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