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Compute Value-at-Risk (VaR) and expected shortfall (ES)

VaR.Rd

Compute Value-at-Risk (VaR) and Expected Shortfall (ES) for a fitted GARCH-APARCH model.

Usage

# S3 method for fGARCH
VaR(dist, p_loss = 0.05, ..., tol)

# S3 method for fGARCH
ES(dist, p_loss = 0.05, ...)

Arguments

dist

an object from class "fGARCH", obtained from garchFit().

p_loss

level, default is 0.05.

...

not used.

tol

tollerance

Details

We provide methods for the generic functions cvar::VaR and cvar::ES.

Note

We use the traditional definition of VaR as the negated lower quantile. For example, if \(X\) are returns on an asset, VAR\({}_\alpha\) = \(-q_\alpha\), where \(q_\alpha\) is the lower \(\alpha\) quantile of \(X\). Equivalently, VAR\({}_\alpha\) is equal to the lower \(1-\alpha\) quantile of \(-X\) (the loss series). For details see the vignette in package cvar availalble at https://cran.r-project.org/package=cvar/vignettes/Guide_cvar.pdf (or by calling vignette("Guide_cvar", package = "cvar")).

If you wish to overlay the VaR or ES over returns, just negate the VaR/ES, see the examples.

See also

VaR and ES in package cvar

Examples

## simulate a time series of returns
x <- garchSim( garchSpec(), n = 500)
class(x)
#> [1] "timeSeries"
#> attr(,"package")
#> [1] "timeSeries"
## fit a GARCH model
fit <- garchFit(~ garch(1, 1), data = x, trace = FALSE)

head(VaR(fit))
#>  2022-12-17  2022-12-18  2022-12-19  2022-12-20  2022-12-21  2022-12-22 
#> 0.005215774 0.005132384 0.005135318 0.005073563 0.005363526 0.005243880 
head(ES(fit))
#>  2022-12-17  2022-12-18  2022-12-19  2022-12-20  2022-12-21  2022-12-22 
#> 0.006544763 0.006440189 0.006443868 0.006366425 0.006730050 0.006580009 

## use plot method for fitted GARCH models
plot(fit, which = 14) # VaR

plot(fit, which = 15) # ES

plot(fit, which = 16) # VaR & ES

## plot(fit) # choose the plot interactively

## diy plots

## overlay VaR and ES over returns
## here x is from class 'timeSeries', so we convert VaR/ES to timeSeries
## don't forget to negate the result of VaR()/ES(),
plot(x)
lines(timeSeries(-VaR(fit)), col = "red")
lines(timeSeries(-ES(fit)), col = "blue")


## alternatively, plot losses (rather than returns) and don't negate VaR()/ES()
plot(-x)
lines(timeSeries(VaR(fit)), col = "red")
lines(timeSeries(ES(fit)), col = "blue")