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#' Plots log normal VaR against confidence level and holding period
#'
#' Plots the VaR of a portfolio against confidence level and holding period assuming that geometric
#' returns are normal distributed, for specified confidence level and
#' holding period.
#'
#' @param ... The input arguments contain either return data or else mean and
#' standard deviation data. Accordingly, number of input arguments is either 4
#' or 5. In case there 4 input arguments, the mean and standard deviation of
#' data is computed from return data. See examples for details.
#'
#' returns Vector of daily geometric return data
#'
#' mu Mean of daily geometric return data
#'
#' sigma Standard deviation of daily geometric return data
#'
#' investment Size of investment
#'
#' cl VaR confidence level and must be a vector
#'
#' hp VaR holding period and must be a vector
#'
#' @references Dowd, K. Measuring Market Risk, Wiley, 2007.
#'
#' @author Dinesh Acharya
#' @examples
#'
#' # Plots VaR against confidene level given geometric return data
#' data <- rnorm(5, .09, .03)
#' LogNormalVaRPlot3D(returns = data, investment = 5, cl = seq(.9,.99,.01), hp = 1:100)
#'
#' # Computes VaR against confidence level given mean and standard deviation of return data
#' LogNormalVaRPlot3D(mu = .012, sigma = .03, investment = 5, cl = seq(.9,.99,.01), hp = 1:100)
#'
#'
#' @export
LogNormalVaRPlot3D <- function(...){
# Determine if there are four or five arguments, and ensure that arguments are read as intended
if (nargs() < 4) {
stop("Too few arguments")
}
if (nargs() > 5) {
stop("Too many arguments")
}
args <- list(...)
if (nargs() == 5) {
mu <- args$mu
investment <- args$investment
cl <- args$cl
sigma <- args$sigma
hp <- args$hp
}
if (nargs() == 4) {
mu <- mean(args$returns)
investment <- args$investment
cl <- args$cl
sigma <- sd(args$returns)
hp <- args$hp
}
# Check that inputs have correct dimensions
mu <- as.matrix(mu)
mu.row <- dim(mu)[1]
mu.col <- dim(mu)[2]
if (max(mu.row, mu.col) > 1) {
stop("Mean must be a scalar")
}
sigma <- as.matrix(sigma)
sigma.row <- dim(sigma)[1]
sigma.col <- dim(sigma)[2]
if (max(sigma.row, sigma.col) > 1) {
stop("Standard deviation must be a scalar")
}
cl <- as.matrix(cl)
cl.row <- dim(cl)[1]
cl.col <- dim(cl)[2]
if (min(cl.row, cl.col) > 1) {
stop("Confidence level must be a vector")
}
hp <- as.matrix(hp)
hp.row <- dim(hp)[1]
hp.col <- dim(hp)[2]
if (min(hp.row, hp.col) > 1) {
stop("Holding period must be a vector")
}
# Check that cl is read as row vector
if (cl.row > cl.col) {
cl <- t(cl)
}
# Check that hp is read as column vector
if (hp.col > hp.row) {
hp <- t(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 greater than 0")
}
if (min(hp) <= 0){
stop("Holding periods must be greater than 0")
}
# VaR estimation
cl.row <- dim(cl)[1]
cl.col <- dim(cl)[2]
VaR <- investment - exp( sigma[1,1] * sqrt(hp) %*% qnorm(1 - cl, 0, 1) + mu[1,1] * hp %*% matrix(1,cl.row,cl.col) + log(investment)) # VaR
# Plotting
persp(x=cl, y=hp, t(VaR), xlab = "Confidence Level",
ylab = "Holding Period", zlab = "VaR", border=NA,
theta = -45, phi = 35, shade = .75, ltheta = 90, cex.axis=.85, cex.lab=.85,
col = "lightgray", ticktype = "detailed", nticks = 5,
main = "Log Normal VaR against CL and HP")
}
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