# VaR: Compute Value-at-Risk (VaR) and expected shortfall (ES) In fGarch: Rmetrics - Autoregressive Conditional Heteroskedastic Modelling

 VaR R Documentation

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

### Description

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

### Usage

## 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{}_\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.

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)

## 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")


fGarch documentation built on May 29, 2024, 8:30 a.m.