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 Nadarajah et al. (2013) . Peterson and Carl (2018) and Dutang et al. (2008) 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.
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.
References
Christophe Dutang, Vincent Goulet, Mathieu Pigeon (2008).
“actuar: An R Package for Actuarial Science.”
Journal of Statistical Software, 25(7), 38.
doi:10.18637/jss.v025.i07
.
Saralees Nadarajah, Stephen Chan, Emmanuel Afuecheta (2013).
VaRES: Computes value at risk and expected shortfall for over 100 parametric distributions.
R package version 1.0, https://CRAN.R-project.org/package=VaRES.
Brian
G. Peterson, Peter Carl (2018).
PerformanceAnalytics: Econometric Tools for Performance and Risk Analysis.
R package version 1.5.2, https://CRAN.R-project.org/package=PerformanceAnalytics.