FrechetES function

Frechet Expected Shortfall

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

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

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.

Details

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

Examples

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

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.