VaR/R/varFW.R

In mnquants/VaR: Portfolio Value at Risk

# Value at Risk Framework
# Author: Kyle Loomis
# Updated: 10/31/17
# Desc: Framework for implementing
#       Value at Risk methods


#' Parametric
#' @param mean Mean return of timeseries data
#' @param sd Standard deviation value of timeseries data
#' @param alpha Alpha value for confidence level
#' @param delta_t Number of days to forecast VaR
#' @return Vector of Adjusted close prices
parametric <- function(mean, sd, alpha, delta_t, ES=FALSE) {
  # qnorm function used to calculate z-score
  parametric2 <- function(alpha) {
    return((mean - (qnorm(1-alpha,0,1)*sd))*sqrt(delta_t))
  }
  if (ES) { return(integrate(parametric2, 0, alpha)$value / alpha) }
  else { return(parametric2(alpha)) }
}

#' Monte Carlo
#' @param mean Sample mean return
#' @param sd Sample standard deviation return
#' @param n Number of iterations
#' @param delta_t Change in time (usually days)
#' @return Vector of simulated returns
#' @export
monteCarlo <- function(mean, sd, n, delta_t) {
  return(mean*delta_t + sd*rnorm(n)*sqrt(delta_t))
}

#' Historical Simulation
#' @param alpha Alpha value for confidence level
#' @param histRet Vector of historical returns
#' @return Max of lowest alpha*100 of histP
historicalSim <- function(histRet, alpha) {
  max((sort(coredata(histRet)))[1:(alpha*length(histRet))])
}

#' Value at Risk Statistics
#' @param calibrationVaR Calibrated VaR
#' @param testMin Minimum return
#' @return Vector of Calibrated VaR and Minimum Return
#' @export
varStats <- function(calibrationVaR, testMin) {
  stats <- c(calibrationVaR, testMin)
  names(stats) <- c("Calibrated VaR","Minumum Return")
  return(stats)
}

#' Value at Risk Wrapper Function
#' @param vLogReturn Vector of Log Returns
#' @param alpha Confidence level
#' @param n Number of iterations. Default: 1000000
#' @param delta_t Time to forecast value at risk. Default: 1
#' @param method Method of calculation. Default: parametric. (montecarlo, historical)
#' @param ES Expected Shortfall (Conditional VaR). Default: FALSE
#' @return Value at Risk value
#' @export
VaR <- function(vLogReturn, alpha=0.05, n=1000000, delta_t=1,
  method="parametric", ES=FALSE) {
  if (method=="historical") { historicalSim(vLogReturn,alpha) }
  else if (method=="montecarlo") { quantile(monteCarlo(mean(vLogReturn),sd(vLogReturn),n,delta_t),alpha) }
  # default case: parametric
  else if (method=="parametric") { parametric(mean(vLogReturn),sd(vLogReturn),alpha,delta_t,ES) }
}