atRisk (version 0.2.0)

f_ES: Expected Shortfall

Description

The function allows to calculate Expected-shortfall for a given distribution. It takes as parameters alpha (risk level), a distribution and the parameters associated with this distribution. For example, for a normal distribution, the user must enter the mean and the standard deviation. Currently, the function can calculate the Expected-shortfall for the normal distribution, the skew-normal distribution and for the skew-t distribution (Azzalini and Capitianio, 2003)

Usage

f_ES(alpha, type_function, params, accuracy = 0.005)

Value

Numeric value for the expected-shortfall given the distribution and the alpha risk.

Arguments

alpha

Numeric argument for Expected-Shortfall, between 0 and 1

type_function

String argument : "gaussian" for normal distribution, "skew-gaussian" for Skew-Normal Distribution or "skew-t" for t-student distribution

params

Numeric vector containing parameters of the distribution

accuracy

Scalar value which regulates the accuracy of the ES (default value 1e-05)

References

Azzalini, Adelchi, and Antonella Capitanio. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 65.2 (2003): 367-389.

Azzalini, Adelchi, and Maintainer Adelchi Azzalini. "Package ‘sn’." The skew-normal and skew-t distributions (2015): 1-3.

Examples

f_ES(0.95, "gaussian", params=c(0,1))
f_ES(0.95, "gaussian", params=c(0,1), accuracy=1e-05)
f_ES(0.95, "gaussian", params=c(0,1), accuracy=1e-04)