Description Details Author(s) References Examples

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.

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.

Georgi N. Boshnakov

—

This is for pkgdown test. The following two phrases should be in separate paragraphs:

First phrase.

Second phrase.

—

First phrase.

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

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