dowd/man/GParetoMultipleMEFPlot.Rd 2015-06-16 14:22:14 UTC (rev 3676)
@@ -0,0 +1,38 @@
+% Generated by roxygen2 (4.1.1): do not edit by hand
+% Please edit documentation in R/GParetoMultipleMEFPlot.R
+\name{GParetoMultipleMEFPlot}
+\alias{GParetoMultipleMEFPlot}
+\title{Plot of Emperical and 2 Generalised Pareto mean excess functions}
+\usage{
+GParetoMultipleMEFPlot(Ra, mu, beta, zeta1, zeta2)
+}
+\arguments{
+\item{Ra}{Vector of daily Profit/Loss data}
+
+\item{mu}{Location parameter}
+
+\item{beta}{Scale parameter}
+
+\item{zeta1}{Assumed tail index for first mean excess function}
+
+\item{zeta2}{Assumed tail index for second mean excess function}
+}
+\description{
+Plots of emperical mean excess function and two generalized pareto mean excess functions which differ in their tail-index value.
+}
+\examples{
+# Computes ES assuming generalised Pareto for following parameters
+ Ra <- 5 * rnorm(100)
+ mu <- 1
+ beta <- 1.2
+ zeta1 <- 1.6
+ zeta2 <- 2.2
+ GParetoMultipleMEFPlot(Ra, mu, beta, zeta1, zeta2)
+}
+\author{
+Dinesh Acharya
+}
+\references{
+Dowd, K. Measuring Market Risk, Wiley, 2007.
+}
+
Added: pkg/Dowd/man/GParetoVaR.Rd
===================================================================
--- pkg/Dowd/man/GParetoVaR.Rd (rev 0)
+++ pkg/Dowd/man/GParetoVaR.Rd 2015-06-16 14:22:14 UTC (rev 3676)
@@ -0,0 +1,45 @@
+% Generated by roxygen2 (4.1.1): do not edit by hand
+% Please edit documentation in R/GParetoVaR.R
+\name{GParetoVaR}
+\alias{GParetoVaR}
+\title{VaR for Generalized Pareto}
+\usage{
+GParetoVaR(Ra, beta, zeta, threshold.prob, cl)
+}
+\arguments{
+\item{Ra}{Vector of daily Profit/Loss data}
+
+\item{beta}{Assumed scale parameter}
+
+\item{zeta}{Assumed tail index}
+
+\item{threshold.prob}{Threshold probability corresponding to threshold u and
+x}
+
+\item{cl}{VaR confidence level}
+}
+\value{
+Expected Shortfall
+}
+\description{
+Estimates the Value at Risk of a portfolio assuming losses are
+distributed as a generalised Pareto.
+}
+\examples{
+# Computes ES assuming generalised Pareto for following parameters
+ Ra <- 5 * randn(100)
+ beta <- 1.2
+ zeta <- 1.6
+ threshold.prob <- .85
+ cl <- .99
+ GParetoVaR(Ra, beta, zeta, threshold.prob, cl)
+}
+\author{
+Dinesh Acharya
+}
+\references{
+Dowd, K. Measuring Market Risk, Wiley, 2007.
+
+McNeil, A., Extreme value theory for risk managers. Mimeo, ETHZ, 1999.
+}
+
Added: pkg/Dowd/man/GumbelES.Rd
===================================================================
--- pkg/Dowd/man/GumbelES.Rd (rev 0)
+++ pkg/Dowd/man/GumbelES.Rd 2015-06-16 14:22:14 UTC (rev 3676)
@@ -0,0 +1,42 @@
+% Generated by roxygen2 (4.1.1): do not edit by hand
+% Please edit documentation in R/GumbelES.R
+\name{GumbelES}
+\alias{GumbelES}
+\title{Gumbel ES}
+\usage{
+GumbelES(mu, sigma, n, cl, hp)
+}
+\arguments{
+\item{mu}{Location parameter for daily L/P}
+
+\item{sigma}{Assumed scale parameter for daily L/P}
+
+\item{n}{Assumed block size from which the maxima are drawn}
+
+\item{cl}{VaR confidence level}
+
+\item{hp}{VaR holding period}
+}
+\value{
+Estimated ES. If cl and hp are scalars, it returns scalar VaR. If cl
+is vector and hp is a scalar, or viceversa, returns vector of VaRs. If both
+cl and hp are vectors, returns a matrix of VaRs.
+}
+\description{
+Estimates the ES of a portfolio assuming extreme losses are
+Gumbel distributed, for specified confidence level and holding period.
+Note that the long-right-hand tail is fitted to losses, not profits.
+}
+\examples{
+# Gumber ES Plot
+ GumbelES(0, 1.2, 100, c(.9,.88, .85, .8), 280)
+}
+\author{
+Dinesh Acharya
+}
+\references{
+Dowd, K. Measuring Market Risk, Wiley, 2007.
+
+National Institute of Standards and Technology, Dataplot Reference Manual. Volume 1: Commands. NIST: Washington, DC, 1997, p. 8-67.
+}
+
Added: pkg/Dowd/man/GumbelESPlot2DCl.Rd
===================================================================
--- pkg/Dowd/man/GumbelESPlot2DCl.Rd (rev 0)
+++ pkg/Dowd/man/GumbelESPlot2DCl.Rd 2015-06-16 14:22:14 UTC (rev 3676)
@@ -0,0 +1,33 @@
+% Generated by roxygen2 (4.1.1): do not edit by hand
+% Please edit documentation in R/GumbelESPlot2DCl.R
+\name{GumbelESPlot2DCl}
+\alias{GumbelESPlot2DCl}
+\title{Gumbel VaR}
+\usage{
+GumbelESPlot2DCl(mu, sigma, n, cl, hp)
+}
+\arguments{
+\item{mu}{Location parameter for daily L/P}
+
+\item{sigma}{Assumed scale parameter for daily L/P}
+
+\item{n}{size from which the maxima are drawn}
+
+\item{cl}{VaR confidence level}
+
+\item{hp}{VaR holding period}
+}
+\description{
+Estimates the EV VaR of a portfolio assuming extreme losses are Gumbel distributed, for specified confidence level and holding period.
+}
+\examples{
+# Plots ES against Cl
+ GumbelESPlot2DCl(0, 1.2, 100, c(.9,.88, .85, .8), 280)
+}
+\author{
+Dinesh Acharya
+}
+\references{
+Dowd, K. Measuring Market Risk, Wiley, 2007.
+}
+
Added: pkg/Dowd/man/GumbelVaR.Rd
===================================================================
--- pkg/Dowd/man/GumbelVaR.Rd (rev 0)
+++ pkg/Dowd/man/GumbelVaR.Rd 2015-06-16 14:22:14 UTC (rev 3676)
@@ -0,0 +1,36 @@
+% Generated by roxygen2 (4.1.1): do not edit by hand
+% Please edit documentation in R/GumbelVaR.R
+\name{GumbelVaR}
+\alias{GumbelVaR}
+\title{Gumbel VaR}
+\usage{
+GumbelVaR(mu, sigma, n, cl, hp)
+}
+\arguments{
+\item{mu}{Location parameter for daily L/P}
+
+\item{sigma}{Assumed scale parameter for daily L/P}
+
+\item{n}{Size from which the maxima are drawn}
+
+\item{cl}{VaR confidence level}
+
+\item{hp}{VaR holding period}
+}
+\value{
+Estimated VaR
+}
+\description{
+Estimates the EV VaR of a portfolio assuming extreme losses are Gumbel distributed, for specified confidence level and holding period.
+}
+\examples{
+# Gumbel VaR
+ GumbelVaR(0, 1.2, 100, c(.9,.88, .85, .8), 280)
+}
+\author{
+Dinesh Acharya
+}
+\references{
+Dowd, K. Measuring Market Risk, Wiley, 2007.
+}
+
Added: pkg/Dowd/man/GumbelVaRPlot2DCl.Rd
===================================================================
--- pkg/Dowd/man/GumbelVaRPlot2DCl.Rd (rev 0)
+++ pkg/Dowd/man/GumbelVaRPlot2DCl.Rd 2015-06-16 14:22:14 UTC (rev 3676)
@@ -0,0 +1,33 @@
+% Generated by roxygen2 (4.1.1): do not edit by hand
+% Please edit documentation in R/GumbelVaRPlot2DCl.R
+\name{GumbelVaRPlot2DCl}
+\alias{GumbelVaRPlot2DCl}
+\title{Gumbel VaR}
+\usage{
+GumbelVaRPlot2DCl(mu, sigma, n, cl, hp)
+}
+\arguments{
+\item{mu}{Location parameter for daily L/P}
+
+\item{sigma}{Assumed scale parameter for daily L/P}
+
+\item{n}{size from which the maxima are drawn}
+
+\item{cl}{VaR confidence level}
+
+\item{hp}{VaR holding period}
+}
+\description{
+Estimates the EV VaR of a portfolio assuming extreme losses are Gumbel distributed, for specified confidence level and holding period.
+}
+\examples{
+# Plots VaR against Cl
+ GumbelVaRPlot2DCl(0, 1.2, 100, c(.9,.88, .85, .8), 280)
+}
+\author{
+Dinesh Acharya
+}
+\references{
+Dowd, K. Measuring Market Risk, Wiley, 2007.
+}
+
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