[Returnanalytics-commits] r3670 - in pkg/Dowd: . R man
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Wed Jun 10 23:08:25 CEST 2015
Author: dacharya
Date: 2015-06-10 23:08:25 +0200 (Wed, 10 Jun 2015)
New Revision: 3670
Added:
pkg/Dowd/R/FrechetES.R
pkg/Dowd/R/FrechetVaR.R
pkg/Dowd/man/FrechetES.Rd
pkg/Dowd/man/FrechetVaR.Rd
Modified:
pkg/Dowd/NAMESPACE
pkg/Dowd/readme.txt
Log:
FrechetES and FrechetVaR: source and documentation
Modified: pkg/Dowd/NAMESPACE
===================================================================
--- pkg/Dowd/NAMESPACE 2015-06-10 18:40:35 UTC (rev 3669)
+++ pkg/Dowd/NAMESPACE 2015-06-10 21:08:25 UTC (rev 3670)
@@ -16,6 +16,8 @@
export(ChristoffersenBacktestForUnconditionalCoverage)
export(CornishFisherES)
export(CornishFisherVaR)
+export(FrechetES)
+export(FrechetVaR)
export(GaussianCopulaVaR)
export(GumbelCopulaVaR)
export(HSES)
Added: pkg/Dowd/R/FrechetES.R
===================================================================
--- pkg/Dowd/R/FrechetES.R (rev 0)
+++ pkg/Dowd/R/FrechetES.R 2015-06-10 21:08:25 UTC (rev 3670)
@@ -0,0 +1,97 @@
+#' Frechet Expected Shortfall
+#'
+#' Plots the ES of a portfolio against confidence level assuming extreme losses
+#' are Frechet distributed, for specified confidence level and a given
+#' 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 Scale parameter for daily L/P
+#' @param tail.index Tail index
+#' @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
+#' 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.
+#'
+#' Embrechts, P., Kluppelberg, C. and Mikosch, T., Modelling Extremal Events for
+#' Insurance and Finance. Springer, Berlin, 1997, p. 324.
+#'
+#' Reiss, R. D. and Thomas, M. Statistical Analysis of Extreme Values from
+#' Insurance, Finance, Hydrology and Other Fields, Birkhaueser, Basel, 1997,
+#' 15-18.
+#'
+#' @author Dinesh Acharya
+#' @examples
+#'
+#' # Computes VaR assuming Frechet Distribution for given parameters
+#' FrechetVaR(3.5, 2.3, 1.6, 10, .95, 30)
+#'
+#' @export
+FrechetES <- function(mu, sigma, tail.index, n, cl, hp){
+
+ # Check that inputs have correct dimensions
+ if (!length(mu) == 1) {
+ stop("mu must be a scalar")
+ }
+ if (!length(sigma) == 1) {
+ stop("sigma must be a scalar")
+ }
+ if (!length(tail.index) == 1) {
+ stop("tail.index must be a scalar")
+ }
+ if (!is.vector(cl)) {
+ stop("cl must be a vector or a scalar")
+ }
+ if (!is.vector(hp)) {
+ stop("hp must be a vector or a scalar")
+ }
+
+ # Change cl and hp to row vector and column vectors respectively
+ cl <- t(as.matrix(cl))
+ hp <- as.matrix(hp)
+
+ # Check that parameters obey sign and value restrictions
+ if (sigma < 0) {
+ stop("Standard deviation must be non-negative")
+ }
+ if (min(tail.index) <= 0) {
+ stop("Tail index must be greater than 0")
+ }
+ 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")
+ }
+ if ( min(cl) <= 0){
+ stop("Holding period(s) must be greater than 0")
+ }
+
+ # VaR estimation
+ VaR <- mu * matrix(1, 1, length(cl)) - (sigma / tail.index) *
+ (1 - ( - n * log(cl)) ^ ( - tail.index))
+
+ # 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, 1, length(cl)) - (sigma / tail.index) *
+ (1 - ( - n * log(cl)) ^ ( - tail.index))
+ # NB Frechet term
+ }
+
+ y <- term / (number.slices - 1)
+
+ return(y)
+
+}
\ No newline at end of file
Added: pkg/Dowd/R/FrechetVaR.R
===================================================================
--- pkg/Dowd/R/FrechetVaR.R (rev 0)
+++ pkg/Dowd/R/FrechetVaR.R 2015-06-10 21:08:25 UTC (rev 3670)
@@ -0,0 +1,81 @@
+#' Frechet Value at Risk
+#'
+#' Plots the VaR of a portfolio against confidence level assuming extreme losses
+#' are Frechet distributed, for specified range of confidence level and a given
+#' 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 Scale parameter for daily L/P
+#' @param tail.index Tail index
+#' @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
+#' 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.
+#'
+#' Embrechts, P., Kluppelberg, C. and Mikosch, T., Modelling Extremal Events for
+#' Insurance and Finance. Springer, Berlin, 1997, p. 324.
+#'
+#' Reiss, R. D. and Thomas, M. Statistical Analysis of Extreme Values from
+#' Insurance, Finance, Hydrology and Other Fields, Birkhaueser, Basel, 1997,
+#' 15-18.
+#'
+#' @author Dinesh Acharya
+#' @examples
+#'
+#' # Computes VaR assuming Frechet Distribution for given parameters
+#' FrechetVaR(3.5, 2.3, 1.6, 10, .95, 30)
+#'
+#' @export
+FrechetVaR <- function(mu, sigma, tail.index, n, cl, hp){
+
+ # Check that inputs have correct dimensions
+ if (!length(mu) == 1) {
+ stop("mu must be a scalar")
+ }
+ if (!length(sigma) == 1) {
+ stop("sigma must be a scalar")
+ }
+ if (!length(tail.index) == 1) {
+ stop("tail.index must be a scalar")
+ }
+ if (!is.vector(cl)) {
+ stop("cl must be a vector or a scalar")
+ }
+ if (!is.vector(hp)) {
+ stop("hp must be a vector or a scalar")
+ }
+
+ # Change cl and hp to row vector and column vectors respectively
+ cl <- t(as.matrix(cl))
+ hp <- as.matrix(hp)
+
+ # Check that parameters obey sign and value restrictions
+ if (sigma < 0) {
+ stop("Standard deviation must be non-negative")
+ }
+ if (min(tail.index) <= 0) {
+ stop("Tail index must be greater than 0")
+ }
+ 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")
+ }
+ if ( min(cl) <= 0){
+ stop("Holding period(s) must be greater than 0")
+ }
+ # VaR estimation
+ y <- mu * matrix(1, 1, length(cl)) - (sigma / tail.index) *
+ (1 - ( - n * log(cl)) ^ ( - tail.index))
+
+ return(y)
+
+}
\ No newline at end of file
Added: pkg/Dowd/man/FrechetES.Rd
===================================================================
--- pkg/Dowd/man/FrechetES.Rd (rev 0)
+++ pkg/Dowd/man/FrechetES.Rd 2015-06-10 21:08:25 UTC (rev 3670)
@@ -0,0 +1,52 @@
+% Generated by roxygen2 (4.1.1): do not edit by hand
+% Please edit documentation in R/FrechetES.R
+\name{FrechetES}
+\alias{FrechetES}
+\title{Frechet Expected Shortfall}
+\usage{
+FrechetES(mu, sigma, tail.index, n, cl, hp)
+}
+\arguments{
+\item{mu}{Location parameter for daily L/P}
+
+\item{sigma}{Scale parameter for daily L/P}
+
+\item{tail.index}{Tail index}
+
+\item{n}{Block size from which maxima are drawn}
+
+\item{cl}{Confidence level}
+
+\item{hp}{Holding period}
+}
+\value{
+Value at Risk. 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{
+Plots the ES of a portfolio against confidence level assuming extreme losses
+are Frechet distributed, for specified confidence level and a given
+holding period.
+}
+\details{
+Note that the long-right-hand tail is fitted to losses, not profits.
+}
+\examples{
+# Computes VaR assuming Frechet Distribution for given parameters
+ FrechetVaR(3.5, 2.3, 1.6, 10, .95, 30)
+}
+\author{
+Dinesh Acharya
+}
+\references{
+Dowd, K. Measuring Market Risk, Wiley, 2007.
+
+Embrechts, P., Kluppelberg, C. and Mikosch, T., Modelling Extremal Events for
+Insurance and Finance. Springer, Berlin, 1997, p. 324.
+
+Reiss, R. D. and Thomas, M. Statistical Analysis of Extreme Values from
+Insurance, Finance, Hydrology and Other Fields, Birkhaueser, Basel, 1997,
+15-18.
+}
+
Added: pkg/Dowd/man/FrechetVaR.Rd
===================================================================
--- pkg/Dowd/man/FrechetVaR.Rd (rev 0)
+++ pkg/Dowd/man/FrechetVaR.Rd 2015-06-10 21:08:25 UTC (rev 3670)
@@ -0,0 +1,52 @@
+% Generated by roxygen2 (4.1.1): do not edit by hand
+% Please edit documentation in R/FrechetVaR.R
+\name{FrechetVaR}
+\alias{FrechetVaR}
+\title{Frechet Value at Risk}
+\usage{
+FrechetVaR(mu, sigma, tail.index, n, cl, hp)
+}
+\arguments{
+\item{mu}{Location parameter for daily L/P}
+
+\item{sigma}{Scale parameter for daily L/P}
+
+\item{tail.index}{Tail index}
+
+\item{n}{Block size from which maxima are drawn}
+
+\item{cl}{Confidence level}
+
+\item{hp}{Holding period}
+}
+\value{
+Value at Risk. 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{
+Plots the VaR of a portfolio against confidence level assuming extreme losses
+are Frechet distributed, for specified range of confidence level and a given
+holding period.
+}
+\details{
+Note that the long-right-hand tail is fitted to losses, not profits.
+}
+\examples{
+# Computes VaR assuming Frechet Distribution for given parameters
+ FrechetVaR(3.5, 2.3, 1.6, 10, .95, 30)
+}
+\author{
+Dinesh Acharya
+}
+\references{
+Dowd, K. Measuring Market Risk, Wiley, 2007.
+
+Embrechts, P., Kluppelberg, C. and Mikosch, T., Modelling Extremal Events for
+Insurance and Finance. Springer, Berlin, 1997, p. 324.
+
+Reiss, R. D. and Thomas, M. Statistical Analysis of Extreme Values from
+Insurance, Finance, Hydrology and Other Fields, Birkhaueser, Basel, 1997,
+15-18.
+}
+
Modified: pkg/Dowd/readme.txt
===================================================================
--- pkg/Dowd/readme.txt 2015-06-10 18:40:35 UTC (rev 3669)
+++ pkg/Dowd/readme.txt 2015-06-10 21:08:25 UTC (rev 3670)
@@ -1,4 +1,11 @@
+#
+# General Notes for Modification:
#***************************************************************
+# FrechetVaR does not use hp and the remark about return value when it is vector is vaccuous.
+#***************************************************************
+# In Normal/t QQ Plots, dowd code does not work for matrices but the code contains parts that
+# work for matrices. some vectors like pvec are not defined anywhere in his code.
+#***************************************************************
# Some error is present in GumbelCopulaVaR and needs correction
#***************************************************************
# Bootstrap is functional (but HSVaR still does not accept matrix P/L
@@ -6,7 +13,6 @@
#***************************************************************
# Jarque-Bera Test:
# It has to be checked Probability of null (H0) or (H1).
-#
#***************************************************************
# Christofferson Backtest for Independence:
# VaR(excess_loss<=0)=[]; Does not make sense. It is still to be checked if it is as intended.
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