# cvar-package: Compute Conditional Value-at-Risk and Value-at-Risk In cvar: Compute Expected Shortfall and Value at Risk for Continuous Distributions

## Description

Compute expected shortfall (ES) and Value at Risk (VaR) from a quantile function, distribution function, random number generator or probability density function. ES is also known as Conditional Value at Risk (CVaR). Virtually any continuous distribution can be specified. The functions are vectorised over the arguments. Some support for GARCH models is provided, as well.

## Details

There is a huge number of functions for computations with distributions in core R and in contributed packages. Pdf's, cdf's, quantile functions and random number generators are covered comprehensively. The coverage of expected shortfall is more patchy but a large collection of distributions, including functions for expected shortfall, is provided by \insertCiteVaRES2013;textualcvar. \insertCitePerformanceAnalytics2018;textualcvar and \insertCiteactuarJSS2008;textualcvar provide packages covering comprehensively various aspects of risk measurement, including some functions for expected shortfall.

Package cvar is a small package with, essentially, two main functions — `ES` for computing the expected shortfall and `VaR` for Value at Risk. The user specifies the distribution by supplying one of the functions that define a continuous distribution—currently this can be a quantile function (qf), cumulative distribution function (cdf) or probability density function (pdf). Virtually any continuous distribution can be specified.

The functions are vectorised over the parameters of the distributions, making bulk computations more convenient, for example for forecasting or model evaluation.

The name of this package, "cvar", comes from Conditional Value at Risk (CVaR), which is an alternative term for expected shortfall.

We chose to use the standard names `ES` and `VaR`, despite the possibility for name clashes with same named functions in other packages, rather than invent possibly difficult to remember alternatives. Just call the functions as `cvar::ES` and `cvar::VaR` if necessary.

Locations-scale transformations can be specified separately from the other distribution parameters. This is useful when such parameters are not provided directly by the distribution at hand. The use of these parameters often leads to more efficient computations and better numerical accuracy even if the distribution has its own parameters for this purpose. Some of the examples for `VaR` and `ES` illustrate this for the Gaussian distribution.

Since VaR is a quantile, functions computing it for a given distribution are convenience functions. `VaR` exported by cvar could be attractive in certain workflows because of its vectorised distribution parameters, the location-scale transformation, and the possibility to compute it from cdf's when quantile functions are not available.

Some support for GARCH models is provided, as well. It is currently under development, see `predict.garch1c1` for current functionality.

## Author(s)

Georgi N. Boshnakov

## References

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## Examples

 `1` ```## see the examples for ES(), VaR(), predict.garch1c1() ```

cvar documentation built on May 2, 2019, 2:09 p.m.