stress_VaR {SWIM}

Stressing Value-at-Risk

Description

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.

Usage

stress_VaR(
  x,
  alpha,
  q_ratio = NULL,
  q = NULL,
  k = 1,
  names = NULL,
  log = FALSE
)

Arguments

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.

Details

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.

Value

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.

Author(s)

Silvana M. Pesenti

References

Pesenti SM, Millossovich P, Tsanakas A (2019). “Reverse sensitivity testing: What does it take to break the model?” European Journal of Operational Research, 274(2), 654–670.

Pesenti S BAMPTA (2020). “Scenario Weights for Importance Measurement (SWIM) - An R package for sensitivity analysis.” Annals of Actuarial Science 15.2 (2021): 458-483. Available at SSRN: https://www.ssrn.com/abstract=3515274.

Csiszar I (1975). “I-divergence geometry of probability distributions and minimization problems.” The Annals of Probability, 146–158.

See Also

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()

Examples

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)