#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
#
# Parametric Value-at-Risk and Expected-Shortfall calculations
#
#-----

VaR_norm = function(alpha,mu,sgma,S=1){
  # The VaR under the assumption of a normal-distribution 
  - S * ( mu + qnorm(alpha) * sgma )
}

ES_norm = function(alpha,mu,sgma,S=1){
  # The ES under the assumption of a normal-distribution
  S * ( - mu + sgma * ( dnorm(qnorm(alpha))/alpha ) )
}

VaR_t = function(alpha,mu,lambda,nu,S=1){
  # The VaR under the assumption of a t-distribution 
  - S * ( mu + qt(alpha,nu) * lambda )
}

ES_t = function(alpha,mu,lambda,nu,S=1){
  # The ES under the assumption of a t-distribution 
  S * ( - mu + lambda * ( dt(qt(alpha,nu),nu) / alpha ) * ( ( nu + qt(alpha,nu)^2 )/( nu - 1 ) ) )
}