Estimates the ES of a portfolio assuming extreme losses are
Gumbel distributed, for specified confidence level and holding period.
Note that the long-right-hand tail is fitted to losses, not profits.
Usage
GumbelES(mu, sigma, n, cl, hp)
Arguments
mu
Location parameter for daily L/P
sigma
Assumed scale parameter for daily L/P
n
Assumed block size from which the maxima are drawn
cl
VaR confidence level
hp
VaR holding period
Value
Estimated ES. If cl and hp are scalars, it returns scalar VaR. If cl
is vector and hp is a scalar, or viceversa, returns vector of VaRs. If both
cl and hp are vectors, returns a matrix of VaRs.
References
Dowd, K. Measuring Market Risk, Wiley, 2007.
National Institute of Standards and Technology, Dataplot Reference Manual.
Volume 1: Commands. NIST: Washington, DC, 1997, p. 8-67.