cvar-package: Compute Expected shortfall (ES) and Value-at-Risk (VaR)

In cvar: Compute Expected Shortfall and Value at Risk for Continuous Distributions

Compute Expected shortfall (ES) and Value-at-Risk (VaR)

Description

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

Details

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

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 distributions are usually obtained by fitting distributions or specialised models to data. Instead of distributions, data for returns or log-returns can be supplied, as well.

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

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.

In practice, we may need to compute VaR associated with data. The distribution comes from fitting a model. In the simplest case, we fit a distribution to the data, assuming that the sample is i.i.d. For example, a normal distribution N(\mu, \sigma^2) can be fitted using the sample mean and sample variance as estimates of the unknown parameters \mu and \sigma^2, see section ‘Examples’. For other common distributions there are specialised functions to fit their parameters and if not, general optimisation routines can be used. More soffisticated models may be used, even time series models such as GARCH and mixture autoregressive models.

The functions VaR and ES are generic (S3). Further methods for them may be defined in other packages.

Author(s)

Georgi N. Boshnakov

References

\insertAllCited

See Also

ES, VaR

Examples

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

cvar documentation built on Dec. 17, 2025, 9:07 a.m.