GumbelES function

Gumbel ES

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.

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

Returns

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.

Examples

# Gumber ES Plot
   GumbelES(0, 1.2, 100, c(.9,.88, .85, .8), 280)

Author(s)

Dinesh Acharya

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.