Description
Computation of the expected shortfall for an extreme value mixture model
Usage
ES(x, ...)# S3 method for evmm
ES(x, values = NULL, cred = 0.95, ...)
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.
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: $$ES_p = \frac{VaR_p}{1-\xi} +\frac{\sigma-\xi u }{1-\xi}$$
References
Lattanzi, Chiara, and Manuele Leonelli. "A changepoint approach for the identification of financial extreme regimes." Brazilian Journal of Probability and Statistics.