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#' @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 * rnorm(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)
}
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