CTE | R Documentation |
Conditional Tail Expectation, also called Tail Value-at-Risk.
TVaR
is an alias for CTE
.
CTE(x, ...)
## S3 method for class 'aggregateDist'
CTE(x, conf.level = c(0.9, 0.95, 0.99),
names = TRUE, ...)
TVaR(x, ...)
x |
an R object. |
conf.level |
numeric vector of probabilities with values
in |
names |
logical; if true, the result has a |
... |
further arguments passed to or from other methods. |
The Conditional Tail Expectation (or Tail Value-at-Risk) measures the
average of losses above the Value at Risk for some given confidence
level, that is E[X|X > \mathrm{VaR}(X)]
where X
is the loss random
variable.
CTE
is a generic function with, currently, only a method for
objects of class "aggregateDist"
.
For the recursive, convolution and simulation methods of
aggregateDist
, the CTE is computed from the definition
using the empirical cdf.
For the normal approximation method, an explicit formula exists:
\mu + \frac{\sigma}{(1 - \alpha) \sqrt{2 \pi}}
e^{-\mathrm{VaR}(X)^2/2},
where \mu
is the mean, \sigma
the standard
deviation and \alpha
the confidence level.
For the Normal Power approximation, the explicit formula given in Castañer et al. (2013) is
\mu + \frac{\sigma}{(1 - \alpha) \sqrt{2 \pi}}
e^{-\mathrm{VaR}(X)^2/2}
\left( 1 + \frac{\gamma}{6} \mathrm{VaR}(X) \right),
where, as above, \mu
is the mean, \sigma
the standard
deviation, \alpha
the confidence level and \gamma
is
the skewness.
A numeric vector, named if names
is TRUE
.
Vincent Goulet vincent.goulet@act.ulaval.ca and Tommy Ouellet
Castañer, A. and Claramunt, M.M. and Mármol, M. (2013), Tail value at risk. An analysis with the Normal-Power approximation. In Statistical and Soft Computing Approaches in Insurance Problems, pp. 87-112. Nova Science Publishers, 2013. ISBN 978-1-62618-506-7.
aggregateDist
; VaR
model.freq <- expression(data = rpois(7))
model.sev <- expression(data = rnorm(9, 2))
Fs <- aggregateDist("simulation", model.freq, model.sev, nb.simul = 1000)
CTE(Fs)
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