R/Risk.R

In OCA: Optimal Capital Allocations

#' Risk
#'
#' @description
#' \loadmathjax{}
#' Risk measures such as Value at Risk (VaR) and Expected Shortfall (ES) with normal and t-student
#' distributions based on variance-covariance method. It is a shortcut for VaR and ES.
#'
#' @param variance It could be either a scalar or a matrix containing the variances and covariances
#'  of the losses. Provide a covariance matrix when analyzing correlated losses or a scalar when dealing
#'  with a single loss.
#' @param alpha The confidence level at which either the VaR or the ES will be computed, by default \code{alpha} is set to 0.95.
#' @param measure An optional character string giving a measure for computing the risk. \code{"VaR"} stands for Value at Risk,
#'  \code{"ES"} stands for Expected Shortfall, and if both is chosen, then the function returns both the VaR
#'   and the ES as a result. By default \code{measure} is set to be \code{"both"}.
#' @param weights A vector containing the weights. It is only needed if \code{variance} is a matrix, if it is not then \code{weights} is set to 1.
#' @param model A character string indicating which probability model has to be used for computing the risk measures, it could only be a
#' normal distribution or a t-student distribution with \mjteqn{v}{v}{} degrees of freedom. The normal distribution is the
#' default model for this function. \code{model} default value is set to \code{'both'}
#'  to show normal and t-student VaR and ES. See example below.
#' @param df An integer (\code{df}>2) denoting the degrees of freedom, only required if \code{model='t-student'}. Otherwise it has to be \code{NULL}.
#' @param percentage Logical indicating whether the file names in the VaR table should be presented in percentage or decimal.
#'
#' @return
#' A \code{data.frame} containing each risk measure at its corresponding confidence level.
#' @references
#' Dhaene J., Tsanakas A., Valdez E. and Vanduffel S. (2011). \emph{Optimal Capital Allocation Principles}. The Journal of Risk and Insurance. Vol. 00, No. 0, 1-28.
#'
#' Urbina, J. (2013) \emph{Quantifying Optimal Capital Allocation Principles based on Risk Measures.} Master Thesis, Universitat Politècnica de Catalunya.
#'
#' Urbina, J. and Guillén, M. (2014). \emph{An application of capital allocation principles to operational risk and the cost of fraud}. Expert Systems with Applications. 41(16):7023-7031.
#'
#' @seealso
#' \code{\link{VaR}}, \code{\link{ES}}
#'
#'@author Jilber Urbina
#' @noMd
#' @export
#' @importFrom mathjaxr preview_rd
#' @importFrom stats cov dnorm dt qnorm qt var
#'@examples
#'# Reproducing Table 2.1 in page 47 of
#'# McNeal A., Frey R. and Embrechts P (2005).
#'alpha <- c(.90, .95, .975, .99, .995)
#'(Risk(variance=(0.2/sqrt(250))^2, alpha=alpha, measure='both', model='both', df=4))*10000
#'
#'# only VaR results
#'(Risk(variance=(0.2/sqrt(250))^2, alpha=alpha, measure='VaR', model='both', df=4))*10000
#'
#'
#'# only SE based on a 4 degrees t-student.
#'(Risk(variance=(0.2/sqrt(250))^2, alpha=alpha, measure='ES', model='t-student', df=4))*10000






Risk <- function(variance, alpha=0.95, measure=c('both', 'VaR', 'ES'),
         weights=NULL, model=c('both', 'normal', 't-student'),
         df=NULL, percentage = FALSE){

  measure <- match.arg(measure)

  if(measure=='VaR' | measure=='both'){
    VaR. <- VaR(variance=variance, alpha=alpha, weights=weights, model=model, df=df, percentage = percentage)
  }

  if(measure=='ES' | measure=='both'){
    ES. <- ES(variance=variance, alpha=alpha, weights=weights, model=model, df=df, percentage = percentage)
  }

  if(measure=='VaR'){
    return(VaR.)
  }
  if(measure=='ES'){
    return(ES.)
  }
  if(measure=='both'){
    return(rbind(VaR., ES.))
  }
}