FrechetVaR function

Frechet Value at Risk

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

FrechetVaR(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

Value at Risk. 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 VaR assuming Frechet Distribution for given parameters
   FrechetVaR(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.