ES: Expected Shortfall

In manueleleonelli/extrememix: Bayesian Estimation of Extreme Value Mixture Models

Expected Shortfall

Description

Computation of the expected shortfall for an extreme value mixture model

Usage

ES(x, ...)

## S3 method for class 'evmm'
ES(x, values = NULL, cred = 0.95, ...)

Arguments

x	the output of a model estimated with extrememix.
...	additional arguments for compatibility.
values	numeric vector of values of which to compute the expected shortfall.
cred	amplitude of the posterior credibility interval.

Details

The expected shortfall is the expectation of a random variable conditional of being larger of a specific Value-at-Risk (quantile). For an extreme value mixture model this is equal to:

ES_p = \frac{VaR_p}{1-\xi} +\frac{\sigma-\xi u }{1-\xi}

Value

A list with the following entries:

• quantiles: a matrix containing the estimated shortfall, the posterior credibility intervals and the empirical estimate.

• data: the dataset used to estimate the expected shortfall.

• complete: a matrix with the expected shortfall for each value in the posterior sample.

References

Lattanzi, Chiara, and Manuele Leonelli. "A changepoint approach for the identification of financial extreme regimes." Brazilian Journal of Probability and Statistics.

See Also

quant, return_level, VaR

Examples

ES(rainfall_ggpd)

manueleleonelli/extrememix documentation built on Oct. 25, 2024, 6:24 p.m.