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

[alexios ghalanos]

Use This:

test_es = df1_var['Mu'] + df1_var['Sigma']*apply(df1_var, 1, function(x) 
  integrate(f,0,0.01, skew = x['Skew'], shape = x['Shape'])$value/0.01)


Best,

Alexios

On 19/06/2013 11:31, Daniel Liebert wrote:
> Thanks for your quick reply!
> Then this should be the answer, isnt it?
>
> # 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) / (0.01)))
>
> Greetings
> Daniel
>
>
> 2013/6/19 Alexios Ghalanos <alexios at 4dscape.com
> <mailto:alexios at 4dscape.com>>
>
>      >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
>     <mailto: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
>      >
>      >    [[alternative HTML version deleted]]
>      >
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