FrechetES {Dowd}

Frechet Expected Shortfall

Description

Estimates the ES of a portfolio assuming extreme losses are Frechet distributed, for specified confidence level and a given holding period.

Usage

FrechetES(mu, sigma, tail.index, n, cl, hp)

Arguments

mu

Location parameter for daily L/P

sigma

Scale parameter for daily L/P

tail.index

Tail index

n

Block size from which maxima are drawn

cl

Confidence level

hp

Holding period

Details

Note that the long-right-hand tail is fitted to losses, not profits.

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.

Author(s)

Dinesh Acharya

References

Dowd, K. Measuring Market Risk, Wiley, 2007.

Embrechts, P., Kluppelberg, C. and Mikosch, T., Modelling Extremal Events for Insurance and Finance. Springer, Berlin, 1997, p. 324.

Reiss, R. D. and Thomas, M. Statistical Analysis of Extreme Values from Insurance, Finance, Hydrology and Other Fields, Birkhaueser, Basel, 1997, 15-18.

Examples

# Computes ES assuming Frechet Distribution for given parameters
   FrechetES(3.5, 2.3, 1.6, 10, .95, 30)