[R-SIG-Finance] CVaR with NIG- GARCH(1,1)

[alexios ghalanos]

Hi Alexandra,

The conditional Expected Shortfall for the NIG (or any other 
standardized rugarch distribution) using the rolling estimation/forecast 
method is given below.

# using your example:
mu=fitlist1[, 'Mu']
sigma=fitlist1[, 'Sigma']
shape=fitlist1[, 'Shape']
skew=fitlist1[, 'Skew']

# for the 5% quantile (adjust 0.05 as appropriate)
f = function(x, mu, sigma, skew, shape) mu + qdist("nig", p=x, mu=0, 
sigma=1, skew=skew, shape=shape)*sigma
for(i in 1:N)
{
ES[i] = integrate(f, 0, 0.05, mu = mu[i], sigma=sigma[i], shape = 
shape[i], skew=skew[i])$value/0.05
}
# Also see the ESTest.

You do not need to load ALL those packages (you only need rugarch for 
this example).

Regards,

Alexios

PS
# its "nig" NOT "snig" (you are confusing the name with that used in
# the fGarch package)...and yes, it is the same standardized
# distribution.
distplot(distribution = "nig", skewbounds = NULL, shapebounds = NULL,
          n.points = NULL)


On 12/05/2013 23:20, Alexandra Allexa wrote:
>
>
> Hello,
>
> My name is Alexandra and I have a very tight deadline for my MSc dissertation. My intention is to do a CVaR/ES using a NIG_GARCH model for estimating the volatility.
>
> With the Alexios's help I did a part of the following code (Thank you very much for your help, Alexios Ghalanos!):
>
> library(timeSeries)
> library(timeDate)
> library(Rcpp)
> library(RcppArmadillo)
> library(parallel)
> library(chron)
> library(Rsolnp)
> library(truncnorm)
> library(rugarch)
> library(fGarch)
> library(timeDate)
> library(PerformanceAnalytics)
> library(AER)
> library(fGarch)
>
> eur_all=timeSeries(eur_2001)
> r_eur1=getReturns(eur_all)
> rand_eur1=r_eur1*100
>
> #-NIG_GARCH
>
> #I. Specification Model and Fitting
>
> spec1 = ugarchspec(variance.model = list(model = 'sGARCH',
>                                           garchOrder = c(1,1)), mean.model =
>                       list(armaOrder = c(1,1), include.mean = TRUE),
>                     distribution.model = "nig")
>
>
>
> #Fit the model
>
>
> tmp = ugarchroll(spec1, rand_eur1, forecast.length = 1500, refit.every = 50,
>                   refit.window = 'moving', windows.size = 1500, solver ='hybrid',
>                   calculate.VaR = TRUE,VaR.alpha = c(0.01, 0.025, 0.05), keep.coef = TRUE)
>
> if (!is.null(tmp at model$noncidx)) {
>
>    tmp = resume(tmp, solver = "solnp", fit.control = list(scale = 1), solver.control = list(tol = 1e-07,
>                                                                                             delta = 1e-06))
>
>    if (!is.null(tmp at model$noncidx))
>
>      fitlist1 = NA
> } else {
>
>    fitlist1 = as.data.frame(tmp, which = 'density')
>
>
> }
>
>
> # Defining NIG distribution
>
> mu=fitlist1[, 'Mu']
> sigma=fitlist1[, 'Sigma']
> shape=fitlist1[, 'Shape']
> skew=fitlist1[, 'Skew']
> lambda =fitlist1[, 'Shape.GIG']
>
> dist=ddist(distribution = "nig", y, mu = mu, sigma = sigma, lambda = lambda, skew = skew,
>             shape = shape)
> pd=pdist(distribution = "nig", q, mu = mu, sigma = sigma, lambda = lambda, skew = skew,
>           shape = shape)
> qst=qdist(distribution = "nig", p, mu = mu, sigma = sigma, lambda = lambda, skew = skew,
>            shape = shape)
> r=rdist(distribution = "nig", n, mu = mu, sigma = sigma, lambda = lambda, skew = skew,
>          shape = shape)
> fitdist(distribution = "nig", fitlist1, control=list())
>
> distplot(distribution = "snig", skewbounds = NULL, shapebounds = NULL,
>           n.points = NULL)
>
> #CVaR/ES
>
> EURLOSS <- timeSeries(-1.0*rand_eur1,
>                        char.vec = time(eur_all))
>
> ESgarch <- function(rand_eur1, p = 0.99){
>    sigma <-fitlist1[, 'Sigma']
>    df <- fitlist1[,"Shape"]
>    ES <- sigma * (dist(qst(p, df), df)/(1 - p)) *
>      ((df + (qst(p, df))^2)/(df - 1))
>    return(ES)
> }
>
>
> from <- time(EURLOSS)[-c((nrow(EURLOSS) - 999) : nrow(EURLOSS))]
> to <- time(EURLOSS)[-c(1:1000)]
> EURSEES <- fapply(EURLOSS, from = from, to = to, FUN = ESgarch)
> EURSEESL1 <- lag(EURSEES, k = 1)
> res <- na.omit(cbind(EURSELOSS, EURSEESL1))
> colnames(res) <- c("EURSELOSS", "ES99")
> plot(res[, 2], col = "red", ylim = range(res),
>       main = "EUR: NIG-GARCH(1,1) ES 99%",
>       ylab = "percentages", xlab = "")
> points(res[, 1], type = "p", cex = 0.2, pch = 19, col = "blue")
> legend("topleft", legend = c("Loss", "ES"),
>         col = c("blue", "pink"), lty = c(NA, 1), pch = c(19, NA))
>
>
>
> My problem is how to define the NIG distribution for such a model?
> How I set the parameters/ vectors: y,p,q and n?
>
> In this situation, it is possible to use the function CVaR or ETL provided by the package {PerformanceAnalytics}? How?
>
> I can applied the same principle used in computing CVaR for CDD/CDaR?
>
> Thank you in advance,
>
> Alexandra Rautoiu
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>
>
>
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