[R-SIG-Finance] Expected Shortfall from GARCH Models with sged Innovation

[Alexios Ghalanos]

From a quick look at your code (am not at my computer), you have forgotten to divide the integration result by the coverage rate (see rugarch::ESTest for an example of the calculation).

Regards,
Alexios

Sent from my iPad

On 19 Jun 2013, at 09:47, Daniel Liebert <liebert.daniel at googlemail.com> wrote:

> Hi all,
> Iam trying to compute the Expected Shortfall from a GARCH(1,1) with sged
> innovations created via the great rugarch package. The problem is that the
> range of values compared to the VaR(99) is totally different and I dont
> know where I have made the mistake.
> Here is my code:
> 
> library(quantmod)
> library(rugarch)
> library(parallel)
> library(PerformanceAnalytics)
> 
> # get Data
> mmm <- getSymbols("MMM", from = "2005-01-01", to = "2013-05-31")
> mmm <- Ad(get(mmm))
> ldr_mmm <- Return.calculate(mmm, method = "log"
> # remove NA observations
> ldr_mmm <- na.omit(ldr_mmm)
> 
> ctrl = list(rho = 1, delta = 1e-9, outer.iter = 1000, tol = 1e-7) # options
> for solver
> cl = makePSOCKcluster(10) # Create a Parallel Socket Cluster
> 
> # Choosing estimation and test window
> n_all_mmm = nrow(mmm)
> n_test_mmm <- nrow(as.xts(ldr_mmm)["2007-01-04/2013-05-31"]) # testing
> window
> n_est_mmm <- n_all_mmm - n_test_mmm # estimation window
> 
> # Fitting a GARCH(1,1) Model with skewed generalized error distribution
> innovations
> fit_MMM_def = ugarchspec(variance.model = list(model = "sGARCH", garchOrder
> = c(1,1)),
>                                         mean.model = list(armaOrder =
> c(0,0), include.mean = TRUE),
>                                         distribution.model = "sged")
> 
> # Calcualte Backtest
> MMM.backtest = ugarchroll(fit_MMM_def, data = ldr_mmm, n.ahead = 1,
>                                                forecast.length =
> n_test_mmm, refit.every = 20, refit.window = "moving",
>                                                solver = "hybrid",
> fit.control = list(), solver.control = ctrl,
>                                                calculate.VaR = TRUE,
> VaR.alpha = c(0.01), # Compute VaR = TRUE
>                                                cluster = cl)
> 
> # Calculate the VaR(99) by your own if calculate.VaR = FALSE @ ugarchroll
> df1_var <- as.data.frame(MMM.backtest, which = "density")
> f = function(x, skew, shape) qdist("sged", p = x, mu = 0, sigma = 1, skew =
> skew, shape = shape)
> test_var = df1_var[, 'Mu'] + qdist("sged", 0.01, 0, 1, skew = df1_var[,
> 'Skew'],
>                                                                 shape =
> df1_var[, 'Shape']) * df1_var[, 'Sigma']
> 
> # Lets compare it with the results from the ugarchroll function
> MMM_GARCH <- MMM.backtest at forecast
> head(cbind(test_var, as.data.frame(MMM_GARCH[["VaR"]]))) # exactly the
> same, thats good!
> 
> # Calcualte the Expected Shortfall (99)
> test_es = apply(df1_var, 1, function(x) x['Mu'] + x['Sigma'] * integrate(f,
> 0, 0.01, skew = x['Skew'], shape = x['Shape'])$value)
> test_es <- as.zoo(as.xts(test_es))
> test_es <- aggregate(test_es, function(tt) as.Date(tt, tz = "")) #convert
> to date
> 
> # Lets compare the VaR(99) and the ES(99)
> layout(1:2)
> plot(test_es) # ES(99)
> plot(as.zoo(MMM.backtest at forecast$VaR[1])) # VaR(99)
> 
> The most of the ideas are from http://www.unstarched.net (rugarch). My clue
> is that the integration is wrong but Iam not sure...
> 
> Thanks in advance
> Daniel
> 
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