VaR function

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

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

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

## S3 method for class '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$_a$ = $-q_a$, where $-q_a$ is the lower $a$ quantile of $X$. Equivalently, VAR$_a$ is equal to the lower $1-a$ 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)
## fit a GARCH model
fit <- garchFit(~ garch(1, 1), data = x, trace = FALSE)

head(VaR(fit))
head(ES(fit))

## 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")