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

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 R<c3><83><c2><bc>schendorf, 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")

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

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Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(QRM)
Loading required package: gsl
Loading required package: Matrix
Loading required package: mvtnorm
Loading required package: numDeriv
Loading required package: timeSeries
Loading required package: timeDate

Attaching package: 'QRM'

The following object is masked from 'package:base':

    lbeta

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/QRM/VaRbound.Rd_%03d_medium.png", width=480, height=480)
> ### Name: VaRbound
> ### Title: Computing lower and upper bounds for the (smallest or largest)
> ###   VaR
> ### Aliases: VaRbound
> ### Keywords: VaR multivariate
> 
> ### ** 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)
   lower    upper 
24.50992 25.07809 
> ## bounds for the smallest VaR
> VaRbound(0.99, N=50, qmargins=qmar, bound="lower")
   lower    upper 
3.084776 5.333898 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>