[R-SIG-Finance] rugarch + VineCopula for value at risk
alexios ghalanos
alexios at 4dscape.com
Thu Aug 21 19:21:49 CEST 2014
Ole,
The email you've sent is really badly formatted and all over the place.
1. Try to send a well structured text-only email (with no special
characters).
2. Make an effort to send a minimally reproducible example.
Telling us that your problem took 8 hours to run is not the way to go.
Take a small subsample of your data which generates the behavior you
want to highlight (try to find one that does), and use that so that we
can investigate with minimal fuss.
-Alexios
On 21/08/2014 17:50, Ole Bueker wrote:
> Hello,
> I am trying to use the R packages rugarch and VineCopula for simulating returns of 112 companies for a time period of 25 days with daily re-estimations. After the simulation, I wish to calculate the 99% and 95% value-at-risk and compare them to the actual returns.I use a moving window of 250 days and 1000 simulations per iteration.
> (This estimation is quite time-intensive as 112 companies might be too many for VineCopula..)
> The overall loop takes around 8 hours on my home computer, so I wouldn�t recommend to actually run the code. My problem is that some of my calculated value at risk forecasts seem to be positive � this is not a �just invert the VaR� kind of problem (at least I don�t think so).
> To summarize the code:
> 1. Fit GARCH models to each series.2. Extract standardized returns (and shape parameters)3. Transform standardized returns to uniform marginals using parametric method (IFM by Joe, 1987).4. Fit vine copulas5. Generate a 1000 x 112 matrix (1000 1-day ahead forecasts for all 112 companies)6. Reverse transform the simulated values.7. Use these transformed forecasts in ugarchsim
> 8. Extract forecasted values & sigmas.9. Calculate Value-at-Risk.
> Anyway, here�s my code so far:# Load Data and define variables
> returns <- read.zoo("E:/Dropbox/my own/Programming/R/returns.csv", header=TRUE, sep=",", format="%d-%m-%y")model<-ugarchspec(variance.model=list(model="sGARCH",garchOrder=c(1,1)),mean.model=list(armaOrder=c(1,0),include.mean=FALSE),distribution.model="ged")times <- as.data.frame(time(returns))windows <- matrix(0, 112, 250)familyset <- c(1:5, 7, 10, 13, 14, 17, 20) # The vine copulas to be testedsim <- array(0, dim = c(1000, 112))residuals2 <- array(0, dim = c(1000, 112))rvine_fitted <- array(0, dim = c(25,1000,112))rvine_sigma <- array(0, dim = c(25,1000,112))VaR01 = VaR05 = array(0, dim = c(25,1000,112))
>
> #Main calculation
> for(i in 1:25){ print(i) windows <- window(returns_crisis, start=times[376-250-24+i,1], end=times[376-25+i,1]) #Define the moving window fit <- lapply(windows, ugarchfit, spec=model, solver="hybrid") #Fit the garch models print("rugarch fitting done") residuals <- sapply(fit, residuals, standardize=TRUE) #Extract residuals & shape parameters shape <- sapply(fit, coef) shape <- shape[5,] UniformResiduals <- pged(residuals, nu = shape) #Transform residuals into uniform marginals if(any(UniformResiduals > 0.99999)) { ix = which(UniformResiduals > 0.99999) UniformResiduals [ix] = 0.99999 } if(any(UniformResiduals < .Machine$double.eps)) { ix = which(UniformResiduals < (1.5*.Machine$double.eps)) UniformResiduals [ix] =
.Machine$double.eps } rvine <- RVineStructureSelect(UniformResiduals, indeptest=TRUE, familyset=familyset) #Fit the Vine copulas print(paste(i,"RVine fitting done")) for(j in 1:1000) #Simulate 1000 1-day ahead using VineCopula { sim[j,] <- RVineSim(1, rvine) # 1000 x 112 matrix of forecasts }print(paste(i,"RVine simulation done")) for(k in 1:112) #Next: ugarchsimulation for all 112 companies { residuals2[,] <- qged(sim[,], nu = shape[k])
# 1000 x 112 matrix of standardized residuals residuals_temp <- residuals2[,k] # 1000 x 1 vector of standardized residuals for individual company rvine_sim <- ugarchsim(fit[[k]], n.sim=1, m.sim=1000, custom.dist = list(name=NA, distfit=residuals_temp)) #1000 simulations using the standardized residuals from Vine copula models for ugarchfit rvine_fitted[i,,k] <- fitted(rvine_sim) #Extract forecasted values - 25 x 1000 x 112 rvine_sigma[i,,k] <- sigma(rvine_sim) #Extract forecasted sigmas - 25 x 1000 x 112 for(j in 1:1000)
#Next: Value at risk { VaR01[,j,k] <- rvine_fitted[,j,k] + rvine_sigma[,j,k] * qdist('ged', 0.01, mu=0, sigma=1, shape = shape[k]) #Value at risk for 99% quantile VaR05[,j,k] <- rvine_fitted[,j,k] + rvine_sigma[,j,k] * qdist('ged', 0.05, mu=0, sigma=1, shape = shape[k]) #Value at risk for 95% quantile } }}remove(i, j, k) #Cleanupremove(windows, fit, residuals, shape, residuals2, residuals_temp, rvine, sim, rvine_sim) #Cleanup Hope I didn�t make any mistakes in my approach, but it seems like this is the �standard� copula + rugarch approach � if anyone is familiar with this, I am open to suggestions on how to speed up the si
mulations.
> So far, so good � the problem I am facing now:
> Some (only a few) of my value at risk values are positive..I have manually checked and it seems like the fitted value is much larger than the sigma, so Value at Risk is positive � which doesn�t really make any economic sense to me.
> Here�s a dropbox link to the returns.csv, in case anyone is interested in running my code: https://www.dropbox.com/s/69i5959f3h4kweb/returns.csv
>
> Best Regards,
> Ole
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