stress_VaR: Stressing Value-at-Risk
In spesenti/SWIM: Scenario Weights for Importance Measurement

Description Usage Arguments Details Value Author(s) 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 quantile at a given level, also known as Value-at-Risk (VaR). Scenario weights are selected by constrained minimisation of the relative entropy to the baseline model.

stress_VaR(
  x,
  alpha,
  q_ratio = NULL,
  q = NULL,
  k = 1,
  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.
`q`	Numeric vector, the stressed VaR at level `alpha`. If `alpha` and `q` are vectors, they must have the same length.
`k`	Numeric, the column of `x` that is stressed `(default = 1)`.
`names`	Character vector, the names of stressed models.
`log`	Boolean, the option to print weights' statistics.

The stressed VaR is the quantile of the chosen model component, subject to the calculated scenario weights. 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).

If one of alpha, q (q_ratio) is a vector, the stressed VaR's of the kth column of x, at levels alpha, are equal to q.

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.

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";
specs, a list, each component corresponds to a different stress and contains k, alpha and q.

See SWIM for details.

Silvana M. Pesenti

\insertRef

Pesenti2019reverseSWIM

\insertRef

Pesenti2020SSRNSWIM

\insertRef

Csiszar1975SWIM

Other stress functions: stress_HARA_RM_w(), stress_RM_mean_sd_w(), stress_RM_w(), stress_VaR_ES(), 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", x = x,
  alpha = 0.9, q_ratio = 1.05)

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