VaRbound: Computing lower and upper bounds for the (smallest or...
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VaRbound

R Documentation

Computing lower and upper bounds for the (smallest or largest) VaR

Description

VaRbound() computes lower and upper bounds for the lower or upper Value-at-Risk bound.

Usage

VaRbound(alpha, N, qmargins, bound = c("upper", "lower"), verbose = FALSE)

Arguments

`alpha`	confidence level in (0,1).
`N`	tail discretization parameter; see Embrechts et al. (2013).
`qmargins`	`list` containing the marginal quantile functions.
`bound`	`character` string indicating the VaR bound to be approximated (largest (default) or smallest).
`verbose`	`logical` indicating whether progress information is displayed.

Details

Due to the nature of the rearrangement algorithm, note that this purely R based implementation can be slow.

Value

numeric vector of length two, containing the lower and upper bound for the (chosen) Value-at-Risk estimate.

Author(s)

Marius Hofert.

References

Embrechts, P., Puccetti, G., and Rüschendorf, L. (2013), Model uncertainty and VaR aggregation, Journal of Banking and Finance 37(8), 2750–2764.

Examples

qPar <- function(p, theta) (1-p)^(-1/theta)-1
qmar <- lapply(1:3, function(j) function(p) qPar(p, theta=2.5))
## bounds for the largest VaR
VaRbound(0.99, N=50, qmargins=qmar)
## bounds for the smallest VaR
VaRbound(0.99, N=50, qmargins=qmar, bound="lower")

QRM documentation built on April 12, 2025, 1:15 a.m.