stress_VaR_ES: Stressing Value-at-Risk and Expected Shortfall
In spesenti/SWIM: Scenario Weights for Importance Measurement

Description Usage Arguments Details Value References See Also Examples

Provides weights on simulated scenarios from a baseline stochastic model, such that a stressed model component (random variable) fulfils a constraint on its Value-at-Risk (VaR) and Expected Shortfall (ES) risk measures, both evaluated at a given level. Scenario weights are selected by constrained minimisation of the relative entropy to the baseline model.

stress_VaR_ES(
  x,
  alpha,
  q_ratio = NULL,
  s_ratio = NULL,
  q = NULL,
  s = NULL,
  k = 1,
  normalise = FALSE,
  names = NULL,
  log = FALSE
)

`x`	A vector, matrix or data frame containing realisations of random variables. Columns of `x` correspond to random variables; OR A `SWIM` object, where `x` corresponds to the underlying data of the `SWIM` object.
`alpha`	Numeric vector, the levels of the stressed VaR.
`q_ratio`	Numeric vector, the ratio of the stressed VaR to the baseline VaR. If `alpha` and `q_ratio` are vectors, they must have the same length.
`s_ratio`	Numeric, vector, the ratio of the stressed ES to the baseline ES. If `q` (`q_ratio`) and `s_ratio` are vectors, they must have the same length.
`q`	Numeric vector, the stressed VaR at level `alpha`. If `alpha` and `q` are vectors, they must have the same length.
`s`	Numeric, vector, the stressed ES at level `alpha`. If `q` and `s` are vectors, they must have the same length.
`k`	Numeric, the column of `x` that is stressed `(default = 1)`.
`normalise`	Logical. If true, values of the columns to be stressed are linearly normalised to the unit interval.
`names`	Character vector, the names of stressed models.
`log`	Boolean, the option to print weights' statistics.

The VaR at level alpha of a random variable with distribution function F is defined as its left-quantile at alpha:

VaR_{alpha} = F^{-1}(alpha).

The ES at level alpha of a random variable with distribution function F is defined by:

ES_{alpha} = 1 / (1 - alpha) * \int_{alpha}^1 VaR_u d u.

The stressed VaR and ES are the risk measures of the chosen model component, subject to the calculated scenario weights. If one of alpha, q, s (q_ratio, s_ratio) is a vector, the stressed VaR's and ES's of the kth column of x, at levels alpha, are equal to q and s, respectively.

The stressed VaR specified, either via q or q_ratio, might not equal the attained empirical VaR of the model component. In this case, stress_VaR will display a message and the specs contain the achieved VaR. Further, ES is then calculated on the bases of the achieved VaR.

Normalising the data may help avoiding numerical issues when the range of values is wide.

A SWIM object containing:

x, a data.frame containing the data;
new_weights, a list of functions, that applied to the kth column of x, generates the vectors of scenario weights. Each component corresponds to a different stress;
type = "VaR ES";
specs, a list, each component corresponds to a different stress and contains k, alpha, q and s.

See SWIM for details.

\insertRef

Pesenti2019reverseSWIM

\insertRef

Pesenti2020SSRNSWIM

\insertRef

Csiszar1975SWIM

Other stress functions: stress_HARA_RM_w(), stress_RM_mean_sd_w(), stress_RM_w(), stress_VaR(), stress_mean_sd_w(), stress_mean_sd(), stress_mean_w(), stress_mean(), stress_moment(), stress_prob(), stress_user(), stress_wass(), stress()

set.seed(0)
x <- as.data.frame(cbind(
  "normal" = rnorm(1000),
  "gamma" = rgamma(1000, shape = 2)))
res1 <- stress(type = "VaR ES", x = x,
  alpha = c(0.9, 0.95), q_ratio = 1.05, s_ratio = 1.08)

## calling stress_VaR_ES directly
## stressing "gamma"
res2 <- stress_VaR_ES(x = x, alpha = 0.9,
  q_ratio = 1.03, s_ratio = c(1.05, 1.08), k = 2)
get_specs(res2)
summary(res2)